Small improvement
Very small improvement in performance. Still, partialDer takes too long to compute. Trying to find ways to improve it.
This commit is contained in:
parent
ba272de4e3
commit
7b7a5c45ca
6 changed files with 788 additions and 837 deletions
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@ -6,7 +6,8 @@ MODULE moduleMesh0D
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TYPE, PUBLIC, EXTENDS(meshNode):: meshNode0D
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INTEGER:: n1
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CONTAINS
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PROCEDURE, PASS:: init => initNode0D
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!meshNode DEFERRED PROCEDURES
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PROCEDURE, PASS:: init => initNode0D
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PROCEDURE, PASS:: getCoordinates => getCoord0D
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END TYPE meshNode0D
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@ -14,20 +15,21 @@ MODULE moduleMesh0D
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TYPE, PUBLIC, EXTENDS(meshCell):: meshCell0D
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CLASS(meshNode), POINTER:: n1
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CONTAINS
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PROCEDURE, PASS:: init => initCell0D
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PROCEDURE, PASS:: getNodes => getNodes0D
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PROCEDURE, PASS:: randPos => randPos0D
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PROCEDURE, PASS:: fPsi => fPsi0D
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PROCEDURE, PASS:: dPsi => dPsi0D
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PROCEDURE, PASS:: detJac => detJ0D
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PROCEDURE, PASS:: invJac => invJ0D
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PROCEDURE, PASS:: elemK => elemK0D
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PROCEDURE, PASS:: elemF => elemF0D
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PROCEDURE, PASS:: gatherElectricField => gatherEF0D
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PROCEDURE, PASS:: gatherMagneticField => gatherMF0D
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PROCEDURE, PASS:: phy2log => phy2log0D
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PROCEDURE, NOPASS:: inside => inside0D
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PROCEDURE, PASS:: nextElement => nextElement0D
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PROCEDURE, PASS:: init => initCell0D
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PROCEDURE, PASS:: getNodes => getNodes0D
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PROCEDURE, PASS:: randPos => randPos0D
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PROCEDURE, NOPASS:: fPsi => fPsi0D
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PROCEDURE, NOPASS:: dPsi => dPsi0D
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PROCEDURE, PASS:: partialDer => partialDer0D
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PROCEDURE, NOPASS:: detJac => detJ0D
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PROCEDURE, NOPASS:: invJac => invJ0D
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PROCEDURE, PASS:: gatherElectricField => gatherEF0D
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PROCEDURE, PASS:: gatherMagneticField => gatherMF0D
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PROCEDURE, PASS:: elemK => elemK0D
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PROCEDURE, PASS:: elemF => elemF0D
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PROCEDURE, PASS:: phy2log => phy2log0D
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PROCEDURE, NOPASS:: inside => inside0D
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PROCEDURE, PASS:: neighbourElement => neighbourElement0D
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END TYPE meshCell0D
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@ -89,6 +91,7 @@ MODULE moduleMesh0D
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END SUBROUTINE initCell0D
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!Get the nodes of the volume
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PURE FUNCTION getNodes0D(self, nNodes) RESULT(n)
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IMPLICIT NONE
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@ -100,6 +103,7 @@ MODULE moduleMesh0D
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END FUNCTION getNodes0D
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!Calculate random position inside the volume
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FUNCTION randPos0D(self) RESULT(r)
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IMPLICIT NONE
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@ -110,10 +114,9 @@ MODULE moduleMesh0D
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END FUNCTION randPos0D
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PURE FUNCTION fPsi0D(self, Xi, nNodes) RESULT(fPsi)
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PURE FUNCTION fPsi0D(Xi, nNodes) RESULT(fPsi)
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IMPLICIT NONE
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CLASS(meshCell0D), INTENT(in):: self
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REAL(8), INTENT(in):: Xi(1:3)
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INTEGER, INTENT(in):: nNodes
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REAL(8):: fPsi(1:nNodes)
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@ -122,10 +125,9 @@ MODULE moduleMesh0D
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END FUNCTION fPsi0D
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PURE FUNCTION dPsi0D(self, Xi, nNodes) RESULT(dPsi)
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PURE FUNCTION dPsi0D(Xi, nNodes) RESULT(dPsi)
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IMPLICIT NONE
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CLASS(meshCell0D), INTENT(in):: self
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REAL(8), INTENT(in):: Xi(1:3)
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INTEGER, INTENT(in):: nNodes
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REAL(8):: dPsi(1:3,1:nNodes)
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@ -134,31 +136,17 @@ MODULE moduleMesh0D
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END FUNCTION dPsi0D
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PURE FUNCTION detJ0D(self, Xi, nNodes, dPsi_in) RESULT(dJ)
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PURE FUNCTION partialDer0D(self, nNodes, dPsi) RESULT(pDer)
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IMPLICIT NONE
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CLASS(meshCell0D), INTENT(in):: self
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REAL(8), INTENT(in):: Xi(1:3)
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INTEGER, INTENT(in):: nNodes
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REAL(8), INTENT(in), OPTIONAL:: dPsi_in(1:3,1:nNodes)
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REAL(8):: dJ
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REAL(8), INTENT(in):: dPsi(1:3,1:nNodes)
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REAL(8):: pDer(1:3, 1:3)
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dJ = 0.D0
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pDer = 0.D0
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END FUNCTION detJ0D
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PURE FUNCTION invJ0D(self, Xi, nNodes, dPsi_in) RESULT(invJ)
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IMPLICIT NONE
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CLASS(meshCell0D), INTENT(in):: self
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REAL(8), INTENT(in):: Xi(1:3)
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INTEGER, INTENT(in):: nNodes
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REAL(8), INTENT(in), OPTIONAL:: dPsi_in(1:3,1:nNodes)
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REAL(8):: invJ(1:3,1:3)
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invJ = 0.D0
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END FUNCTION invJ0D
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END FUNCTION partialDer0D
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PURE FUNCTION elemK0D(self, nNodes) RESULT(localK)
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IMPLICIT NONE
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@ -234,15 +222,36 @@ MODULE moduleMesh0D
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END FUNCTION inside0D
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SUBROUTINE nextElement0D(self, Xi, nextElement)
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SUBROUTINE neighbourElement0D(self, Xi, neighbourElement)
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IMPLICIT NONE
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CLASS(meshCell0D), INTENT(in):: self
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REAL(8), INTENT(in):: Xi(1:3)
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CLASS(meshElement), POINTER, INTENT(out):: nextElement
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CLASS(meshElement), POINTER, INTENT(out):: neighbourElement
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nextElement => NULL()
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neighbourElement => NULL()
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END SUBROUTINE nextElement0D
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END SUBROUTINE neighbourElement0D
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!COMMON FUNCTIONS
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PURE FUNCTION detJ0D(pDer) RESULT(dJ)
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IMPLICIT NONE
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REAL(8), INTENT(in):: pDer(1:3, 1:3)
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REAL(8):: dJ
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dJ = 0.D0
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END FUNCTION detJ0D
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PURE FUNCTION invJ0D(pDer) RESULT(invJ)
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IMPLICIT NONE
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REAL(8), INTENT(in):: pDer(1:3, 1:3)
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REAL(8):: invJ(1:3,1:3)
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invJ = 0.D0
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END FUNCTION invJ0D
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END MODULE moduleMesh0D
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@ -14,7 +14,8 @@ MODULE moduleMesh1DCart
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!Element coordinates
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REAL(8):: x = 0.D0
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CONTAINS
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PROCEDURE, PASS:: init => initNode1DCart
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!meshNode DEFERRED PROCEDURES
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PROCEDURE, PASS:: init => initNode1DCart
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PROCEDURE, PASS:: getCoordinates => getCoord1DCart
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END TYPE meshNode1DCart
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@ -25,6 +26,7 @@ MODULE moduleMesh1DCart
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!Connectivity to nodes
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CLASS(meshNode), POINTER:: n1 => NULL()
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CONTAINS
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!meshEdge DEFERRED PROCEDURES
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PROCEDURE, PASS:: init => initEdge1DCart
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PROCEDURE, PASS:: getNodes => getNodes1DCart
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PROCEDURE, PASS:: intersection => intersection1DCart
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@ -32,27 +34,7 @@ MODULE moduleMesh1DCart
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END TYPE meshEdge1DCart
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TYPE, PUBLIC, ABSTRACT, EXTENDS(meshCell):: meshCell1DCart
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CONTAINS
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PROCEDURE, PASS:: detJac => detJ1DCart
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PROCEDURE, PASS:: invJac => invJ1DCart
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PROCEDURE(partialDer_interface), DEFERRED, PASS:: partialDer
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END TYPE meshCell1DCart
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ABSTRACT INTERFACE
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PURE SUBROUTINE partialDer_interface(self, nNodes, dPsi, dx)
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IMPORT meshCell1DCart
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CLASS(meshCell1DCart), INTENT(in):: self
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INTEGER, INTENT(in):: nNodes
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REAL(8), INTENT(in):: dPsi(1:3,1:nNodes)
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REAL(8), INTENT(out), DIMENSION(1):: dx
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END SUBROUTINE partialDer_interface
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END INTERFACE
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TYPE, PUBLIC, EXTENDS(meshCell1DCart):: meshCell1DCartSegm
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TYPE, PUBLIC, EXTENDS(meshCell):: meshCell1DCartSegm
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!Element coordinates
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REAL(8):: x(1:2)
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!Connectivity to nodes
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@ -61,20 +43,24 @@ MODULE moduleMesh1DCart
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CLASS(meshElement), POINTER:: e1 => NULL(), e2 => NULL()
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REAL(8):: arNodes(1:2)
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CONTAINS
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PROCEDURE, PASS:: init => initCell1DCartSegm
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PROCEDURE, PASS:: randPos => randPos1DCartSegm
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PROCEDURE, PASS:: area => areaSegm
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PROCEDURE, PASS:: fPsi => fPsiSegm
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PROCEDURE, PASS:: dPsi => dPsiSegm
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PROCEDURE, PASS:: partialDer => partialDerSegm
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PROCEDURE, PASS:: elemK => elemKSegm
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PROCEDURE, PASS:: elemF => elemFSegm
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PROCEDURE, PASS:: gatherElectricField => gatherEFSegm
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PROCEDURE, PASS:: gatherMagneticField => gatherMFSegm
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PROCEDURE, NOPASS:: inside => insideSegm
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PROCEDURE, PASS:: getNodes => getNodesSegm
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PROCEDURE, PASS:: phy2log => phy2logSegm
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PROCEDURE, PASS:: nextElement => nextElementSegm
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!meshCell DEFERRED PROCEDURES
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PROCEDURE, PASS:: init => initCell1DCartSegm
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PROCEDURE, PASS:: getNodes => getNodesSegm
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PROCEDURE, PASS:: randPos => randPos1DCartSegm
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PROCEDURE, NOPASS:: fPsi => fPsiSegm
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PROCEDURE, NOPASS:: dPsi => dPsiSegm
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PROCEDURE, PASS:: partialDer => partialDerSegm
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PROCEDURE, NOPASS:: detJac => detJ1DCart
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PROCEDURE, NOPASS:: invJac => invJ1DCart
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PROCEDURE, PASS:: gatherElectricField => gatherEFSegm
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PROCEDURE, PASS:: gatherMagneticField => gatherMFSegm
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PROCEDURE, PASS:: elemK => elemKSegm
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PROCEDURE, PASS:: elemF => elemFSegm
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PROCEDURE, NOPASS:: inside => insideSegm
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PROCEDURE, PASS:: phy2log => phy2logSegm
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PROCEDURE, PASS:: neighbourElement => neighbourElementSegm
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!PARTICLUAR PROCEDURES
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PROCEDURE, PASS, PRIVATE:: area => areaSegm
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END TYPE meshCell1DCartSegm
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@ -219,7 +205,19 @@ MODULE moduleMesh1DCart
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END SUBROUTINE initCell1DCartSegm
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!Calculates a random position in 1D volume
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!Get nodes from 1D volume
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PURE FUNCTION getNodesSegm(self, nNodes) RESULT(n)
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IMPLICIT NONE
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CLASS(meshCell1DCartSegm), INTENT(in):: self
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INTEGER, INTENT(in):: nNodes
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INTEGER:: n(1:nNodes)
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n = (/ self%n1%n, self%n2%n /)
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END FUNCTION getNodesSegm
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!Random position in 1D volume
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FUNCTION randPos1DCartSegm(self) RESULT(r)
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USE moduleRandom
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IMPLICIT NONE
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@ -227,135 +225,63 @@ MODULE moduleMesh1DCart
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CLASS(meshCell1DCartSegm), INTENT(in):: self
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REAL(8):: r(1:3)
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REAL(8):: Xi(1:3)
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REAL(8), ALLOCATABLE:: fPsi(:)
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REAL(8):: fPsi(1:2)
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Xi(1) = random(-1.D0, 1.D0)
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Xi(2:3) = 0.D0
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Xi = 0.D0
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Xi(1) = random(-1.D0, 1.D0)
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fPsi = self%fPsi(Xi, 2)
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r = 0.D0
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r(1) = DOT_PRODUCT(fPsi, self%x)
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END FUNCTION randPos1DCartSegm
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!Computes element area
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PURE SUBROUTINE areaSegm(self)
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IMPLICIT NONE
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CLASS(meshCell1DCartSegm), INTENT(inout):: self
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REAL(8):: l !element length
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REAL(8):: fPsi(1:2)
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REAL(8):: detJ
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REAL(8):: Xi(1:3)
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self%volume = 0.D0
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self%arNodes = 0.D0
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!1 point Gauss integral
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Xi = 0.D0
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fPsi = self%fPsi(Xi, 2)
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detJ = self%detJac(Xi, 2)
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l = 2.D0*detJ
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self%volume = l
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self%arNodes = fPsi*l
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END SUBROUTINE areaSegm
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!Computes element functions at point Xi
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PURE FUNCTION fPsiSegm(self, Xi, nNodes) RESULT(fPsi)
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PURE FUNCTION fPsiSegm(Xi, nNodes) RESULT(fPsi)
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IMPLICIT NONE
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CLASS(meshCell1DCartSegm), INTENT(in):: self
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REAL(8), INTENT(in):: Xi(1:3)
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INTEGER, INTENT(in):: nNodes
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REAL(8):: fPsi(1:nNodes)
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fPsi(1) = 1.D0 - Xi(1)
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fPsi(2) = 1.D0 + Xi(1)
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fPsi = (/ 1.D0 - Xi(1), &
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1.D0 + Xi(1) /)
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fPsi = fPsi * 5.D-1
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fPsi = fPsi * 0.50D0
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END FUNCTION fPsiSegm
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!Computes element derivative shape function at Xi
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PURE FUNCTION dPsiSegm(self, Xi, nNodes) RESULT(dPsi)
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!Derivative element function at coordinates Xi
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PURE FUNCTION dPsiSegm(Xi, nNodes) RESULT(dPsi)
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IMPLICIT NONE
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CLASS(meshCell1DCartSegm), INTENT(in):: self
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REAL(8), INTENT(in):: Xi(1:3)
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INTEGER, INTENT(in):: nNodes
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REAL(8):: dPsi(1:3,1:nNodes)
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dPsi = 0.D0
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dPsi(1, 1) = -5.D-1
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dPsi(1, 2) = 5.D-1
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dPsi(1, 1:2) = (/ -5.D-1, 5.D-1 /)
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END FUNCTION dPsiSegm
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!Computes partial derivatives of coordinates
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PURE SUBROUTINE partialDerSegm(self, nNodes, dPsi, dx)
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!Partial derivative in global coordinates
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PURE FUNCTION partialDerSegm(self, nNodes, dPsi) RESULT(pDer)
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IMPLICIT NONE
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CLASS(meshCell1DCartSegm), INTENT(in):: self
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INTEGER, INTENT(in):: nNodes
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REAL(8), INTENT(in):: dPsi(1:3,1:nNodes)
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REAL(8), INTENT(out), DIMENSION(1):: dx
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REAL(8):: pDer(1:3, 1:3)
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dx(1) = DOT_PRODUCT(dPsi(1,:), self%x)
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pDer = 0.D0
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END SUBROUTINE partialDerSegm
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pDer(1,1) = DOT_PRODUCT(dPsi(1,1:2), self%x(1:2))
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pDer(2,2) = 1.D0
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pDer(3,3) = 1.D0
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!Computes local stiffness matrix
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PURE FUNCTION elemKSegm(self, nNodes) RESULT(localK)
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IMPLICIT NONE
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CLASS(meshCell1DCartSegm), INTENT(in):: self
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INTEGER, INTENT(in):: nNodes
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REAL(8):: localK(1:nNodes,1:nNodes)
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REAL(8):: Xi(1:3)
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REAL(8):: dPsi(1:3, 1:2)
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REAL(8):: invJ(1:3,1:3), detJ
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INTEGER:: l
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localK = 0.D0
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Xi = 0.D0
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DO l = 1, 3
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Xi(1) = corSeg(l)
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dPsi = self%dPsi(Xi, 2)
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detJ = self%detJac(Xi, 2, dPsi)
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invJ = self%invJac(Xi, 2, dPsi)
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localK = localK + MATMUL(RESHAPE(MATMUL(invJ,dPsi), (/ 2, 1/)), &
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RESHAPE(MATMUL(invJ,dPsi), (/ 1, 2/)))* &
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wSeg(l)/detJ
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END DO
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END FUNCTION elemKSegm
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PURE FUNCTION elemFSegm(self, nNodes, source) RESULT(localF)
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IMPLICIT NONE
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CLASS(meshCell1DCartSegm), INTENT(in):: self
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INTEGER, INTENT(in):: nNodes
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REAL(8), INTENT(in):: source(1:nNodes)
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REAL(8):: localF(1:nNodes)
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REAL(8):: fPsi(1:2)
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REAL(8):: detJ, f
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REAL(8):: Xi(1:3)
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INTEGER:: l
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localF = 0.D0
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Xi = 0.D0
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DO l = 1, 3
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Xi(1) = corSeg(l)
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detJ = self%detJac(Xi, 2)
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fPsi = self%fPsi(Xi, 2)
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f = DOT_PRODUCT(fPsi, source)
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localF = localF + f*fPsi*wSeg(l)*detJ
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END DO
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END FUNCTION elemFSegm
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END FUNCTION partialDerSegm
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PURE FUNCTION gatherEFSegm(self, Xi) RESULT(array)
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IMPLICIT NONE
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@ -391,6 +317,68 @@ MODULE moduleMesh1DCart
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END FUNCTION gatherMFSegm
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|
||||
!Computes element local stiffness matrix
|
||||
PURE FUNCTION elemKSegm(self, nNodes) RESULT(localK)
|
||||
IMPLICIT NONE
|
||||
|
||||
CLASS(meshCell1DCartSegm), INTENT(in):: self
|
||||
INTEGER, INTENT(in):: nNodes
|
||||
REAL(8):: localK(1:nNodes,1:nNodes)
|
||||
REAL(8):: Xi(1:3)
|
||||
REAL(8):: dPsi(1:3, 1:2)
|
||||
REAL(8):: pDer(1:3, 1:3)
|
||||
REAL(8):: invJ(1:3,1:3), detJ
|
||||
INTEGER:: l
|
||||
|
||||
localK = 0.D0
|
||||
|
||||
Xi = 0.D0
|
||||
!Start 1D Gauss Quad Integral
|
||||
DO l = 1, 3
|
||||
Xi(1) = corSeg(l)
|
||||
dPsi = self%dPsi(Xi, 2)
|
||||
pDer = self%partialDer(2, dPsi)
|
||||
detJ = self%detJac(pDer)
|
||||
invJ = self%invJac(pDer)
|
||||
localK = localK + MATMUL(RESHAPE(MATMUL(invJ,dPsi), (/ 2, 1/)), &
|
||||
RESHAPE(MATMUL(invJ,dPsi), (/ 1, 2/)))* &
|
||||
wSeg(l)/detJ
|
||||
|
||||
END DO
|
||||
|
||||
END FUNCTION elemKSegm
|
||||
|
||||
!Computes the local source vector for a force f
|
||||
PURE FUNCTION elemFSegm(self, nNodes, source) RESULT(localF)
|
||||
IMPLICIT NONE
|
||||
|
||||
CLASS(meshCell1DCartSegm), INTENT(in):: self
|
||||
INTEGER, INTENT(in):: nNodes
|
||||
REAL(8), INTENT(in):: source(1:nNodes)
|
||||
REAL(8):: localF(1:nNodes)
|
||||
REAL(8):: fPsi(1:2)
|
||||
REAL(8):: dPsi(1:3, 1:2), pDer(1:3, 1:3)
|
||||
REAL(8):: Xi(1:3)
|
||||
REAL(8):: detJ, f
|
||||
INTEGER:: l
|
||||
|
||||
localF = 0.D0
|
||||
|
||||
Xi = 0.D0
|
||||
!Start 1D Gauss Quad Integral
|
||||
DO l = 1, 3
|
||||
Xi(1) = corSeg(l)
|
||||
dPsi = self%dPsi(Xi, 2)
|
||||
pDer = self%partialDer(2, dPsi)
|
||||
detJ = self%detJac(pDer)
|
||||
fPsi = self%fPsi(Xi, 2)
|
||||
f = DOT_PRODUCT(fPsi, source)
|
||||
localF = localF + f*fPsi*wSeg(l)*detJ
|
||||
|
||||
END DO
|
||||
|
||||
END FUNCTION elemFSegm
|
||||
|
||||
PURE FUNCTION insideSegm(Xi) RESULT(ins)
|
||||
IMPLICIT NONE
|
||||
|
||||
|
|
@ -402,101 +390,87 @@ MODULE moduleMesh1DCart
|
|||
|
||||
END FUNCTION insideSegm
|
||||
|
||||
!Get nodes from 1D volume
|
||||
PURE FUNCTION getNodesSegm(self, nNodes) RESULT(n)
|
||||
IMPLICIT NONE
|
||||
|
||||
CLASS(meshCell1DCartSegm), INTENT(in):: self
|
||||
INTEGER, INTENT(in):: nNodes
|
||||
INTEGER:: n(1:nNodes)
|
||||
|
||||
n = (/ self%n1%n, self%n2%n /)
|
||||
|
||||
END FUNCTION getNodesSegm
|
||||
|
||||
PURE FUNCTION phy2logSegm(self, r) RESULT(xN)
|
||||
PURE FUNCTION phy2logSegm(self, r) RESULT(Xi)
|
||||
IMPLICIT NONE
|
||||
|
||||
CLASS(meshCell1DCartSegm), INTENT(in):: self
|
||||
REAL(8), INTENT(in):: r(1:3)
|
||||
REAL(8):: xN(1:3)
|
||||
REAL(8):: Xi(1:3)
|
||||
|
||||
xN = 0.D0
|
||||
xN(1) = 2.D0*(r(1) - self%x(1))/(self%x(2) - self%x(1)) - 1.D0
|
||||
Xi = 0.D0
|
||||
|
||||
Xi(1) = 2.D0*(r(1) - self%x(1))/(self%x(2) - self%x(1)) - 1.D0
|
||||
|
||||
END FUNCTION phy2logSegm
|
||||
|
||||
!Get next element for a logical position Xi
|
||||
SUBROUTINE nextElementSegm(self, Xi, nextElement)
|
||||
!Get the next element for a logical position Xi
|
||||
SUBROUTINE neighbourElementSegm(self, Xi, neighbourElement)
|
||||
IMPLICIT NONE
|
||||
|
||||
CLASS(meshCell1DCartSegm), INTENT(in):: self
|
||||
REAL(8), INTENT(in):: Xi(1:3)
|
||||
CLASS(meshElement), POINTER, INTENT(out):: nextElement
|
||||
CLASS(meshElement), POINTER, INTENT(out):: neighbourElement
|
||||
|
||||
NULLIFY(nextElement)
|
||||
NULLIFY(neighbourElement)
|
||||
IF (Xi(1) < -1.D0) THEN
|
||||
nextElement => self%e2
|
||||
neighbourElement => self%e2
|
||||
|
||||
ELSEIF (Xi(1) > 1.D0) THEN
|
||||
nextElement => self%e1
|
||||
neighbourElement => self%e1
|
||||
|
||||
END IF
|
||||
|
||||
END SUBROUTINE nextElementSegm
|
||||
END SUBROUTINE neighbourElementSegm
|
||||
|
||||
!COMMON FUNCTIONS FOR 1D VOLUME ELEMENTS
|
||||
!Calculates a random position in 1D volume
|
||||
!Computes the element Jacobian determinant
|
||||
PURE FUNCTION detJ1DCart(self, Xi, nNodes, dPsi_in) RESULT(dJ)
|
||||
!Computes element area
|
||||
PURE SUBROUTINE areaSegm(self)
|
||||
IMPLICIT NONE
|
||||
|
||||
CLASS(meshCell1DCart), INTENT(in):: self
|
||||
REAL(8), INTENT(in):: Xi(1:3)
|
||||
INTEGER, INTENT(in):: nNodes
|
||||
REAL(8), INTENT(in), OPTIONAL:: dPsi_in(1:3,1:nNodes)
|
||||
REAL(8):: dPsi(1:3,1:nNodes)
|
||||
CLASS(meshCell1DCartSegm), INTENT(inout):: self
|
||||
REAL(8):: Xi(1:3)
|
||||
REAL(8):: dPsi(1:3, 1:2), pDer(1:3, 1:3)
|
||||
REAL(8):: detJ
|
||||
REAL(8):: fPsi(1:2)
|
||||
|
||||
self%volume = 0.D0
|
||||
self%arNodes = 0.D0
|
||||
!1D 1 point Gauss Quad Integral
|
||||
Xi = 0.D0
|
||||
dPsi = self%dPsi(Xi, 2)
|
||||
pDer = self%partialDer(2, dPsi)
|
||||
detJ = self%detJac(pDer)
|
||||
fPsi = self%fPsi(Xi, 2)
|
||||
!Computes total volume of the cell
|
||||
self%volume = detJ*2.D0
|
||||
!Computes volume per node
|
||||
self%arNodes = fPsi*self%volume
|
||||
|
||||
END SUBROUTINE areaSegm
|
||||
|
||||
!COMMON FUNCTIONS FOR 1D VOLUME ELEMENTS
|
||||
!Computes element Jacobian determinant
|
||||
PURE FUNCTION detJ1DCart(pDer) RESULT(dJ)
|
||||
IMPLICIT NONE
|
||||
|
||||
REAL(8), INTENT(in):: pDer(1:3, 1:3)
|
||||
REAL(8):: dJ
|
||||
REAL(8):: dx(1)
|
||||
|
||||
IF (PRESENT(dPsi_in)) THEN
|
||||
dPsi = dPsi_in
|
||||
|
||||
ELSE
|
||||
dPsi = self%dPsi(Xi, 2)
|
||||
|
||||
END IF
|
||||
|
||||
CALL self%partialDer(2, dPsi, dx)
|
||||
dJ = dx(1)
|
||||
dJ = pDer(1, 1)
|
||||
|
||||
END FUNCTION detJ1DCart
|
||||
|
||||
!Computes the invers Jacobian
|
||||
PURE FUNCTION invJ1DCart(self, Xi, nNodes, dPsi_in) RESULT(invJ)
|
||||
!Computes element Jacobian inverse matrix (without determinant)
|
||||
PURE FUNCTION invJ1DCart(pDer) RESULT(invJ)
|
||||
IMPLICIT NONE
|
||||
|
||||
CLASS(meshCell1DCart), INTENT(in):: self
|
||||
REAL(8), INTENT(in):: Xi(1:3)
|
||||
INTEGER, INTENT(in):: nNodes
|
||||
REAL(8), INTENT(in), OPTIONAL:: dPsi_in(1:3,1:nNodes)
|
||||
REAL(8), INTENT(in):: pDer(1:3, 1:3)
|
||||
REAL(8):: invJ(1:3,1:3)
|
||||
REAL(8):: dPsi(1:3,1:nNodes)
|
||||
REAL(8):: dx(1)
|
||||
|
||||
IF (PRESENT(dPsi_in)) THEN
|
||||
dPsi = dPsi_in
|
||||
|
||||
ELSE
|
||||
dPsi = self%dPsi(Xi, 2)
|
||||
|
||||
END IF
|
||||
|
||||
invJ = 0.D0
|
||||
|
||||
CALL self%partialDer(2, dPsi, dx)
|
||||
|
||||
invJ(1,1) = 1.D0/dx(1)
|
||||
invJ(1, 1) = 1.D0/pDer(1, 1)
|
||||
invJ(2, 2) = 1.D0
|
||||
invJ(3, 3) = 1.D0
|
||||
|
||||
END FUNCTION invJ1DCart
|
||||
|
||||
|
|
|
|||
|
|
@ -8,13 +8,14 @@ MODULE moduleMesh1DRad
|
|||
IMPLICIT NONE
|
||||
|
||||
REAL(8), PARAMETER:: corSeg(1:3) = (/ -DSQRT(3.D0/5.D0), 0.D0, DSQRT(3.D0/5.D0) /)
|
||||
REAL(8), PARAMETER:: wSeg(1:3) = (/ 5.D0/9.D0 , 8.D0/9.D0, 5.D0/9.D0 /)
|
||||
REAL(8), PARAMETER:: wSeg(1:3) = (/ 5.D0/9.D0 , 8.D0/9.D0, 5.D0/9.D0 /)
|
||||
|
||||
TYPE, PUBLIC, EXTENDS(meshNode):: meshNode1DRad
|
||||
!Element coordinates
|
||||
REAL(8):: r = 0.D0
|
||||
CONTAINS
|
||||
PROCEDURE, PASS:: init => initNode1DRad
|
||||
!meshNode DEFERRED PROCEDURES
|
||||
PROCEDURE, PASS:: init => initNode1DRad
|
||||
PROCEDURE, PASS:: getCoordinates => getCoord1DRad
|
||||
|
||||
END TYPE meshNode1DRad
|
||||
|
|
@ -25,6 +26,7 @@ MODULE moduleMesh1DRad
|
|||
!Connectivity to nodes
|
||||
CLASS(meshNode), POINTER:: n1 => NULL()
|
||||
CONTAINS
|
||||
!meshEdge DEFERRED PROCEDURES
|
||||
PROCEDURE, PASS:: init => initEdge1DRad
|
||||
PROCEDURE, PASS:: getNodes => getNodes1DRad
|
||||
PROCEDURE, PASS:: intersection => intersection1DRad
|
||||
|
|
@ -32,28 +34,7 @@ MODULE moduleMesh1DRad
|
|||
|
||||
END TYPE meshEdge1DRad
|
||||
|
||||
TYPE, PUBLIC, ABSTRACT, EXTENDS(meshCell):: meshCell1DRad
|
||||
CONTAINS
|
||||
PROCEDURE, PASS:: detJac => detJ1DRad
|
||||
PROCEDURE, PASS:: invJac => invJ1DRad
|
||||
PROCEDURE(partialDer_interface), DEFERRED, PASS:: partialDer
|
||||
|
||||
END TYPE meshCell1DRad
|
||||
|
||||
ABSTRACT INTERFACE
|
||||
PURE SUBROUTINE partialDer_interface(self, nNodes, dPsi, dx)
|
||||
IMPORT meshCell1DRad
|
||||
|
||||
CLASS(meshCell1DRad), INTENT(in):: self
|
||||
INTEGER, INTENT(in):: nNodes
|
||||
REAL(8), INTENT(in):: dPsi(1:3,1:nNodes)
|
||||
REAL(8), INTENT(out), DIMENSION(1):: dx
|
||||
|
||||
END SUBROUTINE partialDer_interface
|
||||
|
||||
END INTERFACE
|
||||
|
||||
TYPE, PUBLIC, EXTENDS(meshCell1DRad):: meshCell1DRadSegm
|
||||
TYPE, PUBLIC, EXTENDS(meshCell):: meshCell1DRadSegm
|
||||
!Element coordinates
|
||||
REAL(8):: r(1:2)
|
||||
!Connectivity to nodes
|
||||
|
|
@ -62,20 +43,24 @@ MODULE moduleMesh1DRad
|
|||
CLASS(meshElement), POINTER:: e1 => NULL(), e2 => NULL()
|
||||
REAL(8):: arNodes(1:2)
|
||||
CONTAINS
|
||||
PROCEDURE, PASS:: init => initCell1DRadSegm
|
||||
PROCEDURE, PASS:: randPos => randPos1DRadSeg
|
||||
PROCEDURE, PASS:: area => areaRad
|
||||
PROCEDURE, PASS:: fPsi => fPsiRad
|
||||
PROCEDURE, PASS:: dPsi => dPsiRad
|
||||
PROCEDURE, PASS:: partialDer => partialDerRad
|
||||
PROCEDURE, PASS:: elemK => elemKRad
|
||||
PROCEDURE, PASS:: elemF => elemFRad
|
||||
PROCEDURE, PASS:: gatherElectricField => gatherEFRad
|
||||
PROCEDURE, PASS:: gatherMagneticField => gatherMFRad
|
||||
PROCEDURE, NOPASS:: inside => insideRad
|
||||
PROCEDURE, PASS:: getNodes => getNodesRad
|
||||
PROCEDURE, PASS:: phy2log => phy2logRad
|
||||
PROCEDURE, PASS:: nextElement => nextElementRad
|
||||
!meshCell DEFERRED PROCEDURES
|
||||
PROCEDURE, PASS:: init => initCell1DRadSegm
|
||||
PROCEDURE, PASS:: getNodes => getNodesSegm
|
||||
PROCEDURE, PASS:: randPos => randPos1DRadSegm
|
||||
PROCEDURE, NOPASS:: fPsi => fPsiSegm
|
||||
PROCEDURE, NOPASS:: dPsi => dPsiSegm
|
||||
PROCEDURE, PASS:: partialDer => partialDerSegm
|
||||
PROCEDURE, NOPASS:: detJac => detJ1DRad
|
||||
PROCEDURE, NOPASS:: invJac => invJ1DRad
|
||||
PROCEDURE, PASS:: gatherElectricField => gatherEFSegm
|
||||
PROCEDURE, PASS:: gatherMagneticField => gatherMFSegm
|
||||
PROCEDURE, PASS:: elemK => elemKSegm
|
||||
PROCEDURE, PASS:: elemF => elemFSegm
|
||||
PROCEDURE, NOPASS:: inside => insideSegm
|
||||
PROCEDURE, PASS:: phy2log => phy2logSegm
|
||||
PROCEDURE, PASS:: neighbourElement => neighbourElementSegm
|
||||
!PARTICLUAR PROCEDURES
|
||||
PROCEDURE, PASS, PRIVATE:: area => areaSegm
|
||||
|
||||
END TYPE meshCell1DRadSegm
|
||||
|
||||
|
|
@ -139,7 +124,6 @@ MODULE moduleMesh1DRad
|
|||
self%r = r1(1)
|
||||
|
||||
self%normal = (/ 1.D0, 0.D0, 0.D0 /)
|
||||
self%normal = self%normal/NORM2(self%normal)
|
||||
|
||||
!Boundary index
|
||||
self%boundary => boundary(bt)
|
||||
|
|
@ -221,8 +205,20 @@ MODULE moduleMesh1DRad
|
|||
|
||||
END SUBROUTINE initCell1DRadSegm
|
||||
|
||||
!Calculates a random position in 1D volume
|
||||
FUNCTION randPos1DRadSeg(self) RESULT(r)
|
||||
!Get nodes from 1D volume
|
||||
PURE FUNCTION getNodesSegm(self, nNodes) RESULT(n)
|
||||
IMPLICIT NONE
|
||||
|
||||
CLASS(meshCell1DRadSegm), INTENT(in):: self
|
||||
INTEGER, INTENT(in):: nNodes
|
||||
INTEGER:: n(1:nNodes)
|
||||
|
||||
n = (/ self%n1%n, self%n2%n /)
|
||||
|
||||
END FUNCTION getNodesSegm
|
||||
|
||||
!Random position in 1D volume
|
||||
FUNCTION randPos1DRadSegm(self) RESULT(r)
|
||||
USE moduleRandom
|
||||
IMPLICIT NONE
|
||||
|
||||
|
|
@ -231,152 +227,63 @@ MODULE moduleMesh1DRad
|
|||
REAL(8):: Xi(1:3)
|
||||
REAL(8):: fPsi(1:2)
|
||||
|
||||
Xi(1) = random(-1.D0, 1.D0)
|
||||
Xi(2:3) = 0.D0
|
||||
Xi = 0.D0
|
||||
Xi(1) = random(-1.D0, 1.D0)
|
||||
|
||||
fPsi = self%fPsi(Xi, 2)
|
||||
|
||||
r = 0.D0
|
||||
r(1) = DOT_PRODUCT(fPsi, self%r)
|
||||
|
||||
END FUNCTION randPos1DRadSeg
|
||||
|
||||
!Computes element area
|
||||
PURE SUBROUTINE areaRad(self)
|
||||
IMPLICIT NONE
|
||||
|
||||
CLASS(meshCell1DRadSegm), INTENT(inout):: self
|
||||
REAL(8):: l !element length
|
||||
REAL(8):: fPsi(1:2), fPsi_node(1:2)
|
||||
REAL(8):: r
|
||||
REAL(8):: detJ
|
||||
REAL(8):: Xi(1:3)
|
||||
|
||||
self%volume = 0.D0
|
||||
self%arNodes = 0.D0
|
||||
!1 point Gauss integral
|
||||
Xi = 0.D0
|
||||
fPsi = self%fPsi(Xi, 2)
|
||||
detJ = self%detJac(Xi, 2)
|
||||
!Computes total volume of the cell
|
||||
r = DOT_PRODUCT(fPsi, self%r)
|
||||
l = 2.D0*detJ
|
||||
self%volume = r*l
|
||||
!Computes volume per node
|
||||
Xi = (/-5.D-1, 0.D0, 0.D0/)
|
||||
r = self%gatherF(Xi, 2, self%r)
|
||||
self%arNodes(1) = fPsi(1)*r*l
|
||||
Xi = (/ 5.D-1, 0.D0, 0.D0/)
|
||||
r = self%gatherF(Xi, 2, self%r)
|
||||
self%arNodes(2) = fPsi(2)*r*l
|
||||
|
||||
END SUBROUTINE areaRad
|
||||
END FUNCTION randPos1DRadSegm
|
||||
|
||||
!Computes element functions at point Xi
|
||||
PURE FUNCTION fPsiRad(self, Xi, nNodes) RESULT(fPsi)
|
||||
PURE FUNCTION fPsiSegm(Xi, nNodes) RESULT(fPsi)
|
||||
IMPLICIT NONE
|
||||
|
||||
CLASS(meshCell1DRadSegm), INTENT(in):: self
|
||||
REAL(8), INTENT(in):: Xi(1:3)
|
||||
INTEGER, INTENT(in):: nNodes
|
||||
REAL(8):: fPsi(1:nNodes)
|
||||
|
||||
fPsi(1) = 1.D0 - Xi(1)
|
||||
fPsi(2) = 1.D0 + Xi(1)
|
||||
fPsi = (/ 1.D0 - Xi(1), &
|
||||
1.D0 + Xi(1) /)
|
||||
|
||||
fPsi = fPsi * 5.D-1
|
||||
fPsi = fPsi * 0.50D0
|
||||
|
||||
END FUNCTION fPsiRad
|
||||
END FUNCTION fPsiSegm
|
||||
|
||||
!Computes element derivative shape function at Xi
|
||||
PURE FUNCTION dPsiRad(self, Xi, nNodes) RESULT(dPsi)
|
||||
!Derivative element function at coordinates Xi
|
||||
PURE FUNCTION dPsiSegm(Xi, nNodes) RESULT(dPsi)
|
||||
IMPLICIT NONE
|
||||
|
||||
CLASS(meshCell1DRadSegm), INTENT(in):: self
|
||||
REAL(8), INTENT(in):: Xi(1:3)
|
||||
INTEGER, INTENT(in):: nNodes
|
||||
REAL(8):: dPsi(1:3,1:nNodes)
|
||||
|
||||
dPsi = 0.D0
|
||||
|
||||
dPsi(1, 1) = -5.D-1
|
||||
dPsi(1, 2) = 5.D-1
|
||||
dPsi(1, 1:2) = (/ -5.D-1, 5.D-1 /)
|
||||
|
||||
END FUNCTION dPsiRad
|
||||
END FUNCTION dPsiSegm
|
||||
|
||||
!Computes partial derivatives of coordinates
|
||||
PURE SUBROUTINE partialDerRad(self, nNodes, dPsi, dx)
|
||||
!Partial derivative in global coordinates
|
||||
PURE FUNCTION partialDerSegm(self, nNodes, dPsi) RESULT(pDer)
|
||||
IMPLICIT NONE
|
||||
|
||||
CLASS(meshCell1DRadSegm), INTENT(in):: self
|
||||
INTEGER, INTENT(in):: nNodes
|
||||
REAL(8), INTENT(in):: dPsi(1:3,1:nNodes)
|
||||
REAL(8), INTENT(out), DIMENSION(1):: dx
|
||||
REAL(8):: pDer(1:3, 1:3)
|
||||
|
||||
dx(1) = DOT_PRODUCT(dPsi(1,:), self%r)
|
||||
pDer = 0.D0
|
||||
|
||||
END SUBROUTINE partialDerRad
|
||||
pDer(1,1) = DOT_PRODUCT(dPsi(1,1:2), self%r(1:2))
|
||||
pDer(2,2) = 1.D0
|
||||
pDer(3,3) = 1.D0
|
||||
|
||||
!Computes local stiffness matrix
|
||||
PURE FUNCTION elemKRad(self, nNodes) RESULT(localK)
|
||||
USE moduleConstParam, ONLY: PI2
|
||||
IMPLICIT NONE
|
||||
END FUNCTION partialDerSegm
|
||||
|
||||
CLASS(meshCell1DRadSegm), INTENT(in):: self
|
||||
INTEGER, INTENT(in):: nNodes
|
||||
REAL(8):: localK(1:nNodes,1:nNodes)
|
||||
REAL(8):: Xi(1:3)
|
||||
REAL(8):: dPsi(1:3, 1:2)
|
||||
REAL(8):: invJ(1:3,1:3), detJ
|
||||
REAL(8):: r, fPsi(1:2)
|
||||
INTEGER:: l
|
||||
|
||||
localK = 0.D0
|
||||
Xi = 0.D0
|
||||
DO l = 1, 3
|
||||
Xi(1) = corSeg(l)
|
||||
dPsi = self%dPsi(Xi, 2)
|
||||
detJ = self%detJac(Xi, 2, dPsi)
|
||||
invJ = self%invJac(Xi, 2, dPsi)
|
||||
fPsi = self%fPsi(Xi, 2)
|
||||
r = DOT_PRODUCT(fPsi, self%r)
|
||||
localK = localK + MATMUL(RESHAPE(MATMUL(invJ,dPsi), (/ 2, 1/)), &
|
||||
RESHAPE(MATMUL(invJ,dPsi), (/ 1, 2/)))* &
|
||||
r*wSeg(l)/detJ
|
||||
|
||||
END DO
|
||||
|
||||
localK = localK*PI2
|
||||
|
||||
END FUNCTION elemKRad
|
||||
|
||||
PURE FUNCTION elemFRad(self, nNodes, source) RESULT(localF)
|
||||
USE moduleConstParam, ONLY: PI2
|
||||
IMPLICIT NONE
|
||||
|
||||
CLASS(meshCell1DRadSegm), INTENT(in):: self
|
||||
INTEGER, INTENT(in):: nNodes
|
||||
REAL(8), INTENT(in):: source(1:nNodes)
|
||||
REAL(8):: localF(1:nNodes)
|
||||
REAL(8):: fPsi(1:2)
|
||||
REAL(8):: detJ, f, r
|
||||
REAL(8):: Xi(1:3)
|
||||
INTEGER:: l
|
||||
|
||||
localF = 0.D0
|
||||
Xi = 0.D0
|
||||
|
||||
DO l = 1, 3
|
||||
Xi(1) = corSeg(l)
|
||||
detJ = self%detJac(Xi, 2)
|
||||
fPsi = self%fPsi(Xi, 2)
|
||||
r = DOT_PRODUCT(fPsi, self%r)
|
||||
f = DOT_PRODUCT(fPsi, source)
|
||||
localF = localF + f*fPsi*r*wSeg(l)*detJ
|
||||
|
||||
END DO
|
||||
|
||||
END FUNCTION elemFRad
|
||||
|
||||
PURE FUNCTION gatherEFRad(self, Xi) RESULT(array)
|
||||
PURE FUNCTION gatherEFSegm(self, Xi) RESULT(array)
|
||||
IMPLICIT NONE
|
||||
CLASS(meshCell1DRadSegm), INTENT(in):: self
|
||||
REAL(8), INTENT(in):: Xi(1:3)
|
||||
|
|
@ -388,9 +295,9 @@ MODULE moduleMesh1DRad
|
|||
|
||||
array = -self%gatherDF(Xi, 2, phi)
|
||||
|
||||
END FUNCTION gatherEFRad
|
||||
END FUNCTION gatherEFSegm
|
||||
|
||||
PURE FUNCTION gatherMFRad(self, Xi) RESULT(array)
|
||||
PURE FUNCTION gatherMFSegm(self, Xi) RESULT(array)
|
||||
IMPLICIT NONE
|
||||
CLASS(meshCell1DRadSegm), INTENT(in):: self
|
||||
REAL(8), INTENT(in):: Xi(1:3)
|
||||
|
|
@ -408,9 +315,79 @@ MODULE moduleMesh1DRad
|
|||
|
||||
array = self%gatherF(Xi, 2, B)
|
||||
|
||||
END FUNCTION gatherMFRad
|
||||
END FUNCTION gatherMFSegm
|
||||
|
||||
PURE FUNCTION insideRad(Xi) RESULT(ins)
|
||||
!Computes element local stiffness matrix
|
||||
PURE FUNCTION elemKSegm(self, nNodes) RESULT(localK)
|
||||
USE moduleConstParam, ONLY: PI2
|
||||
IMPLICIT NONE
|
||||
|
||||
CLASS(meshCell1DRadSegm), INTENT(in):: self
|
||||
INTEGER, INTENT(in):: nNodes
|
||||
REAL(8):: localK(1:nNodes,1:nNodes)
|
||||
REAL(8):: Xi(1:3)
|
||||
REAL(8):: dPsi(1:3, 1:2)
|
||||
REAL(8):: pDer(1:3, 1:3)
|
||||
REAL(8):: r
|
||||
REAL(8):: invJ(1:3,1:3), detJ
|
||||
INTEGER:: l
|
||||
|
||||
localK = 0.D0
|
||||
|
||||
Xi = 0.D0
|
||||
!Start 1D Gauss Quad Integral
|
||||
DO l = 1, 3
|
||||
Xi(1) = corSeg(l)
|
||||
dPsi = self%dPsi(Xi, 2)
|
||||
pDer = self%partialDer(2, dPsi)
|
||||
detJ = self%detJac(pDer)
|
||||
invJ = self%invJac(pDer)
|
||||
r = self%gatherF(Xi, 4, self%r)
|
||||
localK = localK + MATMUL(RESHAPE(MATMUL(invJ,dPsi), (/ 2, 1/)), &
|
||||
RESHAPE(MATMUL(invJ,dPsi), (/ 1, 2/)))* &
|
||||
r*wSeg(l)/detJ
|
||||
|
||||
END DO
|
||||
localK = localK*PI2
|
||||
|
||||
END FUNCTION elemKSegm
|
||||
|
||||
!Computes the local source vector for a force f
|
||||
PURE FUNCTION elemFSegm(self, nNodes, source) RESULT(localF)
|
||||
USE moduleConstParam, ONLY: PI2
|
||||
IMPLICIT NONE
|
||||
|
||||
CLASS(meshCell1DRadSegm), INTENT(in):: self
|
||||
INTEGER, INTENT(in):: nNodes
|
||||
REAL(8), INTENT(in):: source(1:nNodes)
|
||||
REAL(8):: localF(1:nNodes)
|
||||
REAL(8):: fPsi(1:2)
|
||||
REAL(8):: dPsi(1:3, 1:2), pDer(1:3, 1:3)
|
||||
REAL(8):: Xi(1:3)
|
||||
REAL(8):: detJ, f
|
||||
REAL(8):: r
|
||||
INTEGER:: l
|
||||
|
||||
localF = 0.D0
|
||||
|
||||
Xi = 0.D0
|
||||
!Start 1D Gauss Quad Integral
|
||||
DO l = 1, 3
|
||||
Xi(1) = corSeg(l)
|
||||
dPsi = self%dPsi(Xi, 2)
|
||||
pDer = self%partialDer(2, dPsi)
|
||||
detJ = self%detJac(pDer)
|
||||
fPsi = self%fPsi(Xi, 2)
|
||||
r = DOT_PRODUCT(fPsi, self%r)
|
||||
f = DOT_PRODUCT(fPsi, source)
|
||||
localF = localF + r*f*fPsi*wSeg(l)*detJ
|
||||
|
||||
END DO
|
||||
localF = localF*PI2
|
||||
|
||||
END FUNCTION elemFSegm
|
||||
|
||||
PURE FUNCTION insideSegm(Xi) RESULT(ins)
|
||||
IMPLICIT NONE
|
||||
|
||||
REAL(8), INTENT(in):: Xi(1:3)
|
||||
|
|
@ -419,102 +396,97 @@ MODULE moduleMesh1DRad
|
|||
ins = Xi(1) >=-1.D0 .AND. &
|
||||
Xi(1) <= 1.D0
|
||||
|
||||
END FUNCTION insideRad
|
||||
END FUNCTION insideSegm
|
||||
|
||||
!Get nodes from 1D volume
|
||||
PURE FUNCTION getNodesRad(self, nNodes) RESULT(n)
|
||||
IMPLICIT NONE
|
||||
|
||||
CLASS(meshCell1DRadSegm), INTENT(in):: self
|
||||
INTEGER, INTENT(in):: nNodes
|
||||
INTEGER:: n(1:nNodes)
|
||||
|
||||
n = (/ self%n1%n, self%n2%n /)
|
||||
|
||||
END FUNCTION getNodesRad
|
||||
|
||||
PURE FUNCTION phy2logRad(self, r) RESULT(xN)
|
||||
PURE FUNCTION phy2logSegm(self, r) RESULT(Xi)
|
||||
IMPLICIT NONE
|
||||
|
||||
CLASS(meshCell1DRadSegm), INTENT(in):: self
|
||||
REAL(8), INTENT(in):: r(1:3)
|
||||
REAL(8):: xN(1:3)
|
||||
REAL(8):: Xi(1:3)
|
||||
|
||||
xN = 0.D0
|
||||
xN(1) = 2.D0*(r(1) - self%r(1))/(self%r(2) - self%r(1)) - 1.D0
|
||||
Xi = 0.D0
|
||||
|
||||
END FUNCTION phy2logRad
|
||||
Xi(1) = 2.D0*(r(1) - self%r(1))/(self%r(2) - self%r(1)) - 1.D0
|
||||
|
||||
!Get next element for a logical position Xi
|
||||
SUBROUTINE nextElementRad(self, Xi, nextElement)
|
||||
END FUNCTION phy2logSegm
|
||||
|
||||
!Get the next element for a logical position Xi
|
||||
SUBROUTINE neighbourElementSegm(self, Xi, neighbourElement)
|
||||
IMPLICIT NONE
|
||||
|
||||
CLASS(meshCell1DRadSegm), INTENT(in):: self
|
||||
REAL(8), INTENT(in):: Xi(1:3)
|
||||
CLASS(meshElement), POINTER, INTENT(out):: nextElement
|
||||
CLASS(meshElement), POINTER, INTENT(out):: neighbourElement
|
||||
|
||||
NULLIFY(nextElement)
|
||||
NULLIFY(neighbourElement)
|
||||
IF (Xi(1) < -1.D0) THEN
|
||||
nextElement => self%e2
|
||||
neighbourElement => self%e2
|
||||
|
||||
ELSEIF (Xi(1) > 1.D0) THEN
|
||||
nextElement => self%e1
|
||||
neighbourElement => self%e1
|
||||
|
||||
END IF
|
||||
|
||||
END SUBROUTINE nextElementRad
|
||||
END SUBROUTINE neighbourElementSegm
|
||||
|
||||
!COMMON FUNCTIONS FOR 1D VOLUME ELEMENTS
|
||||
!Computes the element Jacobian determinant
|
||||
PURE FUNCTION detJ1DRad(self, Xi, nNodes, dPsi_in) RESULT(dJ)
|
||||
!Computes element area
|
||||
PURE SUBROUTINE areaSegm(self)
|
||||
USE moduleConstParam, ONLY: PI
|
||||
IMPLICIT NONE
|
||||
|
||||
CLASS(meshCell1DRad), INTENT(in):: self
|
||||
REAL(8), INTENT(in):: Xi(1:3)
|
||||
INTEGER, INTENT(in):: nNodes
|
||||
REAL(8), INTENT(in), OPTIONAL:: dPsi_in(1:3,1:nNodes)
|
||||
REAL(8):: dPsi(1:3,1:nNodes)
|
||||
CLASS(meshCell1DRadSegm), INTENT(inout):: self
|
||||
REAL(8):: Xi(1:3)
|
||||
REAL(8):: dPsi(1:3, 1:2), pDer(1:3, 1:3)
|
||||
REAL(8):: detJ
|
||||
REAL(8):: fPsi(1:2)
|
||||
REAL(8):: r
|
||||
|
||||
self%volume = 0.D0
|
||||
self%arNodes = 0.D0
|
||||
!1D 1 point Gauss Quad Integral
|
||||
Xi = 0.D0
|
||||
dPsi = self%dPsi(Xi, 2)
|
||||
pDer = self%partialDer(2, dPsi)
|
||||
detJ = self%detJac(pDer)
|
||||
fPsi = self%fPsi(Xi, 2)
|
||||
!Computes total volume of the cell
|
||||
r = DOT_PRODUCT(fPsi, self%r)
|
||||
self%volume = r*detJ*2.D0*PI !2PI
|
||||
!Computes volume per node
|
||||
Xi = (/-5.D-1, 0.D0, 0.D0/)
|
||||
r = self%gatherF(Xi, 2, self%r)
|
||||
self%arNodes(1) = fPsi(1)*self%volume
|
||||
Xi = (/ 5.D-1, 0.D0, 0.D0/)
|
||||
r = self%gatherF(Xi, 2, self%r)
|
||||
self%arNodes(2) = fPsi(2)*self%volume
|
||||
|
||||
END SUBROUTINE areaSegm
|
||||
|
||||
!COMMON FUNCTIONS FOR 1D VOLUME ELEMENTS
|
||||
!Computes element Jacobian determinant
|
||||
PURE FUNCTION detJ1DRad(pDer) RESULT(dJ)
|
||||
IMPLICIT NONE
|
||||
|
||||
REAL(8), INTENT(in):: pDer(1:3, 1:3)
|
||||
REAL(8):: dJ
|
||||
REAL(8):: dx(1)
|
||||
|
||||
IF (PRESENT(dPsi_in)) THEN
|
||||
dPsi = dPsi_in
|
||||
|
||||
ELSE
|
||||
dPsi = self%dPsi(Xi, 2)
|
||||
|
||||
END IF
|
||||
|
||||
CALL self%partialDer(nNodes, dPsi, dx)
|
||||
dJ = dx(1)
|
||||
dJ = pDer(1, 1)
|
||||
|
||||
END FUNCTION detJ1DRad
|
||||
|
||||
!Computes the invers Jacobian
|
||||
PURE FUNCTION invJ1DRad(self, Xi, nNodes, dPsi_in) RESULT(invJ)
|
||||
!Computes element Jacobian inverse matrix (without determinant)
|
||||
PURE FUNCTION invJ1DRad(pDer) RESULT(invJ)
|
||||
IMPLICIT NONE
|
||||
|
||||
CLASS(meshCell1DRad), INTENT(in):: self
|
||||
REAL(8), INTENT(in):: Xi(1:3)
|
||||
INTEGER, INTENT(in):: nNodes
|
||||
REAL(8), INTENT(in), OPTIONAL:: dPsi_in(1:3,1:nNodes)
|
||||
REAL(8):: dPsi(1:3,1:nNodes)
|
||||
REAL(8):: dx(1)
|
||||
REAL(8), INTENT(in):: pDer(1:3, 1:3)
|
||||
REAL(8):: invJ(1:3,1:3)
|
||||
|
||||
IF (PRESENT(dPsi_in)) THEN
|
||||
dPsi = dPsi_in
|
||||
|
||||
ELSE
|
||||
dPsi = self%dPsi(Xi, 2)
|
||||
|
||||
END IF
|
||||
|
||||
invJ = 0.D0
|
||||
|
||||
CALL self%partialDer(nNodes, dPsi, dx)
|
||||
|
||||
invJ(1,1) = 1.D0/dx(1)
|
||||
invJ(1, 1) = 1.D0/pDer(1, 1)
|
||||
invJ(2, 2) = 1.D0
|
||||
invJ(3, 3) = 1.D0
|
||||
|
||||
END FUNCTION invJ1DRad
|
||||
|
||||
|
|
|
|||
|
|
@ -19,7 +19,8 @@ MODULE moduleMesh2DCart
|
|||
!Element coordinates
|
||||
REAL(8):: x = 0.D0, y = 0.D0
|
||||
CONTAINS
|
||||
PROCEDURE, PASS:: init => initNode2DCart
|
||||
!meshNode DEFERRED PROCEDURES
|
||||
PROCEDURE, PASS:: init => initNode2DCart
|
||||
PROCEDURE, PASS:: getCoordinates => getCoord2DCart
|
||||
|
||||
END TYPE meshNode2DCart
|
||||
|
|
@ -30,35 +31,16 @@ MODULE moduleMesh2DCart
|
|||
!Connectivity to nodes
|
||||
CLASS(meshNode), POINTER:: n1 => NULL(), n2 => NULL()
|
||||
CONTAINS
|
||||
PROCEDURE, PASS:: init => initEdge2DCart
|
||||
PROCEDURE, PASS:: getNodes => getNodes2DCart
|
||||
!meshEdge DEFERRED PROCEDURES
|
||||
PROCEDURE, PASS:: init => initEdge2DCart
|
||||
PROCEDURE, PASS:: getNodes => getNodes2DCart
|
||||
PROCEDURE, PASS:: intersection => intersection2DCartEdge
|
||||
PROCEDURE, PASS:: randPos => randPosEdge
|
||||
PROCEDURE, PASS:: randPos => randPosEdge
|
||||
|
||||
END TYPE meshEdge2DCart
|
||||
|
||||
TYPE, PUBLIC, ABSTRACT, EXTENDS(meshCell):: meshCell2DCart
|
||||
CONTAINS
|
||||
PROCEDURE, PASS:: detJac => detJ2DCart
|
||||
PROCEDURE, PASS:: invJac => invJ2DCart
|
||||
PROCEDURE(partialDer_interface), DEFERRED, PASS, PRIVATE:: partialDer
|
||||
|
||||
END TYPE meshCell2DCart
|
||||
|
||||
ABSTRACT INTERFACE
|
||||
PURE SUBROUTINE partialDer_interface(self, nNodes, dPsi, dx, dy)
|
||||
IMPORT meshCell2DCart
|
||||
CLASS(meshCell2DCart), INTENT(in):: self
|
||||
INTEGER, INTENT(in):: nNodes
|
||||
REAL(8), INTENT(in):: dPsi(1:3,1:nNodes)
|
||||
REAL(8), INTENT(out), DIMENSION(1:2):: dx, dy
|
||||
|
||||
END SUBROUTINE partialDer_interface
|
||||
|
||||
END INTERFACE
|
||||
|
||||
!Quadrilateral volume element
|
||||
TYPE, PUBLIC, EXTENDS(meshCell2DCart):: meshCell2DCartQuad
|
||||
TYPE, PUBLIC, EXTENDS(meshCell):: meshCell2DCartQuad
|
||||
!Element coordinates
|
||||
REAL(8):: x(1:4) = 0.D0, y(1:4) = 0.D0
|
||||
!Connectivity to nodes
|
||||
|
|
@ -68,25 +50,29 @@ MODULE moduleMesh2DCart
|
|||
REAL(8):: arNodes(1:4) = 0.D0
|
||||
|
||||
CONTAINS
|
||||
PROCEDURE, PASS:: init => initCellQuad2DCart
|
||||
PROCEDURE, PASS:: randPos => randPosCellQuad
|
||||
PROCEDURE, PASS:: area => areaQuad
|
||||
PROCEDURE, PASS:: fPsi => fPsiQuad
|
||||
PROCEDURE, PASS:: dPsi => dPsiQuad
|
||||
PROCEDURE, PASS, PRIVATE:: partialDer => partialDerQuad
|
||||
PROCEDURE, PASS:: elemK => elemKQuad
|
||||
PROCEDURE, PASS:: elemF => elemFQuad
|
||||
PROCEDURE, PASS:: gatherElectricField => gatherEFQuad
|
||||
PROCEDURE, PASS:: gatherMagneticField => gatherMFQuad
|
||||
PROCEDURE, NOPASS:: inside => insideQuad
|
||||
PROCEDURE, PASS:: getNodes => getNodesQuad
|
||||
PROCEDURE, PASS:: phy2log => phy2logQuad
|
||||
PROCEDURE, PASS:: nextElement => nextElementQuad
|
||||
!meshCell DEFERRED PROCEDURES
|
||||
PROCEDURE, PASS:: init => initCellQuad2DCart
|
||||
PROCEDURE, PASS:: getNodes => getNodesQuad
|
||||
PROCEDURE, PASS:: randPos => randPosCellQuad
|
||||
PROCEDURE, NOPASS:: fPsi => fPsiQuad
|
||||
PROCEDURE, NOPASS:: dPsi => dPsiQuad
|
||||
PROCEDURE, PASS:: partialDer => partialDerQuad
|
||||
PROCEDURE, NOPASS:: detJac => detJ2DCart
|
||||
PROCEDURE, NOPASS:: invJac => invJ2DCart
|
||||
PROCEDURE, PASS:: gatherElectricField => gatherEFQuad
|
||||
PROCEDURE, PASS:: gatherMagneticField => gatherMFQuad
|
||||
PROCEDURE, PASS:: elemK => elemKQuad
|
||||
PROCEDURE, PASS:: elemF => elemFQuad
|
||||
PROCEDURE, NOPASS:: inside => insideQuad
|
||||
PROCEDURE, PASS:: phy2log => phy2logQuad
|
||||
PROCEDURE, PASS:: neighbourElement => neighbourElementQuad
|
||||
!PARTICLUAR PROCEDURES
|
||||
PROCEDURE, PASS, PRIVATE:: area => areaQuad
|
||||
|
||||
END TYPE meshCell2DCartQuad
|
||||
|
||||
!Triangular volume element
|
||||
TYPE, PUBLIC, EXTENDS(meshCell2DCart):: meshCell2DCartTria
|
||||
TYPE, PUBLIC, EXTENDS(meshCell):: meshCell2DCartTria
|
||||
!Element coordinates
|
||||
REAL(8):: x(1:3) = 0.D0, y(1:3) = 0.D0
|
||||
!Connectivity to nodes
|
||||
|
|
@ -96,20 +82,24 @@ MODULE moduleMesh2DCart
|
|||
REAL(8):: arNodes(1:3) = 0.D0
|
||||
|
||||
CONTAINS
|
||||
PROCEDURE, PASS:: init => initCellTria2DCart
|
||||
PROCEDURE, PASS:: randPos => randPosCellTria
|
||||
PROCEDURE, PASS:: area => areaTria
|
||||
PROCEDURE, PASS:: fPsi => fPsiTria
|
||||
PROCEDURE, PASS:: dPsi => dPsiTria
|
||||
PROCEDURE, PASS, PRIVATE:: partialDer => partialDerTria
|
||||
PROCEDURE, PASS:: elemK => elemKTria
|
||||
PROCEDURE, PASS:: elemF => elemFTria
|
||||
PROCEDURE, PASS:: gatherElectricField => gatherEFTria
|
||||
PROCEDURE, PASS:: gatherMagneticField => gatherMFTria
|
||||
PROCEDURE, NOPASS:: inside => insideTria
|
||||
PROCEDURE, PASS:: getNodes => getNodesTria
|
||||
PROCEDURE, PASS:: phy2log => phy2logTria
|
||||
PROCEDURE, PASS:: nextElement => nextElementTria
|
||||
!meshCell DEFERRED PROCEDURES
|
||||
PROCEDURE, PASS:: init => initCellTria2DCart
|
||||
PROCEDURE, PASS:: getNodes => getNodesTria
|
||||
PROCEDURE, PASS:: randPos => randPosCellTria
|
||||
PROCEDURE, NOPASS:: fPsi => fPsiTria
|
||||
PROCEDURE, NOPASS:: dPsi => dPsiTria
|
||||
PROCEDURE, PASS:: partialDer => partialDerTria
|
||||
PROCEDURE, NOPASS:: detJac => detJ2DCart
|
||||
PROCEDURE, NOPASS:: invJac => invJ2DCart
|
||||
PROCEDURE, PASS:: gatherElectricField => gatherEFTria
|
||||
PROCEDURE, PASS:: gatherMagneticField => gatherMFTria
|
||||
PROCEDURE, PASS:: elemK => elemKTria
|
||||
PROCEDURE, PASS:: elemF => elemFTria
|
||||
PROCEDURE, NOPASS:: inside => insideTria
|
||||
PROCEDURE, PASS:: phy2log => phy2logTria
|
||||
PROCEDURE, PASS:: neighbourElement => neighbourElementTria
|
||||
!PARTICULAR PROCEDURES
|
||||
PROCEDURE, PASS, PRIVATE:: area => areaTria
|
||||
|
||||
END TYPE meshCell2DCartTria
|
||||
|
||||
|
|
@ -175,6 +165,7 @@ MODULE moduleMesh2DCart
|
|||
r2 = self%n2%getCoordinates()
|
||||
self%x = (/r1(1), r2(1)/)
|
||||
self%y = (/r1(2), r2(2)/)
|
||||
self%weight = 1.D0
|
||||
!Normal vector
|
||||
self%normal = (/ -(self%y(2)-self%y(1)), &
|
||||
self%x(2)-self%x(1) , &
|
||||
|
|
@ -290,84 +281,17 @@ MODULE moduleMesh2DCart
|
|||
|
||||
END SUBROUTINE initCellQuad2DCart
|
||||
|
||||
!Computes element area
|
||||
PURE SUBROUTINE areaQuad(self)
|
||||
IMPLICIT NONE
|
||||
|
||||
CLASS(meshCell2DCartQuad), INTENT(inout):: self
|
||||
REAL(8):: Xi(1:3)
|
||||
REAL(8):: detJ
|
||||
REAL(8):: fPsi(1:4)
|
||||
|
||||
self%volume = 0.D0
|
||||
self%arNodes = 0.D0
|
||||
!2D 1 point Gauss Quad Integral
|
||||
Xi = 0.D0
|
||||
detJ = self%detJac(Xi, 4)*4.D0 !4
|
||||
fPsi = self%fPsi(Xi, 4)
|
||||
self%volume = detJ
|
||||
self%arNodes = fPsi*detJ
|
||||
|
||||
END SUBROUTINE areaQuad
|
||||
|
||||
!Computes element functions in point Xi
|
||||
PURE FUNCTION fPsiQuad(self, Xi, nNodes) RESULT(fPsi)
|
||||
IMPLICIT NONE
|
||||
|
||||
CLASS(meshCell2DCartQuad), INTENT(in):: self
|
||||
REAL(8), INTENT(in):: Xi(1:3)
|
||||
INTEGER, INTENT(in):: nNodes
|
||||
REAL(8):: fPsi(1:nNodes)
|
||||
|
||||
fPsi(1) = (1.D0-Xi(1)) * (1.D0-Xi(2))
|
||||
fPsi(2) = (1.D0+Xi(1)) * (1.D0-Xi(2))
|
||||
fPsi(3) = (1.D0+Xi(1)) * (1.D0+Xi(2))
|
||||
fPsi(4) = (1.D0-Xi(1)) * (1.D0+Xi(2))
|
||||
|
||||
fPsi = fPsi*0.25D0
|
||||
|
||||
END FUNCTION fPsiQuad
|
||||
|
||||
!Derivative element function at coordinates Xi
|
||||
PURE FUNCTION dPsiQuad(self, Xi, nNodes) RESULT(dPsi)
|
||||
IMPLICIT NONE
|
||||
|
||||
CLASS(meshCell2DCartQuad), INTENT(in):: self
|
||||
REAL(8), INTENT(in):: Xi(1:3)
|
||||
INTEGER, INTENT(in):: nNodes
|
||||
REAL(8):: dPsi(1:3,1:nNodes)
|
||||
|
||||
dPsi = 0.D0
|
||||
|
||||
dPsi(1,:) = (/ -(1.D0 - Xi(2)), &
|
||||
(1.D0 - Xi(2)), &
|
||||
(1.D0 + Xi(2)), &
|
||||
-(1.D0 + Xi(2)) /)
|
||||
|
||||
dPsi(2,:) = (/ -(1.D0 - Xi(1)), &
|
||||
-(1.D0 + Xi(1)), &
|
||||
(1.D0 + Xi(1)), &
|
||||
(1.D0 - Xi(1)) /)
|
||||
|
||||
dPsi = dPsi * 0.25D0
|
||||
|
||||
END FUNCTION dPsiQuad
|
||||
|
||||
!Partial derivative in global coordinates
|
||||
PURE SUBROUTINE partialDerQuad(self, nNodes, dPsi, dx, dy)
|
||||
!Get nodes from quadrilateral element
|
||||
PURE FUNCTION getNodesQuad(self, nNodes) RESULT(n)
|
||||
IMPLICIT NONE
|
||||
|
||||
CLASS(meshCell2DCartQuad), INTENT(in):: self
|
||||
INTEGER, INTENT(in):: nNodes
|
||||
REAL(8), INTENT(in):: dPsi(1:3,1:nNodes)
|
||||
REAL(8), INTENT(out), DIMENSION(1:2):: dx, dy
|
||||
INTEGER:: n(1:nNodes)
|
||||
|
||||
dx = (/ DOT_PRODUCT(dPsi(1,1:4),self%x(1:4)), &
|
||||
DOT_PRODUCT(dPsi(2,1:4),self%x(1:4)) /)
|
||||
dy = (/ DOT_PRODUCT(dPsi(1,1:4),self%y(1:4)), &
|
||||
DOT_PRODUCT(dPsi(2,1:4),self%y(1:4)) /)
|
||||
n = (/ self%n1%n, self%n2%n, self%n3%n, self%n4%n /)
|
||||
|
||||
END SUBROUTINE partialDerQuad
|
||||
END FUNCTION getNodesQuad
|
||||
|
||||
!Random position in quadrilateral volume
|
||||
FUNCTION randPosCellQuad(self) RESULT(r)
|
||||
|
|
@ -379,78 +303,77 @@ MODULE moduleMesh2DCart
|
|||
REAL(8):: Xi(1:3)
|
||||
REAL(8):: fPsi(1:4)
|
||||
|
||||
Xi = 0.D0
|
||||
Xi(1) = random(-1.D0, 1.D0)
|
||||
Xi(2) = random(-1.D0, 1.D0)
|
||||
Xi(3) = 0.D0
|
||||
|
||||
fPsi = self%fPsi(Xi, 4)
|
||||
|
||||
r = 0.D0
|
||||
r(1) = DOT_PRODUCT(fPsi, self%x)
|
||||
r(2) = DOT_PRODUCT(fPsi, self%y)
|
||||
r(3) = 0.D0
|
||||
|
||||
END FUNCTION randPosCellQuad
|
||||
|
||||
!Computes element local stiffness matrix
|
||||
PURE FUNCTION elemKQuad(self, nNodes) RESULT(localK)
|
||||
!Computes element functions in point Xi
|
||||
PURE FUNCTION fPsiQuad(Xi, nNodes) RESULT(fPsi)
|
||||
IMPLICIT NONE
|
||||
|
||||
REAL(8), INTENT(in):: Xi(1:3)
|
||||
INTEGER, INTENT(in):: nNodes
|
||||
REAL(8):: fPsi(1:nNodes)
|
||||
|
||||
fPsi = (/ (1.D0-Xi(1)) * (1.D0-Xi(2)), &
|
||||
(1.D0+Xi(1)) * (1.D0-Xi(2)), &
|
||||
(1.D0+Xi(1)) * (1.D0+Xi(2)), &
|
||||
(1.D0-Xi(1)) * (1.D0+Xi(2)) /)
|
||||
|
||||
fPsi = fPsi * 0.25D0
|
||||
|
||||
END FUNCTION fPsiQuad
|
||||
|
||||
!Derivative element function at coordinates Xi
|
||||
PURE FUNCTION dPsiQuad(Xi, nNodes) RESULT(dPsi)
|
||||
IMPLICIT NONE
|
||||
|
||||
REAL(8), INTENT(in):: Xi(1:3)
|
||||
INTEGER, INTENT(in):: nNodes
|
||||
REAL(8):: dPsi(1:3,1:nNodes)
|
||||
|
||||
dPsi = 0.D0
|
||||
|
||||
dPsi(1, 1:4) = (/ -(1.D0 - Xi(2)), &
|
||||
(1.D0 - Xi(2)), &
|
||||
(1.D0 + Xi(2)), &
|
||||
-(1.D0 + Xi(2)) /)
|
||||
|
||||
dPsi(2, 1:4) = (/ -(1.D0 - Xi(1)), &
|
||||
-(1.D0 + Xi(1)), &
|
||||
(1.D0 + Xi(1)), &
|
||||
(1.D0 - Xi(1)) /)
|
||||
|
||||
dPsi = dPsi * 0.25D0
|
||||
|
||||
END FUNCTION dPsiQuad
|
||||
|
||||
!Partial derivative in global coordinates
|
||||
PURE FUNCTION partialDerQuad(self, nNodes, dPsi) RESULT(pDer)
|
||||
IMPLICIT NONE
|
||||
|
||||
CLASS(meshCell2DCartQuad), INTENT(in):: self
|
||||
INTEGER, INTENT(in):: nNodes
|
||||
REAL(8):: localK(1:nNodes,1:nNodes)
|
||||
REAL(8):: Xi(1:3)
|
||||
REAL(8):: fPsi(1:4), dPsi(1:3,1:4)
|
||||
REAL(8):: invJ(1:3,1:3), detJ
|
||||
INTEGER:: l, m
|
||||
REAL(8), INTENT(in):: dPsi(1:3,1:nNodes)
|
||||
REAL(8):: pDer(1:3, 1:3)
|
||||
|
||||
localK=0.D0
|
||||
Xi=0.D0
|
||||
!Start 2D Gauss Quad Integral
|
||||
DO l=1, 3
|
||||
Xi(2) = corQuad(l)
|
||||
DO m = 1, 3
|
||||
Xi(1) = corQuad(m)
|
||||
fPsi = self%fPsi(Xi, 4)
|
||||
dPsi = self%dPsi(Xi, 4)
|
||||
detJ = self%detJac(Xi, 4, dPsi)
|
||||
invJ = self%invJac(Xi, 4, dPsi)
|
||||
localK = localK + MATMUL(TRANSPOSE(MATMUL(invJ,dPsi)), &
|
||||
MATMUL(invJ,dPsi))* &
|
||||
wQuad(l)*wQuad(m)/detJ
|
||||
pDer = 0.D0
|
||||
|
||||
END DO
|
||||
END DO
|
||||
pDer(1, 1:2) = (/ DOT_PRODUCT(dPsi(1,1:4),self%x(1:4)), &
|
||||
DOT_PRODUCT(dPsi(2,1:4),self%x(1:4)) /)
|
||||
pDer(2, 1:2) = (/ DOT_PRODUCT(dPsi(1,1:4),self%y(1:4)), &
|
||||
DOT_PRODUCT(dPsi(2,1:4),self%y(1:4)) /)
|
||||
pDer(3,3) = 1.D0
|
||||
|
||||
END FUNCTION elemKQuad
|
||||
|
||||
!Computes the local source vector for a force f
|
||||
PURE FUNCTION elemFQuad(self, nNodes, source) RESULT(localF)
|
||||
IMPLICIT NONE
|
||||
|
||||
CLASS(meshCell2DCartQuad), INTENT(in):: self
|
||||
INTEGER, INTENT(in):: nNodes
|
||||
REAL(8), INTENT(in):: source(1:nNodes)
|
||||
REAL(8):: localF(1:nNodes)
|
||||
REAL(8):: Xi(1:3)
|
||||
REAL(8):: fPsi(1:4)
|
||||
REAL(8):: detJ, f
|
||||
INTEGER:: l, m
|
||||
|
||||
localF = 0.D0
|
||||
Xi = 0.D0
|
||||
DO l=1, 3
|
||||
Xi(1) = corQuad(l)
|
||||
DO m = 1, 3
|
||||
Xi(2) = corQuad(m)
|
||||
detJ = self%detJac(Xi, 4)
|
||||
fPsi = self%fPsi(Xi, 4)
|
||||
f = DOT_PRODUCT(fPsi,source)
|
||||
localF = localF + f*fPsi*wQuad(l)*wQuad(m)*detJ
|
||||
|
||||
END DO
|
||||
END DO
|
||||
|
||||
END FUNCTION elemFQuad
|
||||
END FUNCTION partialDerQuad
|
||||
|
||||
PURE FUNCTION gatherEFQuad(self, Xi) RESULT(array)
|
||||
IMPLICIT NONE
|
||||
|
|
@ -494,6 +417,75 @@ MODULE moduleMesh2DCart
|
|||
|
||||
END FUNCTION gatherMFQuad
|
||||
|
||||
!Computes element local stiffness matrix
|
||||
PURE FUNCTION elemKQuad(self, nNodes) RESULT(localK)
|
||||
IMPLICIT NONE
|
||||
|
||||
CLASS(meshCell2DCartQuad), INTENT(in):: self
|
||||
INTEGER, INTENT(in):: nNodes
|
||||
REAL(8):: localK(1:nNodes,1:nNodes)
|
||||
REAL(8):: Xi(1:3)
|
||||
REAL(8):: dPsi(1:3, 1:4)
|
||||
REAL(8):: pDer(1:3, 1:3)
|
||||
REAL(8):: r
|
||||
REAL(8):: invJ(1:3,1:3), detJ
|
||||
INTEGER:: l, m
|
||||
|
||||
localK = 0.D0
|
||||
|
||||
Xi = 0.D0
|
||||
!Start 2D Gauss Quad Integral
|
||||
DO l = 1, 3
|
||||
Xi(2) = corQuad(l)
|
||||
DO m = 1, 3
|
||||
Xi(1) = corQuad(m)
|
||||
dPsi = self%dPsi(Xi, 4)
|
||||
pDer = self%partialDer(4, dPsi)
|
||||
detJ = self%detJac(pDer)
|
||||
invJ = self%invJac(pDer)
|
||||
localK = localK + MATMUL(TRANSPOSE(MATMUL(invJ,dPsi)), &
|
||||
MATMUL(invJ,dPsi))* &
|
||||
wQuad(l)*wQuad(m)/detJ
|
||||
|
||||
END DO
|
||||
END DO
|
||||
|
||||
END FUNCTION elemKQuad
|
||||
|
||||
!Computes the local source vector for a force f
|
||||
PURE FUNCTION elemFQuad(self, nNodes, source) RESULT(localF)
|
||||
IMPLICIT NONE
|
||||
|
||||
CLASS(meshCell2DCartQuad), INTENT(in):: self
|
||||
INTEGER, INTENT(in):: nNodes
|
||||
REAL(8), INTENT(in):: source(1:nNodes)
|
||||
REAL(8):: localF(1:nNodes)
|
||||
REAL(8):: Xi(1:3)
|
||||
REAL(8):: fPsi(1:4)
|
||||
REAL(8):: dPsi(1:3, 1:4)
|
||||
REAL(8):: pDer(1:3, 1:3)
|
||||
REAL(8):: detJ, f
|
||||
INTEGER:: l, m
|
||||
|
||||
localF = 0.D0
|
||||
|
||||
Xi = 0.D0
|
||||
DO l = 1, 3
|
||||
Xi(1) = corQuad(l)
|
||||
DO m = 1, 3
|
||||
Xi(2) = corQuad(m)
|
||||
dPsi = self%dPsi(Xi, 4)
|
||||
pDer = self%partialDer(4, dPsi)
|
||||
detJ = self%detJac(pDer)
|
||||
fPsi = self%fPsi(Xi, 4)
|
||||
f = DOT_PRODUCT(fPsi,source)
|
||||
localF = localF + f*fPsi*wQuad(l)*wQuad(m)*detJ
|
||||
|
||||
END DO
|
||||
END DO
|
||||
|
||||
END FUNCTION elemFQuad
|
||||
|
||||
!Checks if a particle is inside a quad element
|
||||
PURE FUNCTION insideQuad(Xi) RESULT(ins)
|
||||
IMPLICIT NONE
|
||||
|
|
@ -506,18 +498,6 @@ MODULE moduleMesh2DCart
|
|||
|
||||
END FUNCTION insideQuad
|
||||
|
||||
!Gets nodes from quadrilateral element
|
||||
PURE FUNCTION getNodesQuad(self, nNodes) RESULT(n)
|
||||
IMPLICIT NONE
|
||||
|
||||
CLASS(meshCell2DCartQuad), INTENT(in):: self
|
||||
INTEGER, INTENT(in):: nNodes
|
||||
INTEGER:: n(1:nNodes)
|
||||
|
||||
n = (/self%n1%n, self%n2%n, self%n3%n, self%n4%n /)
|
||||
|
||||
END FUNCTION getNodesQuad
|
||||
|
||||
!Transforms physical coordinates to element coordinates
|
||||
PURE FUNCTION phy2logQuad(self,r) RESULT(Xi)
|
||||
IMPLICIT NONE
|
||||
|
|
@ -527,6 +507,7 @@ MODULE moduleMesh2DCart
|
|||
REAL(8):: Xi(1:3)
|
||||
REAL(8):: XiO(1:3), detJ, invJ(1:3,1:3), f(1:3)
|
||||
REAL(8):: dPsi(1:3,1:4), fPsi(1:4)
|
||||
REAL(8):: pDer(1:3, 1:3)
|
||||
REAL(8):: conv
|
||||
|
||||
!Iterative newton method to transform coordinates
|
||||
|
|
@ -535,7 +516,9 @@ MODULE moduleMesh2DCart
|
|||
|
||||
DO WHILE(conv > 1.D-2)
|
||||
dPsi = self%dPsi(XiO, 4)
|
||||
invJ = self%invJac(XiO, 4, dPsi)
|
||||
pDer = self%partialDer(4, dPsi)
|
||||
detJ = self%detJac(pDer)
|
||||
invJ = self%invJac(pDer)
|
||||
fPsi = self%fPsi(XiO, 4)
|
||||
f = (/ DOT_PRODUCT(fPsi,self%x), &
|
||||
DOT_PRODUCT(fPsi,self%y), &
|
||||
|
|
@ -550,31 +533,56 @@ MODULE moduleMesh2DCart
|
|||
END FUNCTION phy2logQuad
|
||||
|
||||
!Gets the next element for a logical position Xi
|
||||
SUBROUTINE nextElementQuad(self, Xi, nextElement)
|
||||
SUBROUTINE neighbourElementQuad(self, Xi, neighbourElement)
|
||||
IMPLICIT NONE
|
||||
|
||||
CLASS(meshCell2DCartQuad), INTENT(in):: self
|
||||
REAL(8), INTENT(in):: Xi(1:3)
|
||||
CLASS(meshElement), POINTER, INTENT(out):: nextElement
|
||||
CLASS(meshElement), POINTER, INTENT(out):: neighbourElement
|
||||
REAL(8):: XiArray(1:4)
|
||||
INTEGER:: nextInt
|
||||
|
||||
XiArray = (/ -Xi(2), Xi(1), Xi(2), -Xi(1) /)
|
||||
nextInt = MAXLOC(XiArray,1)
|
||||
!Selects the higher value of directions and searches in that direction
|
||||
NULLIFY(nextElement)
|
||||
NULLIFY(neighbourElement)
|
||||
SELECT CASE (nextInt)
|
||||
CASE (1)
|
||||
nextElement => self%e1
|
||||
neighbourElement => self%e1
|
||||
CASE (2)
|
||||
nextElement => self%e2
|
||||
neighbourElement => self%e2
|
||||
CASE (3)
|
||||
nextElement => self%e3
|
||||
neighbourElement => self%e3
|
||||
CASE (4)
|
||||
nextElement => self%e4
|
||||
neighbourElement => self%e4
|
||||
END SELECT
|
||||
|
||||
END SUBROUTINE nextElementQuad
|
||||
END SUBROUTINE neighbourElementQuad
|
||||
|
||||
!Computes element area
|
||||
PURE SUBROUTINE areaQuad(self)
|
||||
IMPLICIT NONE
|
||||
|
||||
CLASS(meshCell2DCartQuad), INTENT(inout):: self
|
||||
REAL(8):: Xi(1:3)
|
||||
REAL(8):: detJ
|
||||
REAL(8):: fPsi(1:4)
|
||||
REAL(8):: dPsi(1:3, 1:4), pDer(1:3, 1:3)
|
||||
|
||||
self%volume = 0.D0
|
||||
self%arNodes = 0.D0
|
||||
!2D 1 point Gauss Quad Integral
|
||||
Xi = 0.D0
|
||||
dPsi = self%dPsi(Xi, 4)
|
||||
pDer = self%partialDer(4, dPsi)
|
||||
detJ = self%detJac(pDer)
|
||||
fPsi = self%fPsi(Xi, 4)
|
||||
!Computes total volume of the cell
|
||||
self%volume = detJ
|
||||
!Computes volume per node
|
||||
self%arNodes = fPsi*detJ
|
||||
|
||||
END SUBROUTINE areaQuad
|
||||
|
||||
!TRIA ELEMENT
|
||||
!Init tria element
|
||||
|
|
@ -617,6 +625,18 @@ MODULE moduleMesh2DCart
|
|||
|
||||
END SUBROUTINE initCellTria2DCart
|
||||
|
||||
!Gets node indexes from triangular element
|
||||
PURE FUNCTION getNodesTria(self, nNodes) RESULT(n)
|
||||
IMPLICIT NONE
|
||||
|
||||
CLASS(meshCell2DCartTria), INTENT(in):: self
|
||||
INTEGER, INTENT(in):: nNodes
|
||||
INTEGER:: n(1:nNodes)
|
||||
|
||||
n = (/self%n1%n, self%n2%n, self%n3%n /)
|
||||
|
||||
END FUNCTION getNodesTria
|
||||
|
||||
!Random position in quadrilateral volume
|
||||
FUNCTION randPosCellTria(self) RESULT(r)
|
||||
USE moduleRandom
|
||||
|
|
@ -639,31 +659,10 @@ MODULE moduleMesh2DCart
|
|||
|
||||
END FUNCTION randPosCellTria
|
||||
|
||||
!Calculates area for triangular element
|
||||
PURE SUBROUTINE areaTria(self)
|
||||
IMPLICIT NONE
|
||||
|
||||
CLASS(meshCell2DCartTria), INTENT(inout):: self
|
||||
REAL(8):: Xi(1:3)
|
||||
REAL(8):: detJ
|
||||
REAL(8):: fPsi(1:3)
|
||||
|
||||
self%volume = 0.D0
|
||||
self%arNodes = 0.D0
|
||||
!2D 1 point Gauss Quad Integral
|
||||
Xi = (/1.D0/3.D0, 1.D0/3.D0, 0.D0 /)
|
||||
detJ = self%detJac(Xi, 4)/2.D0
|
||||
fPsi = self%fPsi(Xi, 4)
|
||||
self%volume = detJ
|
||||
self%arNodes = fPsi*detJ
|
||||
|
||||
END SUBROUTINE areaTria
|
||||
|
||||
!Shape functions for triangular element
|
||||
PURE FUNCTION fPsiTria(self, Xi, nNodes) RESULT(fPsi)
|
||||
PURE FUNCTION fPsiTria(Xi, nNodes) RESULT(fPsi)
|
||||
IMPLICIT NONE
|
||||
|
||||
CLASS(meshCell2DCartTria), INTENT(in):: self
|
||||
REAL(8), INTENT(in):: Xi(1:3)
|
||||
INTEGER, INTENT(in):: nNodes
|
||||
REAL(8):: fPsi(1:nNodes)
|
||||
|
|
@ -675,10 +674,9 @@ MODULE moduleMesh2DCart
|
|||
END FUNCTION fPsiTria
|
||||
|
||||
!Derivative element function at coordinates Xi
|
||||
PURE FUNCTION dPsiTria(self, Xi, nNodes) RESULT(dPsi)
|
||||
PURE FUNCTION dPsiTria(Xi, nNodes) RESULT(dPsi)
|
||||
IMPLICIT NONE
|
||||
|
||||
CLASS(meshCell2DCartTria), INTENT(in):: self
|
||||
REAL(8), INTENT(in):: Xi(1:3)
|
||||
INTEGER, INTENT(in):: nNodes
|
||||
REAL(8):: dPsi(1:3,1:nNodes)
|
||||
|
|
@ -690,76 +688,22 @@ MODULE moduleMesh2DCart
|
|||
|
||||
END FUNCTION dPsiTria
|
||||
|
||||
PURE SUBROUTINE partialDerTria(self, nNodes, dPsi, dx, dy)
|
||||
PURE FUNCTION partialDerTria(self, nNodes, dPsi) RESULT(pDer)
|
||||
IMPLICIT NONE
|
||||
|
||||
CLASS(meshCell2DCartTria), INTENT(in):: self
|
||||
INTEGER, INTENT(in):: nNodes
|
||||
REAL(8), INTENT(in):: dPsi(1:3,1:nNodes)
|
||||
REAL(8), INTENT(out), DIMENSION(1:2):: dx, dy
|
||||
REAL(8):: pDer(1:3, 1:3)
|
||||
|
||||
dx = (/ DOT_PRODUCT(dPsi(1,:),self%x), &
|
||||
DOT_PRODUCT(dPsi(2,:),self%x) /)
|
||||
dy = (/ DOT_PRODUCT(dPsi(1,:),self%y), &
|
||||
DOT_PRODUCT(dPsi(2,:),self%y) /)
|
||||
pDer = 0.D0
|
||||
|
||||
END SUBROUTINE partialDerTria
|
||||
pDer(1, 1:2) = (/ DOT_PRODUCT(dPsi(1,1:3),self%x(1:3)), &
|
||||
DOT_PRODUCT(dPsi(2,1:3),self%x(1:3)) /)
|
||||
pDer(2, 1:2) = (/ DOT_PRODUCT(dPsi(1,1:3),self%y(1:3)), &
|
||||
DOT_PRODUCT(dPsi(2,1:3),self%y(1:3)) /)
|
||||
|
||||
!Computes element local stiffness matrix
|
||||
PURE FUNCTION elemKTria(self, nNodes) RESULT(localK)
|
||||
IMPLICIT NONE
|
||||
|
||||
CLASS(meshCell2DCartTria), INTENT(in):: self
|
||||
INTEGER, INTENT(in):: nNodes
|
||||
REAL(8):: localK(1:nNodes,1:nNodes)
|
||||
REAL(8):: Xi(1:3)
|
||||
REAL(8):: fPsi(1:3), dPsi(1:3,1:3)
|
||||
REAL(8):: invJ(1:3,1:3), detJ
|
||||
INTEGER:: l
|
||||
|
||||
localK=0.D0
|
||||
Xi=0.D0
|
||||
!Start 2D Gauss Quad Integral
|
||||
DO l=1, 4
|
||||
Xi(1) = Xi1Tria(l)
|
||||
Xi(2) = Xi2Tria(l)
|
||||
dPsi = self%dPsi(Xi, 3)
|
||||
detJ = self%detJac(Xi, 3, dPsi)
|
||||
invJ = self%invJac(Xi, 3, dPsi)
|
||||
fPsi = self%fPsi(Xi, 3)
|
||||
localK = localK + MATMUL(TRANSPOSE(MATMUL(invJ,dPsi)),MATMUL(invJ,dPsi))*wTria(l)/detJ
|
||||
|
||||
END DO
|
||||
|
||||
END FUNCTION elemKTria
|
||||
|
||||
!Computes element local source vector
|
||||
PURE FUNCTION elemFTria(self, nNodes, source) RESULT(localF)
|
||||
IMPLICIT NONE
|
||||
|
||||
CLASS(meshCell2DCartTria), INTENT(in):: self
|
||||
INTEGER, INTENT(in):: nNodes
|
||||
REAL(8), INTENT(in):: source(1:nNodes)
|
||||
REAL(8):: localF(1:nNodes)
|
||||
REAL(8):: fPsi(1:3)
|
||||
REAL(8):: Xi(1:3)
|
||||
REAL(8):: detJ, f
|
||||
INTEGER:: l
|
||||
|
||||
localF = 0.D0
|
||||
Xi = 0.D0
|
||||
!Start 2D Gauss Quad Integral
|
||||
DO l=1, 4
|
||||
Xi(1) = Xi1Tria(l)
|
||||
Xi(2) = Xi2Tria(l)
|
||||
detJ = self%detJac(Xi, 3)
|
||||
fPsi = self%fPsi(Xi, 3)
|
||||
f = DOT_PRODUCT(fPsi,source)
|
||||
localF = localF + f*fPsi*wTria(l)*detJ
|
||||
|
||||
END DO
|
||||
|
||||
END FUNCTION elemFTria
|
||||
END FUNCTION partialDerTria
|
||||
|
||||
PURE FUNCTION gatherEFTria(self, Xi) RESULT(array)
|
||||
IMPLICIT NONE
|
||||
|
|
@ -799,6 +743,66 @@ MODULE moduleMesh2DCart
|
|||
|
||||
END FUNCTION gatherMFTria
|
||||
|
||||
!Computes element local stiffness matrix
|
||||
PURE FUNCTION elemKTria(self, nNodes) RESULT(localK)
|
||||
IMPLICIT NONE
|
||||
|
||||
CLASS(meshCell2DCartTria), INTENT(in):: self
|
||||
INTEGER, INTENT(in):: nNodes
|
||||
REAL(8):: localK(1:nNodes,1:nNodes)
|
||||
REAL(8):: Xi(1:3)
|
||||
REAL(8):: dPsi(1:3,1:3)
|
||||
REAL(8):: pDer(1:3, 1:3)
|
||||
REAL(8):: invJ(1:3,1:3), detJ
|
||||
INTEGER:: l
|
||||
|
||||
localK=0.D0
|
||||
Xi=0.D0
|
||||
!Start 2D Gauss Quad Integral
|
||||
DO l=1, 4
|
||||
Xi(1) = Xi1Tria(l)
|
||||
Xi(2) = Xi2Tria(l)
|
||||
dPsi = self%dPsi(Xi, 3)
|
||||
pDer = self%partialDer(3, dPsi)
|
||||
detJ = self%detJac(pDer)
|
||||
invJ = self%invJac(pDer)
|
||||
localK = localK + MATMUL(TRANSPOSE(MATMUL(invJ,dPsi)),MATMUL(invJ,dPsi))*wTria(l)/detJ
|
||||
|
||||
END DO
|
||||
|
||||
END FUNCTION elemKTria
|
||||
|
||||
!Computes element local source vector
|
||||
PURE FUNCTION elemFTria(self, nNodes, source) RESULT(localF)
|
||||
IMPLICIT NONE
|
||||
|
||||
CLASS(meshCell2DCartTria), INTENT(in):: self
|
||||
INTEGER, INTENT(in):: nNodes
|
||||
REAL(8), INTENT(in):: source(1:nNodes)
|
||||
REAL(8):: localF(1:nNodes)
|
||||
REAL(8):: fPsi(1:3)
|
||||
REAL(8):: dPsi(1:3, 1:3), pDer(1:3, 1:3)
|
||||
REAL(8):: Xi(1:3)
|
||||
REAL(8):: detJ, f
|
||||
INTEGER:: l
|
||||
|
||||
localF = 0.D0
|
||||
Xi = 0.D0
|
||||
!Start 2D Gauss Quad Integral
|
||||
DO l=1, 4
|
||||
Xi(1) = Xi1Tria(l)
|
||||
Xi(2) = Xi2Tria(l)
|
||||
dPsi = self%dPsi(Xi, 3)
|
||||
pDer = self%partialDer(3, dPsi)
|
||||
detJ = self%detJac(pDer)
|
||||
fPsi = self%fPsi(Xi, 3)
|
||||
f = DOT_PRODUCT(fPsi,source)
|
||||
localF = localF + f*fPsi*wTria(l)*detJ
|
||||
|
||||
END DO
|
||||
|
||||
END FUNCTION elemFTria
|
||||
|
||||
PURE FUNCTION insideTria(Xi) RESULT(ins)
|
||||
IMPLICIT NONE
|
||||
|
||||
|
|
@ -811,18 +815,6 @@ MODULE moduleMesh2DCart
|
|||
|
||||
END FUNCTION insideTria
|
||||
|
||||
!Gets node indexes from triangular element
|
||||
PURE FUNCTION getNodesTria(self, nNodes) RESULT(n)
|
||||
IMPLICIT NONE
|
||||
|
||||
CLASS(meshCell2DCartTria), INTENT(in):: self
|
||||
INTEGER, INTENT(in):: nNodes
|
||||
INTEGER:: n(1:nNodes)
|
||||
|
||||
n = (/self%n1%n, self%n2%n, self%n3%n /)
|
||||
|
||||
END FUNCTION getNodesTria
|
||||
|
||||
!Transforms physical coordinates to element coordinates
|
||||
PURE FUNCTION phy2logTria(self,r) RESULT(Xi)
|
||||
IMPLICIT NONE
|
||||
|
|
@ -830,96 +822,94 @@ MODULE moduleMesh2DCart
|
|||
CLASS(meshCell2DCartTria), INTENT(in):: self
|
||||
REAL(8), INTENT(in):: r(1:3)
|
||||
REAL(8):: Xi(1:3)
|
||||
REAL(8):: invJ(1:3,1:3), detJ
|
||||
REAL(8):: deltaR(1:3)
|
||||
REAL(8):: dPsi(1:3,1:3)
|
||||
REAL(8):: dPsi(1:3, 1:3)
|
||||
REAL(8):: pDer(1:3, 1:3)
|
||||
REAL(8):: invJ(1:3, 1:3), detJ
|
||||
|
||||
!Direct method to convert coordinates
|
||||
Xi = 0.D0
|
||||
deltaR = (/ r(1) - self%x(1), r(2) - self%y(1), 0.D0 /)
|
||||
dPsi = self%dPsi(Xi, 3)
|
||||
invJ = self%invJac(Xi, 3, dPsi)
|
||||
detJ = self%detJac(Xi, 3, dPsi)
|
||||
pDer = self%partialDer(3, dPsi)
|
||||
invJ = self%invJac(pDer)
|
||||
detJ = self%detJac(pDer)
|
||||
Xi = MATMUL(invJ,deltaR)/detJ
|
||||
|
||||
END FUNCTION phy2logTria
|
||||
|
||||
SUBROUTINE nextElementTria(self, Xi, nextElement)
|
||||
SUBROUTINE neighbourElementTria(self, Xi, neighbourElement)
|
||||
IMPLICIT NONE
|
||||
|
||||
CLASS(meshCell2DCartTria), INTENT(in):: self
|
||||
REAL(8), INTENT(in):: Xi(1:3)
|
||||
CLASS(meshElement), POINTER, INTENT(out):: nextElement
|
||||
CLASS(meshElement), POINTER, INTENT(out):: neighbourElement
|
||||
REAL(8):: XiArray(1:3)
|
||||
INTEGER:: nextInt
|
||||
|
||||
XiArray = (/ Xi(2), 1.D0-Xi(1)-Xi(2), Xi(1) /)
|
||||
nextInt = MINLOC(XiArray,1)
|
||||
NULLIFY(nextElement)
|
||||
NULLIFY(neighbourElement)
|
||||
SELECT CASE (nextInt)
|
||||
CASE (1)
|
||||
nextElement => self%e1
|
||||
neighbourElement => self%e1
|
||||
CASE (2)
|
||||
nextElement => self%e2
|
||||
neighbourElement => self%e2
|
||||
CASE (3)
|
||||
nextElement => self%e3
|
||||
neighbourElement => self%e3
|
||||
END SELECT
|
||||
|
||||
END SUBROUTINE nextElementTria
|
||||
END SUBROUTINE neighbourElementTria
|
||||
|
||||
!Calculates area for triangular element
|
||||
PURE SUBROUTINE areaTria(self)
|
||||
IMPLICIT NONE
|
||||
|
||||
CLASS(meshCell2DCartTria), INTENT(inout):: self
|
||||
REAL(8):: Xi(1:3)
|
||||
REAL(8):: dPsi(1:3, 1:3), pDer(1:3, 1:3)
|
||||
REAL(8):: detJ
|
||||
REAL(8):: fPsi(1:3)
|
||||
|
||||
self%volume = 0.D0
|
||||
self%arNodes = 0.D0
|
||||
!2D 1 point Gauss Quad Integral
|
||||
Xi = (/ 1.D0/3.D0, 1.D0/3.D0, 0.D0 /)
|
||||
dPsi = self%dPsi(Xi, 3)
|
||||
pDer = self%partialDer(3, dPsi)
|
||||
detJ = self%detJac(pDer)
|
||||
fPsi = self%fPsi(Xi, 4)
|
||||
!Computes total volume of the cell
|
||||
self%volume = detJ
|
||||
!Computes volume per node
|
||||
self%arNodes = fPsi*detJ
|
||||
|
||||
END SUBROUTINE areaTria
|
||||
|
||||
!COMMON FUNCTIONS FOR CARTESIAN VOLUME ELEMENTS IN 2D
|
||||
!Computes element Jacobian determinant
|
||||
PURE FUNCTION detJ2DCart(self, Xi, nNodes, dPsi_in) RESULT(dJ)
|
||||
PURE FUNCTION detJ2DCart(pDer) RESULT(dJ)
|
||||
IMPLICIT NONE
|
||||
|
||||
CLASS(meshCell2DCart), INTENT(in):: self
|
||||
REAL(8), INTENT(in):: Xi(1:3)
|
||||
INTEGER, INTENT(in):: nNodes
|
||||
REAL(8), INTENT(in), OPTIONAL:: dPsi_in(1:3,1:nNodes)
|
||||
REAL(8), INTENT(in):: pDer(1:3, 1:3)
|
||||
REAL(8):: dJ
|
||||
REAL(8):: dPsi(1:3,1:nNodes)
|
||||
REAL(8):: dx(1:2), dy(1:2)
|
||||
|
||||
IF(PRESENT(dPsi_in)) THEN
|
||||
dPsi = dPsi_in
|
||||
|
||||
ELSE
|
||||
dPsi = self%dPsi(Xi, 4)
|
||||
|
||||
END IF
|
||||
|
||||
CALL self%partialDer(nNodes, dPsi, dx, dy)
|
||||
|
||||
dJ = dx(1)*dy(2)-dx(2)*dy(1)
|
||||
dJ = pDer(1,1)*pDer(2,2)-pDer(1,2)*pDer(2,1)
|
||||
|
||||
END FUNCTION detJ2DCart
|
||||
|
||||
!Computes element Jacobian inverse matrix (without determinant)
|
||||
PURE FUNCTION invJ2DCart(self, Xi, nNodes, dPsi_in) RESULT(invJ)
|
||||
PURE FUNCTION invJ2DCart(pDer) RESULT(invJ)
|
||||
IMPLICIT NONE
|
||||
|
||||
CLASS(meshCell2DCart), INTENT(in):: self
|
||||
REAL(8), INTENT(in):: Xi(1:3)
|
||||
INTEGER, INTENT(in):: nNodes
|
||||
REAL(8), INTENT(in), OPTIONAL:: dPsi_in(1:3,1:nNodes)
|
||||
REAL(8), INTENT(in):: pDer(1:3, 1:3)
|
||||
REAL(8):: invJ(1:3,1:3)
|
||||
REAL(8):: dPsi(1:3,1:nNodes)
|
||||
REAL(8):: dx(1:2), dy(1:2)
|
||||
|
||||
IF(PRESENT(dPsi_in)) THEN
|
||||
dPsi=dPsi_in
|
||||
|
||||
ELSE
|
||||
dPsi = self%dPsi(Xi, 4)
|
||||
|
||||
END IF
|
||||
|
||||
invJ = 0.D0
|
||||
|
||||
CALL self%partialDer(nNodes, dPsi, dx, dy)
|
||||
|
||||
invJ(1,1:2) = (/ dy(2), -dx(2) /)
|
||||
invJ(2,1:2) = (/ -dy(1), dx(1) /)
|
||||
invJ(1, 1:2) = (/ pDer(2,2), -pDer(1,2) /)
|
||||
invJ(2, 1:2) = (/ -pDer(2,1), pDer(1,1) /)
|
||||
invJ(3, 3) = 1.D0
|
||||
|
||||
END FUNCTION invJ2DCart
|
||||
|
||||
|
|
|
|||
|
|
@ -67,7 +67,7 @@ MODULE moduleMesh2DCyl
|
|||
PROCEDURE, PASS:: phy2log => phy2logQuad
|
||||
PROCEDURE, PASS:: neighbourElement => neighbourElementQuad
|
||||
!PARTICLUAR PROCEDURES
|
||||
PROCEDURE, PASS:: area => areaQuad
|
||||
PROCEDURE, PASS, PRIVATE:: area => areaQuad
|
||||
|
||||
END TYPE meshCell2DCylQuad
|
||||
|
||||
|
|
@ -99,7 +99,7 @@ MODULE moduleMesh2DCyl
|
|||
PROCEDURE, PASS:: phy2log => phy2logTria
|
||||
PROCEDURE, PASS:: neighbourElement => neighbourElementTria
|
||||
!PARTICULAR PROCEDURES
|
||||
PROCEDURE, PASS:: area => areaTria
|
||||
PROCEDURE, PASS, PRIVATE:: area => areaTria
|
||||
|
||||
END TYPE meshCell2DCylTria
|
||||
|
||||
|
|
@ -256,8 +256,13 @@ MODULE moduleMesh2DCyl
|
|||
TYPE(meshNodeCont), INTENT(in), TARGET:: nodes(:)
|
||||
REAL(8), DIMENSION(1:3):: r1, r2, r3, r4
|
||||
|
||||
!Assign node index
|
||||
self%n = n
|
||||
|
||||
!Assign number of nodes of cell
|
||||
self%nNodes = SIZE(p)
|
||||
|
||||
!Assign nodes to element
|
||||
self%n1 => nodes(p(1))%obj
|
||||
self%n2 => nodes(p(2))%obj
|
||||
self%n3 => nodes(p(3))%obj
|
||||
|
|
@ -428,7 +433,7 @@ MODULE moduleMesh2DCyl
|
|||
INTEGER, INTENT(in):: nNodes
|
||||
REAL(8):: localK(1:nNodes,1:nNodes)
|
||||
REAL(8):: Xi(1:3)
|
||||
REAL(8):: fPsi(1:4), dPsi(1:3, 1:4)
|
||||
REAL(8):: dPsi(1:3, 1:4)
|
||||
REAL(8):: pDer(1:3, 1:3)
|
||||
REAL(8):: r
|
||||
REAL(8):: invJ(1:3,1:3), detJ
|
||||
|
|
@ -445,8 +450,7 @@ MODULE moduleMesh2DCyl
|
|||
pDer = self%partialDer(4, dPsi)
|
||||
detJ = self%detJac(pDer)
|
||||
invJ = self%invJac(pDer)
|
||||
fPsi = self%fPsi(Xi, 4)
|
||||
r = DOT_PRODUCT(fPsi,self%r)
|
||||
r = self%gatherF(Xi, 4, self%r)
|
||||
localK = localK + MATMUL(TRANSPOSE(MATMUL(invJ,dPsi)), &
|
||||
MATMUL(invJ,dPsi))* &
|
||||
r*wQuad(l)*wQuad(m)/detJ
|
||||
|
|
@ -467,7 +471,8 @@ MODULE moduleMesh2DCyl
|
|||
REAL(8), INTENT(in):: source(1:nNodes)
|
||||
REAL(8):: localF(1:nNodes)
|
||||
REAL(8):: Xi(1:3)
|
||||
REAL(8):: fPsi(1:4), dPsi(1:3, 1:4)
|
||||
REAL(8):: fPsi(1:4)
|
||||
REAL(8):: dPsi(1:3, 1:4)
|
||||
REAL(8):: pDer(1:3, 1:3)
|
||||
REAL(8):: r
|
||||
REAL(8):: detJ, f
|
||||
|
|
@ -483,7 +488,7 @@ MODULE moduleMesh2DCyl
|
|||
pDer = self%partialDer(4, dPsi)
|
||||
detJ = self%detJac(pDer)
|
||||
fPsi = self%fPsi(Xi, 4)
|
||||
r = DOT_PRODUCT(fPsi,self%r)
|
||||
r = DOT_PRODUCT(fPsi, self%r)
|
||||
f = DOT_PRODUCT(fPsi,source)
|
||||
localF = localF + r*f*fPsi*wQuad(l)*wQuad(m)*detJ
|
||||
|
||||
|
|
@ -539,7 +544,7 @@ MODULE moduleMesh2DCyl
|
|||
|
||||
END FUNCTION phy2logQuad
|
||||
|
||||
!Gets the next element for a logical position Xi
|
||||
!Get the next element for a logical position Xi
|
||||
SUBROUTINE neighbourElementQuad(self, Xi, neighbourElement)
|
||||
IMPLICIT NONE
|
||||
|
||||
|
|
@ -572,7 +577,8 @@ MODULE moduleMesh2DCyl
|
|||
IMPLICIT NONE
|
||||
|
||||
CLASS(meshCell2DCylQuad), INTENT(inout):: self
|
||||
REAL(8):: r, Xi(1:3)
|
||||
REAL(8):: Xi(1:3)
|
||||
REAL(8):: r
|
||||
REAL(8):: detJ
|
||||
REAL(8):: fPsi(1:4)
|
||||
REAL(8):: dPsi(1:3, 1:4), pDer(1:3, 1:3)
|
||||
|
|
@ -583,24 +589,24 @@ MODULE moduleMesh2DCyl
|
|||
Xi = 0.D0
|
||||
dPsi = self%dPsi(Xi, 4)
|
||||
pDer = self%partialDer(4, dPsi)
|
||||
detJ = self%detJac(pDer)*PI8 !4*2*pi
|
||||
detJ = self%detJac(pDer)
|
||||
fPsi = self%fPsi(Xi, 4)
|
||||
!Computes total volume of the cell
|
||||
r = DOT_PRODUCT(fPsi,self%r)
|
||||
self%volume = r*detJ
|
||||
self%volume = r*detJ*PI8 !4*2*pi
|
||||
!Computes volume per node
|
||||
Xi = (/-5.D-1, -5.D-1, 0.D0/)
|
||||
r = self%gatherF(Xi, 4, self%r)
|
||||
self%arNodes(1) = fPsi(1)*r*detJ
|
||||
self%arNodes(1) = fPsi(1)*self%volume
|
||||
Xi = (/ 5.D-1, -5.D-1, 0.D0/)
|
||||
r = self%gatherF(Xi, 4, self%r)
|
||||
self%arNodes(2) = fPsi(2)*r*detJ
|
||||
self%arNodes(2) = fPsi(2)*self%volume
|
||||
Xi = (/ 5.D-1, 5.D-1, 0.D0/)
|
||||
r = self%gatherF(Xi, 4, self%r)
|
||||
self%arNodes(3) = fPsi(3)*r*detJ
|
||||
self%arNodes(3) = fPsi(3)*self%volume
|
||||
Xi = (/-5.D-1, 5.D-1, 0.D0/)
|
||||
r = self%gatherF(Xi, 4, self%r)
|
||||
self%arNodes(4) = fPsi(4)*r*detJ
|
||||
self%arNodes(4) = fPsi(4)*self%volume
|
||||
|
||||
END SUBROUTINE areaQuad
|
||||
|
||||
|
|
@ -619,7 +625,7 @@ MODULE moduleMesh2DCyl
|
|||
!Assign node index
|
||||
self%n = n
|
||||
|
||||
!Assign nomber of nodes to cell
|
||||
!Assign number of nodes of cell
|
||||
self%nNodes = SIZE(p)
|
||||
|
||||
!Assign nodes to element
|
||||
|
|
@ -736,7 +742,7 @@ MODULE moduleMesh2DCyl
|
|||
self%n2%emData%phi, &
|
||||
self%n3%emData%phi /)
|
||||
|
||||
array = -self%gatherDF(Xi, 4, phi)
|
||||
array = -self%gatherDF(Xi, 3, phi)
|
||||
|
||||
END FUNCTION gatherEFTria
|
||||
|
||||
|
|
@ -772,8 +778,8 @@ MODULE moduleMesh2DCyl
|
|||
INTEGER, INTENT(in):: nNodes
|
||||
REAL(8):: localK(1:nNodes,1:nNodes)
|
||||
REAL(8):: Xi(1:3)
|
||||
REAL(8):: dPsi(1:3,1:3)
|
||||
REAL(8):: r
|
||||
REAL(8):: fPsi(1:3), dPsi(1:3,1:3)
|
||||
REAL(8):: pDer(1:3, 1:3)
|
||||
REAL(8):: invJ(1:3,1:3), detJ
|
||||
INTEGER:: l
|
||||
|
|
@ -788,8 +794,7 @@ MODULE moduleMesh2DCyl
|
|||
pDer = self%partialDer(3, dPsi)
|
||||
detJ = self%detJac(pDer)
|
||||
invJ = self%invJac(pDer)
|
||||
fPsi = self%fPsi(Xi, 3)
|
||||
r = DOT_PRODUCT(fPsi,self%r)
|
||||
r = self%gatherF(Xi, 3, self%r)
|
||||
localK = localK + MATMUL(TRANSPOSE(MATMUL(invJ,dPsi)),MATMUL(invJ,dPsi))*r*wTria(l)/detJ
|
||||
|
||||
END DO
|
||||
|
|
@ -809,22 +814,23 @@ MODULE moduleMesh2DCyl
|
|||
REAL(8):: fPsi(1:3)
|
||||
REAL(8):: dPsi(1:3, 1:3), pDer(1:3, 1:3)
|
||||
REAL(8):: Xi(1:3)
|
||||
REAL(8):: r
|
||||
REAL(8):: detJ, f
|
||||
REAL(8):: r
|
||||
INTEGER:: l
|
||||
|
||||
localF = 0.D0
|
||||
Xi = 0.D0
|
||||
|
||||
Xi = 0.D0
|
||||
!Start 2D Gauss Quad Integral
|
||||
DO l=1, 4
|
||||
DO l = 1, 4
|
||||
Xi(1) = Xi1Tria(l)
|
||||
Xi(2) = Xi2Tria(l)
|
||||
dPsi = self%dPsi(Xi, 3)
|
||||
pDer = self%partialDer(3, dPsi)
|
||||
detJ = self%detJac(pDer)
|
||||
fPsi = self%fPsi(Xi, 3)
|
||||
r = DOT_PRODUCT(fPsi,self%r)
|
||||
f = DOT_PRODUCT(fPsi,source)
|
||||
r = DOT_PRODUCT(fPsi, self%r)
|
||||
f = DOT_PRODUCT(fPsi, source)
|
||||
localF = localF + r*f*fPsi*wTria(l)*detJ
|
||||
|
||||
END DO
|
||||
|
|
@ -897,10 +903,10 @@ MODULE moduleMesh2DCyl
|
|||
|
||||
CLASS(meshCell2DCylTria), INTENT(inout):: self
|
||||
REAL(8):: Xi(1:3)
|
||||
REAL(8):: r
|
||||
REAL(8):: dPsi(1:3, 1:3), pDer(1:3, 1:3)
|
||||
REAL(8):: detJ
|
||||
REAL(8):: fPsi(1:3)
|
||||
REAL(8):: r
|
||||
|
||||
self%volume = 0.D0
|
||||
self%arNodes = 0.D0
|
||||
|
|
@ -908,13 +914,13 @@ MODULE moduleMesh2DCyl
|
|||
Xi = (/ 1.D0/3.D0, 1.D0/3.D0, 0.D0 /)
|
||||
dPsi = self%dPsi(Xi, 3)
|
||||
pDer = self%partialDer(3, dPsi)
|
||||
detJ = self%detJac(pDer)*PI !2PI*1/2
|
||||
fPsi = self%fPsi(Xi, 4)
|
||||
detJ = self%detJac(pDer)
|
||||
fPsi = self%fPsi(Xi, 3)
|
||||
!Computes total volume of the cell
|
||||
r = DOT_PRODUCT(fPsi,self%r)
|
||||
self%volume = r*detJ
|
||||
r = DOT_PRODUCT(fPsi, self%r)
|
||||
self%volume = r*detJ*PI !2PI*1/2
|
||||
!Computes volume per node
|
||||
self%arNodes = fPsi*r*detJ
|
||||
self%arNodes = fPsi*self%volume
|
||||
|
||||
END SUBROUTINE areaTria
|
||||
|
||||
|
|
@ -939,9 +945,9 @@ MODULE moduleMesh2DCyl
|
|||
|
||||
invJ = 0.D0
|
||||
|
||||
invJ(1,1:2) = (/ pDer(2,2), -pDer(1,2) /)
|
||||
invJ(2,1:2) = (/ -pDer(2,1), pDer(1,1) /)
|
||||
invJ(3,3) = 1.D0
|
||||
invJ(1, 1:2) = (/ pDer(2,2), -pDer(1,2) /)
|
||||
invJ(2, 1:2) = (/ -pDer(2,1), pDer(1,1) /)
|
||||
invJ(3, 3) = 1.D0
|
||||
|
||||
END FUNCTION invJ2DCyl
|
||||
|
||||
|
|
|
|||
|
|
@ -30,7 +30,7 @@ MODULE moduleMesh3DCart
|
|||
PROCEDURE, PASS:: intersection => intersection3DCartTria
|
||||
PROCEDURE, PASS:: randPos => randPosEdgeTria
|
||||
!PARTICULAR PROCEDURES
|
||||
PROCEDURE, NOPASS:: fPsi => fPsiEdgeTria
|
||||
PROCEDURE, NOPASS, PRIVATE:: fPsi => fPsiEdgeTria
|
||||
|
||||
END TYPE meshEdge3DCartTria
|
||||
|
||||
|
|
@ -60,7 +60,7 @@ MODULE moduleMesh3DCart
|
|||
PROCEDURE, PASS:: phy2log => phy2logTetra
|
||||
PROCEDURE, PASS:: neighbourElement => neighbourElementTetra
|
||||
!PARTICULAR PROCEDURES
|
||||
PROCEDURE, PASS:: calcVol => volumeTetra
|
||||
PROCEDURE, PASS, PRIVATE:: calcVol => volumeTetra
|
||||
|
||||
END TYPE meshCell3DCartTetra
|
||||
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue