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:
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ba272de4e3
commit
7b7a5c45ca
6 changed files with 788 additions and 837 deletions
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@ -19,7 +19,8 @@ MODULE moduleMesh2DCart
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!Element coordinates
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REAL(8):: x = 0.D0, y = 0.D0
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CONTAINS
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PROCEDURE, PASS:: init => initNode2DCart
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!meshNode DEFERRED PROCEDURES
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PROCEDURE, PASS:: init => initNode2DCart
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PROCEDURE, PASS:: getCoordinates => getCoord2DCart
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END TYPE meshNode2DCart
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@ -30,35 +31,16 @@ MODULE moduleMesh2DCart
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!Connectivity to nodes
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CLASS(meshNode), POINTER:: n1 => NULL(), n2 => NULL()
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CONTAINS
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PROCEDURE, PASS:: init => initEdge2DCart
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PROCEDURE, PASS:: getNodes => getNodes2DCart
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!meshEdge DEFERRED PROCEDURES
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PROCEDURE, PASS:: init => initEdge2DCart
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PROCEDURE, PASS:: getNodes => getNodes2DCart
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PROCEDURE, PASS:: intersection => intersection2DCartEdge
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PROCEDURE, PASS:: randPos => randPosEdge
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PROCEDURE, PASS:: randPos => randPosEdge
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END TYPE meshEdge2DCart
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TYPE, PUBLIC, ABSTRACT, EXTENDS(meshCell):: meshCell2DCart
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CONTAINS
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PROCEDURE, PASS:: detJac => detJ2DCart
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PROCEDURE, PASS:: invJac => invJ2DCart
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PROCEDURE(partialDer_interface), DEFERRED, PASS, PRIVATE:: partialDer
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END TYPE meshCell2DCart
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ABSTRACT INTERFACE
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PURE SUBROUTINE partialDer_interface(self, nNodes, dPsi, dx, dy)
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IMPORT meshCell2DCart
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CLASS(meshCell2DCart), 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(1:2):: dx, dy
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END SUBROUTINE partialDer_interface
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END INTERFACE
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!Quadrilateral volume element
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TYPE, PUBLIC, EXTENDS(meshCell2DCart):: meshCell2DCartQuad
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TYPE, PUBLIC, EXTENDS(meshCell):: meshCell2DCartQuad
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!Element coordinates
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REAL(8):: x(1:4) = 0.D0, y(1:4) = 0.D0
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!Connectivity to nodes
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@ -68,25 +50,29 @@ MODULE moduleMesh2DCart
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REAL(8):: arNodes(1:4) = 0.D0
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CONTAINS
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PROCEDURE, PASS:: init => initCellQuad2DCart
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PROCEDURE, PASS:: randPos => randPosCellQuad
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PROCEDURE, PASS:: area => areaQuad
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PROCEDURE, PASS:: fPsi => fPsiQuad
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PROCEDURE, PASS:: dPsi => dPsiQuad
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PROCEDURE, PASS, PRIVATE:: partialDer => partialDerQuad
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PROCEDURE, PASS:: elemK => elemKQuad
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PROCEDURE, PASS:: elemF => elemFQuad
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PROCEDURE, PASS:: gatherElectricField => gatherEFQuad
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PROCEDURE, PASS:: gatherMagneticField => gatherMFQuad
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PROCEDURE, NOPASS:: inside => insideQuad
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PROCEDURE, PASS:: getNodes => getNodesQuad
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PROCEDURE, PASS:: phy2log => phy2logQuad
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PROCEDURE, PASS:: nextElement => nextElementQuad
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!meshCell DEFERRED PROCEDURES
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PROCEDURE, PASS:: init => initCellQuad2DCart
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PROCEDURE, PASS:: getNodes => getNodesQuad
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PROCEDURE, PASS:: randPos => randPosCellQuad
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PROCEDURE, NOPASS:: fPsi => fPsiQuad
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PROCEDURE, NOPASS:: dPsi => dPsiQuad
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PROCEDURE, PASS:: partialDer => partialDerQuad
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PROCEDURE, NOPASS:: detJac => detJ2DCart
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PROCEDURE, NOPASS:: invJac => invJ2DCart
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PROCEDURE, PASS:: gatherElectricField => gatherEFQuad
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PROCEDURE, PASS:: gatherMagneticField => gatherMFQuad
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PROCEDURE, PASS:: elemK => elemKQuad
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PROCEDURE, PASS:: elemF => elemFQuad
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PROCEDURE, NOPASS:: inside => insideQuad
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PROCEDURE, PASS:: phy2log => phy2logQuad
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PROCEDURE, PASS:: neighbourElement => neighbourElementQuad
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!PARTICLUAR PROCEDURES
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PROCEDURE, PASS, PRIVATE:: area => areaQuad
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END TYPE meshCell2DCartQuad
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!Triangular volume element
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TYPE, PUBLIC, EXTENDS(meshCell2DCart):: meshCell2DCartTria
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TYPE, PUBLIC, EXTENDS(meshCell):: meshCell2DCartTria
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!Element coordinates
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REAL(8):: x(1:3) = 0.D0, y(1:3) = 0.D0
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!Connectivity to nodes
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@ -96,20 +82,24 @@ MODULE moduleMesh2DCart
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REAL(8):: arNodes(1:3) = 0.D0
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CONTAINS
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PROCEDURE, PASS:: init => initCellTria2DCart
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PROCEDURE, PASS:: randPos => randPosCellTria
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PROCEDURE, PASS:: area => areaTria
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PROCEDURE, PASS:: fPsi => fPsiTria
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PROCEDURE, PASS:: dPsi => dPsiTria
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PROCEDURE, PASS, PRIVATE:: partialDer => partialDerTria
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PROCEDURE, PASS:: elemK => elemKTria
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PROCEDURE, PASS:: elemF => elemFTria
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PROCEDURE, PASS:: gatherElectricField => gatherEFTria
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PROCEDURE, PASS:: gatherMagneticField => gatherMFTria
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PROCEDURE, NOPASS:: inside => insideTria
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PROCEDURE, PASS:: getNodes => getNodesTria
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PROCEDURE, PASS:: phy2log => phy2logTria
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PROCEDURE, PASS:: nextElement => nextElementTria
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!meshCell DEFERRED PROCEDURES
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PROCEDURE, PASS:: init => initCellTria2DCart
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PROCEDURE, PASS:: getNodes => getNodesTria
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PROCEDURE, PASS:: randPos => randPosCellTria
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PROCEDURE, NOPASS:: fPsi => fPsiTria
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PROCEDURE, NOPASS:: dPsi => dPsiTria
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PROCEDURE, PASS:: partialDer => partialDerTria
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PROCEDURE, NOPASS:: detJac => detJ2DCart
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PROCEDURE, NOPASS:: invJac => invJ2DCart
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PROCEDURE, PASS:: gatherElectricField => gatherEFTria
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PROCEDURE, PASS:: gatherMagneticField => gatherMFTria
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PROCEDURE, PASS:: elemK => elemKTria
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PROCEDURE, PASS:: elemF => elemFTria
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PROCEDURE, NOPASS:: inside => insideTria
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PROCEDURE, PASS:: phy2log => phy2logTria
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PROCEDURE, PASS:: neighbourElement => neighbourElementTria
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!PARTICULAR PROCEDURES
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PROCEDURE, PASS, PRIVATE:: area => areaTria
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END TYPE meshCell2DCartTria
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@ -175,6 +165,7 @@ MODULE moduleMesh2DCart
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r2 = self%n2%getCoordinates()
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self%x = (/r1(1), r2(1)/)
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self%y = (/r1(2), r2(2)/)
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self%weight = 1.D0
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!Normal vector
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self%normal = (/ -(self%y(2)-self%y(1)), &
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self%x(2)-self%x(1) , &
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@ -290,84 +281,17 @@ MODULE moduleMesh2DCart
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END SUBROUTINE initCellQuad2DCart
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!Computes element area
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PURE SUBROUTINE areaQuad(self)
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IMPLICIT NONE
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CLASS(meshCell2DCartQuad), INTENT(inout):: self
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REAL(8):: Xi(1:3)
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REAL(8):: detJ
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REAL(8):: fPsi(1:4)
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self%volume = 0.D0
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self%arNodes = 0.D0
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!2D 1 point Gauss Quad Integral
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Xi = 0.D0
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detJ = self%detJac(Xi, 4)*4.D0 !4
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fPsi = self%fPsi(Xi, 4)
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self%volume = detJ
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self%arNodes = fPsi*detJ
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END SUBROUTINE areaQuad
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!Computes element functions in point Xi
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PURE FUNCTION fPsiQuad(self, Xi, nNodes) RESULT(fPsi)
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IMPLICIT NONE
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CLASS(meshCell2DCartQuad), 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)) * (1.D0-Xi(2))
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fPsi(2) = (1.D0+Xi(1)) * (1.D0-Xi(2))
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fPsi(3) = (1.D0+Xi(1)) * (1.D0+Xi(2))
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fPsi(4) = (1.D0-Xi(1)) * (1.D0+Xi(2))
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fPsi = fPsi*0.25D0
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END FUNCTION fPsiQuad
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!Derivative element function at coordinates Xi
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PURE FUNCTION dPsiQuad(self, Xi, nNodes) RESULT(dPsi)
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IMPLICIT NONE
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CLASS(meshCell2DCartQuad), 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.D0 - Xi(2)), &
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(1.D0 - Xi(2)), &
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(1.D0 + Xi(2)), &
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-(1.D0 + Xi(2)) /)
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dPsi(2,:) = (/ -(1.D0 - Xi(1)), &
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-(1.D0 + Xi(1)), &
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(1.D0 + Xi(1)), &
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(1.D0 - Xi(1)) /)
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dPsi = dPsi * 0.25D0
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END FUNCTION dPsiQuad
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!Partial derivative in global coordinates
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PURE SUBROUTINE partialDerQuad(self, nNodes, dPsi, dx, dy)
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!Get nodes from quadrilateral element
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PURE FUNCTION getNodesQuad(self, nNodes) RESULT(n)
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IMPLICIT NONE
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CLASS(meshCell2DCartQuad), 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(1:2):: dx, dy
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INTEGER:: n(1:nNodes)
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dx = (/ DOT_PRODUCT(dPsi(1,1:4),self%x(1:4)), &
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DOT_PRODUCT(dPsi(2,1:4),self%x(1:4)) /)
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dy = (/ DOT_PRODUCT(dPsi(1,1:4),self%y(1:4)), &
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DOT_PRODUCT(dPsi(2,1:4),self%y(1:4)) /)
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n = (/ self%n1%n, self%n2%n, self%n3%n, self%n4%n /)
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END SUBROUTINE partialDerQuad
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END FUNCTION getNodesQuad
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!Random position in quadrilateral volume
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FUNCTION randPosCellQuad(self) RESULT(r)
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@ -379,78 +303,77 @@ MODULE moduleMesh2DCart
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REAL(8):: Xi(1:3)
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REAL(8):: fPsi(1:4)
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Xi = 0.D0
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Xi(1) = random(-1.D0, 1.D0)
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Xi(2) = random(-1.D0, 1.D0)
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Xi(3) = 0.D0
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fPsi = self%fPsi(Xi, 4)
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r = 0.D0
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r(1) = DOT_PRODUCT(fPsi, self%x)
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r(2) = DOT_PRODUCT(fPsi, self%y)
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r(3) = 0.D0
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END FUNCTION randPosCellQuad
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!Computes element local stiffness matrix
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PURE FUNCTION elemKQuad(self, nNodes) RESULT(localK)
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!Computes element functions in point Xi
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PURE FUNCTION fPsiQuad(Xi, nNodes) RESULT(fPsi)
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IMPLICIT NONE
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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.D0-Xi(1)) * (1.D0-Xi(2)), &
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(1.D0+Xi(1)) * (1.D0-Xi(2)), &
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(1.D0+Xi(1)) * (1.D0+Xi(2)), &
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(1.D0-Xi(1)) * (1.D0+Xi(2)) /)
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fPsi = fPsi * 0.25D0
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END FUNCTION fPsiQuad
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!Derivative element function at coordinates Xi
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PURE FUNCTION dPsiQuad(Xi, nNodes) RESULT(dPsi)
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IMPLICIT NONE
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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, 1:4) = (/ -(1.D0 - Xi(2)), &
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(1.D0 - Xi(2)), &
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(1.D0 + Xi(2)), &
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-(1.D0 + Xi(2)) /)
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dPsi(2, 1:4) = (/ -(1.D0 - Xi(1)), &
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-(1.D0 + Xi(1)), &
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(1.D0 + Xi(1)), &
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(1.D0 - Xi(1)) /)
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dPsi = dPsi * 0.25D0
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END FUNCTION dPsiQuad
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!Partial derivative in global coordinates
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PURE FUNCTION partialDerQuad(self, nNodes, dPsi) RESULT(pDer)
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IMPLICIT NONE
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CLASS(meshCell2DCartQuad), 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):: fPsi(1:4), dPsi(1:3,1:4)
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REAL(8):: invJ(1:3,1:3), detJ
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INTEGER:: l, m
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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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localK=0.D0
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Xi=0.D0
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!Start 2D Gauss Quad Integral
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DO l=1, 3
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Xi(2) = corQuad(l)
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DO m = 1, 3
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Xi(1) = corQuad(m)
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fPsi = self%fPsi(Xi, 4)
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dPsi = self%dPsi(Xi, 4)
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detJ = self%detJac(Xi, 4, dPsi)
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invJ = self%invJac(Xi, 4, dPsi)
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localK = localK + MATMUL(TRANSPOSE(MATMUL(invJ,dPsi)), &
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MATMUL(invJ,dPsi))* &
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wQuad(l)*wQuad(m)/detJ
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pDer = 0.D0
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END DO
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END DO
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pDer(1, 1:2) = (/ DOT_PRODUCT(dPsi(1,1:4),self%x(1:4)), &
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DOT_PRODUCT(dPsi(2,1:4),self%x(1:4)) /)
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pDer(2, 1:2) = (/ DOT_PRODUCT(dPsi(1,1:4),self%y(1:4)), &
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DOT_PRODUCT(dPsi(2,1:4),self%y(1:4)) /)
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pDer(3,3) = 1.D0
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END FUNCTION elemKQuad
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!Computes the local source vector for a force f
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PURE FUNCTION elemFQuad(self, nNodes, source) RESULT(localF)
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IMPLICIT NONE
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CLASS(meshCell2DCartQuad), 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):: Xi(1:3)
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REAL(8):: fPsi(1:4)
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REAL(8):: detJ, f
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INTEGER:: l, m
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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) = corQuad(l)
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DO m = 1, 3
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Xi(2) = corQuad(m)
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detJ = self%detJac(Xi, 4)
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fPsi = self%fPsi(Xi, 4)
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f = DOT_PRODUCT(fPsi,source)
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localF = localF + f*fPsi*wQuad(l)*wQuad(m)*detJ
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END DO
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END DO
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END FUNCTION elemFQuad
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END FUNCTION partialDerQuad
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PURE FUNCTION gatherEFQuad(self, Xi) RESULT(array)
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IMPLICIT NONE
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@ -494,6 +417,75 @@ MODULE moduleMesh2DCart
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END FUNCTION gatherMFQuad
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!Computes element local stiffness matrix
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PURE FUNCTION elemKQuad(self, nNodes) RESULT(localK)
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IMPLICIT NONE
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CLASS(meshCell2DCartQuad), 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, 1:4)
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REAL(8):: pDer(1:3, 1:3)
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REAL(8):: r
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REAL(8):: invJ(1:3,1:3), detJ
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INTEGER:: l, m
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localK = 0.D0
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Xi = 0.D0
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!Start 2D Gauss Quad Integral
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DO l = 1, 3
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Xi(2) = corQuad(l)
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DO m = 1, 3
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Xi(1) = corQuad(m)
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dPsi = self%dPsi(Xi, 4)
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pDer = self%partialDer(4, dPsi)
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detJ = self%detJac(pDer)
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invJ = self%invJac(pDer)
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localK = localK + MATMUL(TRANSPOSE(MATMUL(invJ,dPsi)), &
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MATMUL(invJ,dPsi))* &
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wQuad(l)*wQuad(m)/detJ
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END DO
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END DO
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END FUNCTION elemKQuad
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!Computes the local source vector for a force f
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PURE FUNCTION elemFQuad(self, nNodes, source) RESULT(localF)
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IMPLICIT NONE
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CLASS(meshCell2DCartQuad), INTENT(in):: self
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INTEGER, INTENT(in):: nNodes
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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
|
||||
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue