Files renamed and makefile make compatible with ifort.

This commit is contained in:
Jorge Gonzalez 2020-12-10 19:25:17 +01:00
commit af74205932
25 changed files with 5439 additions and 0 deletions

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!moduleMesh1D: 1D cartesian module
! x == x
! y == unused
! z == unused
MODULE moduleMesh1D
USE moduleMesh
IMPLICIT NONE
TYPE, PUBLIC, EXTENDS(meshNode):: meshNode1D
!Element coordinates
REAL(8):: x = 0.D0
CONTAINS
PROCEDURE, PASS:: init => initNode1D
PROCEDURE, PASS:: getCoordinates => getCoord1D
END TYPE meshNode1D
TYPE, PUBLIC, ABSTRACT, EXTENDS(meshEdge):: meshEdge1D
!Element coordinates
REAL(8):: x = 0.D0
!Connectivity to nodes
CLASS(meshNode), POINTER:: n1 => NULL()
CONTAINS
PROCEDURE, PASS:: init => initEdge1D
PROCEDURE, PASS:: getNodes => getNodes1D
PROCEDURE, PASS:: randPos => randPos1D
END TYPE meshEdge1D
TYPE, PUBLIC, ABSTRACT, EXTENDS(meshVol):: meshVol1D
CONTAINS
PROCEDURE, PASS:: detJac => detJ1D
PROCEDURE, PASS:: invJac => invJ1D
PROCEDURE(fPsi_interface), DEFERRED, NOPASS:: fPsi
PROCEDURE(dPsi_interface), DEFERRED, NOPASS:: dPsi
PROCEDURE(partialDer_interface), DEFERRED, PASS:: partialDer
END TYPE meshVol1D
ABSTRACT INTERFACE
PURE FUNCTION fPsi_interface(xi) RESULT(fPsi)
REAL(8), INTENT(in):: xi(1:3)
REAL(8), ALLOCATABLE:: fPsi(:)
END FUNCTION fPsi_interface
PURE FUNCTION dPsi_interface(xi) RESULT(dPsi)
REAL(8), INTENT(in):: xi(1:3)
REAL(8), ALLOCATABLE:: dPsi(:,:)
END FUNCTION dPsi_interface
PURE SUBROUTINE partialDer_interface(self, dPsi, dx)
IMPORT meshVol1D
CLASS(meshVol1D), INTENT(in):: self
REAL(8), INTENT(in):: dPsi(1:,1:)
REAL(8), INTENT(out), DIMENSION(1):: dx
END SUBROUTINE partialDer_interface
END INTERFACE
TYPE, PUBLIC, EXTENDS(meshVol1D):: meshVol1DSegm
!Element coordinates
REAL(8):: x(1:2)
!Connectivity to nodes
CLASS(meshNode), POINTER:: n1 => NULL(), n2 => NULL()
!Connectivity to adjacent elements
CLASS(*), POINTER:: e1 => NULL(), e2 => NULL()
REAL(8):: arNodes(1:2)
CONTAINS
PROCEDURE, PASS:: init => initVol1DSegm
PROCEDURE, PASS:: area => areaSegm
PROCEDURE, NOPASS:: fPsi => fPsiSegm
PROCEDURE, NOPASS:: dPsi => dPsiSegm
PROCEDURE, PASS:: partialDer => partialDerSegm
PROCEDURE, PASS:: elemK => elemKSegm
PROCEDURE, PASS:: elemF => elemFSegm
PROCEDURE, NOPASS:: weight => weightSegm
PROCEDURE, NOPASS:: inside => insideSegm
PROCEDURE, PASS:: scatter => scatterSegm
PROCEDURE, PASS:: gatherEF => gatherEFSegm
PROCEDURE, PASS:: getNodes => getNodesSegm
PROCEDURE, PASS:: phy2log => phy2logSegm
PROCEDURE, PASS:: nextElement => nextElementSegm
PROCEDURE, PASS:: resetOutput => resetOutputSegm
END TYPE meshVol1DSegm
CONTAINS
!NODE FUNCTIONS
!Init node element
SUBROUTINE initNode1D(self, n, r)
USE moduleSpecies
USE moduleRefParam
IMPLICIT NONE
CLASS(meshNode1D), INTENT(out):: self
INTEGER, INTENT(in):: n
REAL(8), INTENT(in):: r(1:3)
self%n = n
self%x = r(1)/L_ref
!Node volume, to be determined in mesh
self%v = 0.D0
!Allocates output
ALLOCATE(self%output(1:nSpecies))
END SUBROUTINE initNode1D
PURE FUNCTION getCoord1D(self) RESULT(r)
IMPLICIT NONE
CLASS(meshNode1D), INTENT(in):: self
REAL(8):: r(1:3)
r = (/ self%x, 0.D0, 0.D0 /)
END FUNCTION getCoord1D
!EDGE FUNCTIONS
!Inits edge element
SUBROUTINE initEdge1D(self, n, p, bt, physicalSurface)
IMPLICIT NONE
CLASS(meshEdge1D), INTENT(out):: self
INTEGER, INTENT(in):: n
INTEGER, INTENT(in):: p(:)
INTEGER, INTENT(in):: bt
INTEGER, INTENT(in):: physicalSurface
REAL(8), DIMENSION(1:3):: r1
self%n = n
self%n1 => mesh%nodes(p(1))%obj
!Get element coordinates
r1 = self%n1%getCoordinates()
self%x = r1(1)
self%normal = (/ 1.D0, 0.D0, 0.D0 /)
!Boundary index
self%bt = bt
!Physical Surface
self%physicalSurface = physicalSurface
END SUBROUTINE initEdge1D
!Get nodes from edge
PURE FUNCTION getNodes1D(self) RESULT(n)
IMPLICIT NONE
CLASS(meshEdge1D), INTENT(in):: self
INTEGER, ALLOCATABLE:: n(:)
ALLOCATE(n(1))
n = (/ self%n1%n /)
END FUNCTION getNodes1D
!Calculates a 'random' position in edge
FUNCTION randPos1D(self) RESULT(r)
CLASS(meshEdge1D), INTENT(in):: self
REAL(8):: r(1:3)
r = (/ self%x, 0.D0, 0.D0 /)
END FUNCTION randPos1D
!VOLUME FUNCTIONS
!SEGMENT FUNCTIONS
!Init segment element
SUBROUTINE initVol1DSegm(self, n, p)
USE moduleRefParam
IMPLICIT NONE
CLASS(meshVol1DSegm), INTENT(out):: self
INTEGER, INTENT(in):: n
INTEGER, INTENT(in):: p(:)
REAL(8), DIMENSION(1:3):: r1, r2
self%n = n
self%n1 => mesh%nodes(p(1))%obj
self%n2 => mesh%nodes(p(2))%obj
!Get element coordinates
r1 = self%n1%getCoordinates()
r2 = self%n2%getCoordinates()
self%x = (/ r1(1), r2(1) /)
!Assign node volume
CALL self%area()
self%n1%v = self%n1%v + self%arNodes(1)
self%n2%v = self%n2%v + self%arNodes(2)
self%sigmaVrelMax = sigma_ref/L_ref**2
CALL OMP_INIT_LOCK(self%lock)
END SUBROUTINE initVol1DSegm
!Computes element area
PURE SUBROUTINE areaSegm(self)
IMPLICIT NONE
CLASS(meshVol1DSegm), INTENT(inout):: self
REAL(8):: l !element length
REAL(8):: fPsi(1:2)
REAL(8):: detJ
REAL(8):: Xii(1:3)
self%volume = 0.D0
self%arNodes = 0.D0
!1 point Gauss integral
Xii = 0.D0
fPsi = self%fPsi(Xii)
detJ = self%detJac(Xii)
l = 2.D0*detJ
self%volume = l
self%arNodes = fPsi*l
END SUBROUTINE areaSegm
!Computes element functions at point xii
PURE FUNCTION fPsiSegm(xi) RESULT(fPsi)
IMPLICIT NONE
REAL(8), INTENT(in):: xi(1:3)
REAL(8), ALLOCATABLE:: fPsi(:)
ALLOCATE(fPsi(1:2))
fPsi(1) = 1.D0 - xi(1)
fPsi(2) = 1.D0 + xi(1)
fPsi = fPsi * 5.D-1
END FUNCTION fPsiSegm
!Computes element derivative shape function at Xii
PURE FUNCTION dPsiSegm(xi) RESULT(dPsi)
IMPLICIT NONE
REAL(8), INTENT(in):: xi(1:3)
REAL(8), ALLOCATABLE:: dPsi(:,:)
ALLOCATE(dPsi(1:1, 1:2))
dPsi(1, 1) = -5.D-1
dPsi(1, 2) = 5.D-1
END FUNCTION dPsiSegm
!Computes partial derivatives of coordinates
PURE SUBROUTINE partialDerSegm(self, dPsi, dx)
IMPLICIT NONE
CLASS(meshVol1DSegm), INTENT(in):: self
REAL(8), INTENT(in):: dPsi(1:,1:)
REAL(8), INTENT(out), DIMENSION(1):: dx
dx(1) = DOT_PRODUCT(dPsi(1,:), self%x)
END SUBROUTINE partialDerSegm
!Computes local stiffness matrix
PURE FUNCTION elemKSegm(self) RESULT(ke)
IMPLICIT NONE
CLASS(meshVol1DSegm), INTENT(in):: self
REAL(8):: ke(1:2,1:2)
REAL(8):: Xii(1:3)
REAL(8):: dPsi(1:1, 1:2)
REAL(8):: invJ
ke = 0.D0
Xii = (/ 0.D0, 0.D0, 0.D0 /)
dPsi = self%dPsi(Xii)
invJ = self%invJac(Xii, dPsi)
ke(1,:) = (/ dPsi(1,1)*dPsi(1,1), dPsi(1,1)*dPsi(1,2) /)
ke(2,:) = (/ dPsi(1,2)*dPsi(1,1), dPsi(1,2)*dPsi(1,2) /)
ke = 2.D0*ke*invJ
END FUNCTION elemKSegm
PURE FUNCTION elemFSegm(self, source) RESULT(localF)
IMPLICIT NONE
CLASS(meshVol1DSegm), INTENT(in):: self
REAL(8), INTENT(in):: source(1:)
REAL(8), ALLOCATABLE:: localF(:)
REAL(8):: fPsi(1:2)
REAL(8):: detJ
REAL(8):: Xii(1:3)
Xii = 0.D0
fPsi = self%fPsi(Xii)
detJ = self%detJac(Xii)
ALLOCATE(localF(1:2))
localF = 2.D0*DOT_PRODUCT(fPsi, source)*detJ
END FUNCTION elemFSegm
PURE FUNCTION weightSegm(xi) RESULT(w)
IMPLICIT NONE
REAL(8), INTENT(in):: xi(1:3)
REAL(8):: w(1:2)
w = fPsiSegm(xi)
END FUNCTION weightSegm
PURE FUNCTION insideSegm(xi) RESULT(ins)
IMPLICIT NONE
REAL(8), INTENT(in):: xi(1:3)
LOGICAL:: ins
ins = xi(1) >=-1.D0 .AND. &
xi(1) <= 1.D0
END FUNCTION insideSegm
SUBROUTINE scatterSegm(self, part)
USE moduleOutput
USE moduleSpecies
IMPLICIT NONE
CLASS(meshVol1DSegm), INTENT(in):: self
CLASS(particle), INTENT(in):: part
TYPE(outputNode), POINTER:: vertex
REAL(8):: w_p(1:2)
REAL(8):: tensorS(1:3,1:3)
w_p = self%weight(part%xi)
tensorS = outerProduct(part%v, part%v)
vertex => self%n1%output(part%sp)
vertex%den = vertex%den + part%weight*w_p(1)
vertex%mom(:) = vertex%mom(:) + part%weight*w_p(1)*part%v(:)
vertex%tensorS(:,:) = vertex%tensorS(:,:) + part%weight*w_p(1)*tensorS
vertex => self%n2%output(part%sp)
vertex%den = vertex%den + part%weight*w_p(2)
vertex%mom(:) = vertex%mom(:) + part%weight*w_p(2)*part%v(:)
vertex%tensorS(:,:) = vertex%tensorS(:,:) + part%weight*w_p(2)*tensorS
END SUBROUTINE scatterSegm
!Gathers EF at position Xii
PURE FUNCTION gatherEFSegm(self, xi) RESULT(EF)
IMPLICIT NONE
CLASS(meshVol1DSegm), INTENT(in):: self
REAL(8), INTENT(in):: xi(1:3)
REAL(8):: dPsi(1, 1:2)
REAL(8):: phi(1:2)
REAL(8):: EF(1:3)
REAL(8):: invJ
phi = (/ self%n1%emData%phi, &
self%n2%emData%phi /)
dPsi = self%dPsi(xi)
invJ = self%invJac(xi, dPsi)
EF(1) = -DOT_PRODUCT(dPsi(1, :), phi)*invJ
EF(2) = 0.D0
EF(3) = 0.D0
END FUNCTION gatherEFSegm
!Get nodes from 1D volume
PURE FUNCTION getNodesSegm(self) RESULT(n)
IMPLICIT NONE
CLASS(meshVol1DSegm), INTENT(in):: self
INTEGER, ALLOCATABLE:: n(:)
ALLOCATE(n(1:2))
n = (/ self%n1%n, self%n2%n /)
END FUNCTION getNodesSegm
PURE FUNCTION phy2logSegm(self, r) RESULT(xN)
IMPLICIT NONE
CLASS(meshVol1DSegm), INTENT(in):: self
REAL(8), INTENT(in):: r(1:3)
REAL(8):: xN(1:3)
xN = 0.D0
xN(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)
IMPLICIT NONE
CLASS(meshVol1DSegm), INTENT(in):: self
REAL(8), INTENT(in):: xi(1:3)
CLASS(*), POINTER, INTENT(out):: nextElement
NULLIFY(nextElement)
IF (xi(1) < -1.D0) THEN
nextElement => self%e2
ELSEIF (xi(1) > 1.D0) THEN
nextElement => self%e1
END IF
END SUBROUTINE nextElementSegm
!Reset the output of nodes in element
PURE SUBROUTINE resetOutputSegm(self)
USE moduleSpecies
USE moduleOutput
IMPLICIT NONE
CLASS(meshVol1DSegm), INTENT(inout):: self
INTEGER:: k
DO k = 1, nSpecies
self%n1%output(k)%den = 0.D0
self%n1%output(k)%mom = 0.D0
self%n1%output(k)%tensorS = 0.D0
self%n2%output(k)%den = 0.D0
self%n2%output(k)%mom = 0.D0
self%n2%output(k)%tensorS = 0.D0
END DO
END SUBROUTINE resetOutputSegm
!COMMON FUNCTIONS FOR 1D VOLUME ELEMENTS
!Computes the element Jacobian determinant
PURE FUNCTION detJ1D(self, xi, dPsi_in) RESULT(dJ)
IMPLICIT NONE
CLASS(meshVol1D), INTENT(in):: self
REAL(8), INTENT(in):: xi(1:3)
REAL(8), INTENT(in), OPTIONAL:: dPsi_in(1:,1:)
REAL(8), ALLOCATABLE:: dPsi(:,:)
REAL(8):: dJ
REAL(8):: dx(1)
IF (PRESENT(dPsi_in)) THEN
dPsi = dPsi_in
ELSE
dPsi = self%dPsi(xi)
END IF
CALL self%partialDer(dPsi, dx)
dJ = dx(1)
END FUNCTION detJ1D
!Computes the invers Jacobian
PURE FUNCTION invJ1D(self, xi, dPsi_in) RESULT(invJ)
IMPLICIT NONE
CLASS(meshVol1D), INTENT(in):: self
REAL(8), INTENT(in):: xi(1:3)
REAL(8), INTENT(in), OPTIONAL:: dPsi_in(1:,1:)
REAL(8), ALLOCATABLE:: dPsi(:,:)
REAL(8):: dx(1)
REAL(8):: invJ
IF (PRESENT(dPsi_in)) THEN
dPsi = dPsi_in
ELSE
dPsi = self%dPsi(xi)
END IF
CALL self%partialDer(dPsi, dx)
invJ = 1.D0/dx(1)
END FUNCTION invJ1D
END MODULE moduleMesh1D

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MODULE moduleMesh1DBoundary
USE moduleMesh1D
TYPE, PUBLIC, EXTENDS(meshEdge1D):: meshEdge1DRef
CONTAINS
PROCEDURE, PASS:: fBoundary => reflection
END TYPE meshEdge1DRef
TYPE, PUBLIC, EXTENDS(meshEdge1D):: meshEdge1DAbs
CONTAINS
PROCEDURE, PASS:: fBoundary => absorption
END TYPE meshEdge1DAbs
CONTAINS
SUBROUTINE reflection(self, part)
USE moduleSpecies
IMPLICIT NONE
CLASS(meshEdge1DRef), INTENT(inout):: self
CLASS(particle), INTENT(inout):: part
part%v(1) = -part%v(1)
part%r(1) = 2.D0*self%x - part%r(1)
END SUBROUTINE reflection
SUBROUTINE absorption(self, part)
USE moduleSpecies
IMPLICIT NONE
CLASS(meshEdge1DAbs), INTENT(inout):: self
CLASS(particle), INTENT(inout):: part
part%n_in = .FALSE.
END SUBROUTINE absorption
END MODULE moduleMesh1DBoundary

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MODULE moduleMesh1DRead
USE moduleMesh
USE moduleMesh1D
USE moduleMesh1DBoundary
!TODO: make this abstract to allow different mesh formats
TYPE, EXTENDS(meshGeneric):: mesh1DGeneric
CONTAINS
PROCEDURE, PASS:: init => init1DMesh
PROCEDURE, PASS:: readMesh => readMesh1D
END TYPE
INTERFACE connected
MODULE PROCEDURE connectedVolVol, connectedVolEdge
END INTERFACE connected
CONTAINS
!Init 1D mesh
SUBROUTINE init1DMesh(self, meshFormat)
USE moduleMesh
USE moduleErrors
IMPLICIT NONE
CLASS(mesh1DGeneric), INTENT(out):: self
CHARACTER(:), ALLOCATABLE, INTENT(in):: meshFormat
SELECT CASE(meshFormat)
CASE ("gmsh")
self%printOutput => printOutputGmsh
self%printColl => printCollGmsh
self%printEM => printEMGmsh
CASE DEFAULT
CALL criticalError("Mesh type " // meshFormat // " not supported.", "init1D")
END SELECT
END SUBROUTINE init1DMesh
!Reads 1D mesh
SUBROUTINE readMesh1D(self, filename)
USE moduleBoundary
IMPLICIT NONE
CLASS(mesh1DGeneric), INTENT(inout):: self
CHARACTER(:), ALLOCATABLE, INTENT(in):: filename
REAL(8):: x
INTEGER:: p(1:2)
INTEGER:: e, et, n, eTemp, elemType, bt
INTEGER:: totalNumElem
INTEGER:: boundaryType
!Open file mesh
OPEN(10, FILE=TRIM(filename))
!Skip header
READ(10, *)
READ(10, *)
READ(10, *)
READ(10, *)
!Read number of nodes
READ(10, *) self%numNodes
!Allocate required matrices and vectors
ALLOCATE(self%nodes(1:self%numNodes))
ALLOCATE(self%K(1:self%numNodes, 1:self%numNodes))
ALLOCATE(self%IPIV(1:self%numNodes, 1:self%numNodes))
self%K = 0.D0
self%IPIV = 0
!Read nodes coordinates. Only relevant for x
DO e = 1, self%numNodes
READ(10, *) n, x
ALLOCATE(meshNode1D:: self%nodes(n)%obj)
CALL self%nodes(n)%obj%init(n, (/ x, 0.D0, 0.D0 /))
END DO
!Skips comments
READ(10, *)
READ(10, *)
!Reads the total number of elements (edges+vol)
READ(10, *) totalNumElem
self%numEdges = 0
DO e = 1, totalNumElem
READ(10, *) eTemp, elemType
IF (elemType == 15) THEN !15 is physical node in GMSH
self%numEdges = e
END IF
END DO
!Substract the number of edges to the total number of elements
!to obtain the number of volume elements
self%numVols = totalNumelem - self%numEdges
!Allocates arrays
ALLOCATE(self%edges(1:self%numEdges))
ALLOCATE(self%vols(1:self%numVols))
!Go back to the beginning of reading elements
DO e = 1, totalNumelem
BACKSPACE(10)
END DO
!Reads edges
DO e = 1, self%numEdges
READ(10, *) n, elemType, eTemp, boundaryType, eTemp, p(1)
!Associate boundary condition
bt = getBoundaryId(boundaryType)
SELECT CASE(boundary(bt)%obj%boundaryType)
CASE ('reflection')
ALLOCATE(meshEdge1DRef:: self%edges(e)%obj)
CASE ('absorption')
ALLOCATE(meshEdge1DAbs:: self%edges(e)%obj)
END SELECT
CALL self%edges(e)%obj%init(n, p(1:1), bt, boundaryType)
END DO
!Read and initialize volumes
DO e = 1, self%numVols
READ(10, *) n, elemType, eTemp, eTemp, eTemp, p(1:2)
ALLOCATE(meshVol1DSegm:: self%vols(e)%obj)
CALL self%vols(e)%obj%init(n - self%numEdges, p(1:2))
END DO
CLOSE(10)
!Build connectivity between elements
DO e = 1, self%numVols
!Connectivity between volumes
DO et = 1, self%numVols
IF (e /= et) THEN
CALL connected(self%vols(e)%obj, self%vols(et)%obj)
END IF
END DO
!Connectivity betwen vols and edges
DO et = 1, self%numEdges
CALL connected(self%vols(e)%obj, self%edges(et)%obj)
END DO
!Constructs the global K matrix
CALL constructGlobalK(self%K, self%vols(e)%obj)
END DO
END SUBROUTINE readMesh1D
SUBROUTINE connectedVolVol(elemA, elemB)
IMPLICIT NONE
CLASS(meshVol), INTENT(inout):: elemA
CLASS(meshVol), INTENT(inout):: elemB
SELECT TYPE(elemA)
TYPE IS(meshVol1DSegm)
SELECT TYPE(elemB)
TYPE IS(meshVol1DSegm)
CALL connectedSegmSegm(elemA, elemB)
END SELECT
END SELECT
END SUBROUTINE connectedVolVol
SUBROUTINE connectedSegmSegm(elemA, elemB)
IMPLICIT NONE
CLASS(meshVol1DSegm), INTENT(inout), TARGET:: elemA
CLASS(meshVol1DSegm), INTENT(inout), TARGET:: elemB
IF (.NOT. ASSOCIATED(elemA%e1) .AND. &
elemA%n2%n == elemB%n1%n) THEN
elemA%e1 => elemB
elemB%e2 => elemA
END IF
IF (.NOT. ASSOCIATED(elemA%e2) .AND. &
elemA%n1%n == elemB%n2%n) THEN
elemA%e2 => elemB
elemB%e1 => elemA
END IF
END SUBROUTINE connectedSegmSegm
SUBROUTINE connectedVolEdge(elemA, elemB)
IMPLICIT NONE
CLASS(meshVol), INTENT(inout):: elemA
CLASS(meshEdge), INTENT(inout):: elemB
SELECT TYPE(elemA)
TYPE IS (meshVol1DSegm)
SELECT TYPE(elemB)
CLASS IS(meshEdge1D)
CALL connectedSegmEdge(elemA, elemB)
END SELECT
END SELECT
END SUBROUTINE connectedVolEdge
SUBROUTINE connectedSegmEdge(elemA, elemB)
IMPLICIT NONE
CLASS(meshVol1DSegm), INTENT(inout), TARGET:: elemA
CLASS(meshEdge1D), INTENT(inout), TARGET:: elemB
IF (.NOT. ASSOCIATED(elemA%e1) .AND. &
elemA%n2%n == elemB%n1%n) THEN
elemA%e1 => elemB
elemB%e2 => elemA
END IF
IF (.NOT. ASSOCIATED(elemA%e2) .AND. &
elemA%n1%n == elemB%n1%n) THEN
elemA%e2 => elemB
elemB%e1 => elemA
END IF
END SUBROUTINE connectedSegmEdge
SUBROUTINE constructGlobalK(K, elem)
IMPLICIT NONE
REAL(8), INTENT(inout):: K(1:,1:)
CLASS(meshVol), INTENT(in):: elem
REAL(8):: localK(1:2,1:2)
INTEGER:: i, j
INTEGER:: n(1:2)
SELECT TYPE(elem)
TYPE IS(meshVol1DSegm)
localK = elem%elemK()
n = (/ elem%n1%n, elem%n2%n /)
CLASS DEFAULT
n = 0
localK = 0.D0
END SELECT
DO i = 1, 2
DO j = 1, 2
K(n(i), n(j)) = K(n(i), n(j)) + localK(i, j)
END DO
END DO
END SUBROUTINE constructGlobalK
END MODULE moduleMesh1DRead