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fPsi no longer allocates memory

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I noticed that phy2logquad had a lot of overhead. Trying to reducing it
by simplifying calls to fPsi, dPsi and such.

The function for fPsi has been made so no memory is allocated and works
under the assumption that the input array has the right size (1:numNodes)
This commit is contained in:
Jorge Gonzalez 2023-01-01 12:12:06 +01:00
commit 0db76083ec
8 changed files with 408 additions and 409 deletions
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6
src/modules/init/moduleInput.f90
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@ -361,14 +361,14 @@ MODULE moduleInput
!Density at centroid of cell !Density at centroid of cell
nodes = mesh%vols(e)%obj%getNodes() nodes = mesh%vols(e)%obj%getNodes()
nNodes = SIZE(nodes) nNodes = SIZE(nodes)
fPsi = mesh%vols(e)%obj%fPsi((/0.D0, 0.D0, 0.D0/)) ALLOCATE(fPsi(1:nNodes))
CALL mesh%vols(e)%obj%fPsi((/0.D0, 0.D0, 0.D0/), fPsi)
ALLOCATE(source(1:nNodes)) ALLOCATE(source(1:nNodes))
DO j = 1, nNodes DO j = 1, nNodes
source(j) = density(nodes(j)) source(j) = density(nodes(j))
END DO END DO
densityCen = DOT_PRODUCT(fPsi, source) densityCen = DOT_PRODUCT(fPsi, source)
DEALLOCATE(fPsi)
!Calculate number of particles !Calculate number of particles
nNewPart = INT(densityCen * (mesh%vols(e)%obj%volume*Vol_ref) / species(sp)%obj%weight) nNewPart = INT(densityCen * (mesh%vols(e)%obj%volume*Vol_ref) / species(sp)%obj%weight)
@ -380,7 +380,7 @@ MODULE moduleInput
partNew%r = mesh%vols(e)%obj%randPos() partNew%r = mesh%vols(e)%obj%randPos()
partNew%xi = mesh%vols(e)%obj%phy2log(partNew%r) partNew%xi = mesh%vols(e)%obj%phy2log(partNew%r)
!Get mean velocity at particle position !Get mean velocity at particle position
fPsi = mesh%vols(e)%obj%fPsi(partNew%xi) CALL mesh%vols(e)%obj%fPsi(partNew%xi, fPsi)
DO j = 1, nNodes DO j = 1, nNodes
source(j) = velocity(nodes(j), 1) source(j) = velocity(nodes(j), 1)

7
src/modules/mesh/0D/moduleMesh0D.f90
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@ -106,14 +106,13 @@ MODULE moduleMesh0D
END FUNCTION randPos0D END FUNCTION randPos0D
PURE FUNCTION fPsi0D(xi) RESULT(fPsi) PURE SUBROUTINE fPsi0D(xi, fPsi)
REAL(8), INTENT(in):: xi(1:3) REAL(8), INTENT(in):: xi(1:3)
REAL(8), ALLOCATABLE:: fPsi(:) REAL(8), INTENT(out):: fPsi(:)
ALLOCATE(fPsi(1:1))
fPsi = 1.D0 fPsi = 1.D0
END FUNCTION fPsi0D END SUBROUTINE fPsi0D
PURE FUNCTION gatherEF0D(self, xi) RESULT(EF) PURE FUNCTION gatherEF0D(self, xi) RESULT(EF)
IMPLICIT NONE IMPLICIT NONE

54
src/modules/mesh/1DCart/moduleMesh1DCart.f90
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@ -230,13 +230,13 @@ MODULE moduleMesh1DCart
CLASS(meshVol1DCartSegm), INTENT(in):: self CLASS(meshVol1DCartSegm), INTENT(in):: self
REAL(8):: r(1:3) REAL(8):: r(1:3)
REAL(8):: xii(1:3) REAL(8):: Xi(1:3)
REAL(8), ALLOCATABLE:: fPsi(:) REAL(8), ALLOCATABLE:: fPsi(:)
xii(1) = random(-1.D0, 1.D0) Xi(1) = random(-1.D0, 1.D0)
xii(2:3) = 0.D0 Xi(2:3) = 0.D0
fPsi = self%fPsi(xii) CALL self%fPsi(Xi, fPsi)
r(1) = DOT_PRODUCT(fPsi, self%x) r(1) = DOT_PRODUCT(fPsi, self%x)
END FUNCTION randPos1DCartSeg END FUNCTION randPos1DCartSeg
@ -249,36 +249,34 @@ MODULE moduleMesh1DCart
REAL(8):: l !element length REAL(8):: l !element length
REAL(8):: fPsi(1:2) REAL(8):: fPsi(1:2)
REAL(8):: detJ REAL(8):: detJ
REAL(8):: Xii(1:3) REAL(8):: Xi(1:3)
self%volume = 0.D0 self%volume = 0.D0
self%arNodes = 0.D0 self%arNodes = 0.D0
!1 point Gauss integral !1 point Gauss integral
Xii = 0.D0 Xi = 0.D0
fPsi = self%fPsi(Xii) CALL self%fPsi(Xi, fPsi)
detJ = self%detJac(Xii) detJ = self%detJac(Xi)
l = 2.D0*detJ l = 2.D0*detJ
self%volume = l self%volume = l
self%arNodes = fPsi*l self%arNodes = fPsi*l
END SUBROUTINE areaSegm END SUBROUTINE areaSegm
!Computes element functions at point xii !Computes element functions at point Xi
PURE FUNCTION fPsiSegm(xi) RESULT(fPsi) PURE SUBROUTINE fPsiSegm(xi, fPsi)
IMPLICIT NONE IMPLICIT NONE
REAL(8), INTENT(in):: xi(1:3) REAL(8), INTENT(in):: xi(1:3)
REAL(8), ALLOCATABLE:: fPsi(:) REAL(8), INTENT(out):: fPsi(:)
ALLOCATE(fPsi(1:2))
fPsi(1) = 1.D0 - xi(1) fPsi(1) = 1.D0 - xi(1)
fPsi(2) = 1.D0 + xi(1) fPsi(2) = 1.D0 + xi(1)
fPsi = fPsi * 5.D-1 fPsi = fPsi * 5.D-1
END FUNCTION fPsiSegm END SUBROUTINE fPsiSegm
!Computes element derivative shape function at Xii !Computes element derivative shape function at Xi
PURE FUNCTION dPsiSegm(xi) RESULT(dPsi) PURE FUNCTION dPsiSegm(xi) RESULT(dPsi)
IMPLICIT NONE IMPLICIT NONE
@ -310,19 +308,19 @@ MODULE moduleMesh1DCart
CLASS(meshVol1DCartSegm), INTENT(in):: self CLASS(meshVol1DCartSegm), INTENT(in):: self
REAL(8), ALLOCATABLE:: localK(:,:) REAL(8), ALLOCATABLE:: localK(:,:)
REAL(8):: Xii(1:3) REAL(8):: Xi(1:3)
REAL(8):: dPsi(1:1, 1:2) REAL(8):: dPsi(1:1, 1:2)
REAL(8):: invJ(1), detJ REAL(8):: invJ(1), detJ
INTEGER:: l INTEGER:: l
ALLOCATE(localK(1:2,1:2)) ALLOCATE(localK(1:2,1:2))
localK = 0.D0 localK = 0.D0
Xii = 0.D0 Xi = 0.D0
DO l = 1, 3 DO l = 1, 3
xii(1) = corSeg(l) Xi(1) = corSeg(l)
dPsi = self%dPsi(Xii) dPsi = self%dPsi(Xi)
detJ = self%detJac(Xii, dPsi) detJ = self%detJac(Xi, dPsi)
invJ = self%invJac(Xii, dPsi) invJ = self%invJac(Xi, dPsi)
localK = localK + MATMUL(RESHAPE(MATMUL(invJ,dPsi), (/ 2, 1/)), & localK = localK + MATMUL(RESHAPE(MATMUL(invJ,dPsi), (/ 2, 1/)), &
RESHAPE(MATMUL(invJ,dPsi), (/ 1, 2/)))* & RESHAPE(MATMUL(invJ,dPsi), (/ 1, 2/)))* &
wSeg(l)/detJ wSeg(l)/detJ
@ -339,17 +337,17 @@ MODULE moduleMesh1DCart
REAL(8), ALLOCATABLE:: localF(:) REAL(8), ALLOCATABLE:: localF(:)
REAL(8):: fPsi(1:2) REAL(8):: fPsi(1:2)
REAL(8):: detJ, f REAL(8):: detJ, f
REAL(8):: Xii(1:3) REAL(8):: Xi(1:3)
INTEGER:: l INTEGER:: l
ALLOCATE(localF(1:2)) ALLOCATE(localF(1:2))
localF = 0.D0 localF = 0.D0
Xii = 0.D0 Xi = 0.D0
DO l = 1, 3 DO l = 1, 3
xii(1) = corSeg(l) Xi(1) = corSeg(l)
detJ = self%detJac(Xii) detJ = self%detJac(Xi)
fPsi = self%fPsi(Xii) CALL self%fPsi(Xi, fPsi)
f = DOT_PRODUCT(fPsi, source) f = DOT_PRODUCT(fPsi, source)
localF = localF + f*fPsi*wSeg(l)*detJ localF = localF + f*fPsi*wSeg(l)*detJ
@ -368,7 +366,7 @@ MODULE moduleMesh1DCart
END FUNCTION insideSegm END FUNCTION insideSegm
!Gathers EF at position Xii !Gathers EF at position Xi
PURE FUNCTION gatherEFSegm(self, xi) RESULT(EF) PURE FUNCTION gatherEFSegm(self, xi) RESULT(EF)
IMPLICIT NONE IMPLICIT NONE
@ -407,7 +405,7 @@ MODULE moduleMesh1DCart
MF_Nodes(1:2,3) = (/ self%n1%emData%B(3), & MF_Nodes(1:2,3) = (/ self%n1%emData%B(3), &
self%n2%emData%B(3) /) self%n2%emData%B(3) /)
fPsi = self%fPsi(xi) CALL self%fPsi(xi, fPsi)
MF = MATMUL(fPsi, MF_Nodes) MF = MATMUL(fPsi, MF_Nodes)
END FUNCTION gatherMFSegm END FUNCTION gatherMFSegm

68
src/modules/mesh/1DRad/moduleMesh1DRad.f90
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@ -232,13 +232,13 @@ MODULE moduleMesh1DRad
CLASS(meshVol1DRadSegm), INTENT(in):: self CLASS(meshVol1DRadSegm), INTENT(in):: self
REAL(8):: r(1:3) REAL(8):: r(1:3)
REAL(8):: xii(1:3) REAL(8):: Xi(1:3)
REAL(8), ALLOCATABLE:: fPsi(:) REAL(8), ALLOCATABLE:: fPsi(:)
xii(1) = random(-1.D0, 1.D0) Xi(1) = random(-1.D0, 1.D0)
xii(2:3) = 0.D0 Xi(2:3) = 0.D0
fPsi = self%fPsi(xii) CALL self%fPsi(Xi, fPsi)
r(1) = DOT_PRODUCT(fPsi, self%r) r(1) = DOT_PRODUCT(fPsi, self%r)
END FUNCTION randPos1DRadSeg END FUNCTION randPos1DRadSeg
@ -249,47 +249,47 @@ MODULE moduleMesh1DRad
CLASS(meshVol1DRadSegm), INTENT(inout):: self CLASS(meshVol1DRadSegm), INTENT(inout):: self
REAL(8):: l !element length REAL(8):: l !element length
REAL(8):: fPsi(1:2) REAL(8):: fPsi(1:2), fPsi_node(1:2)
REAL(8):: r REAL(8):: r
REAL(8):: detJ REAL(8):: detJ
REAL(8):: Xii(1:3) REAL(8):: Xi(1:3)
self%volume = 0.D0 self%volume = 0.D0
self%arNodes = 0.D0 self%arNodes = 0.D0
!1 point Gauss integral !1 point Gauss integral
Xii = 0.D0 Xi = 0.D0
fPsi = self%fPsi(Xii) CALL self%fPsi(Xi, fPsi)
detJ = self%detJac(Xii) detJ = self%detJac(Xi)
!Computes total volume of the cell !Computes total volume of the cell
r = DOT_PRODUCT(fPsi, self%r) r = DOT_PRODUCT(fPsi, self%r)
l = 2.D0*detJ l = 2.D0*detJ
self%volume = r*l self%volume = r*l
!Computes volume per node !Computes volume per node
Xii = (/-5.D-1, 0.D0, 0.D0/) Xi = (/-5.D-1, 0.D0, 0.D0/)
r = DOT_PRODUCT(self%fPsi(Xii),self%r) CALL self%fPsi(Xi, fPsi_node)
r = DOT_PRODUCT(fPsi_node,self%r)
self%arNodes(1) = fPsi(1)*r*l self%arNodes(1) = fPsi(1)*r*l
Xii = (/ 5.D-1, 0.D0, 0.D0/) Xi = (/ 5.D-1, 0.D0, 0.D0/)
r = DOT_PRODUCT(self%fPsi(Xii),self%r) CALL self%fPsi(Xi, fPsi_node)
r = DOT_PRODUCT(fPsi_node,self%r)
self%arNodes(2) = fPsi(2)*r*l self%arNodes(2) = fPsi(2)*r*l
END SUBROUTINE areaRad END SUBROUTINE areaRad
!Computes element functions at point xii !Computes element functions at point Xi
PURE FUNCTION fPsiRad(xi) RESULT(fPsi) PURE SUBROUTINE fPsiRad(xi, fPsi)
IMPLICIT NONE IMPLICIT NONE
REAL(8), INTENT(in):: xi(1:3) REAL(8), INTENT(in):: xi(1:3)
REAL(8), ALLOCATABLE:: fPsi(:) REAL(8), INTENT(out):: fPsi(:)
ALLOCATE(fPsi(1:2))
fPsi(1) = 1.D0 - xi(1) fPsi(1) = 1.D0 - xi(1)
fPsi(2) = 1.D0 + xi(1) fPsi(2) = 1.D0 + xi(1)
fPsi = fPsi * 5.D-1 fPsi = fPsi * 5.D-1
END FUNCTION fPsiRad END SUBROUTINE fPsiRad
!Computes element derivative shape function at Xii !Computes element derivative shape function at Xi
PURE FUNCTION dPsiRad(xi) RESULT(dPsi) PURE FUNCTION dPsiRad(xi) RESULT(dPsi)
IMPLICIT NONE IMPLICIT NONE
@ -322,7 +322,7 @@ MODULE moduleMesh1DRad
CLASS(meshVol1DRadSegm), INTENT(in):: self CLASS(meshVol1DRadSegm), INTENT(in):: self
REAL(8), ALLOCATABLE:: localK(:,:) REAL(8), ALLOCATABLE:: localK(:,:)
REAL(8):: Xii(1:3) REAL(8):: Xi(1:3)
REAL(8):: dPsi(1:1, 1:2) REAL(8):: dPsi(1:1, 1:2)
REAL(8):: invJ(1), detJ REAL(8):: invJ(1), detJ
REAL(8):: r, fPsi(1:2) REAL(8):: r, fPsi(1:2)
@ -330,13 +330,13 @@ MODULE moduleMesh1DRad
ALLOCATE(localK(1:2, 1:2)) ALLOCATE(localK(1:2, 1:2))
localK = 0.D0 localK = 0.D0
Xii = 0.D0 Xi = 0.D0
DO l = 1, 3 DO l = 1, 3
xii(1) = corSeg(l) Xi(1) = corSeg(l)
dPsi = self%dPsi(Xii) dPsi = self%dPsi(Xi)
detJ = self%detJac(Xii, dPsi) detJ = self%detJac(Xi, dPsi)
invJ = self%invJac(Xii, dPsi) invJ = self%invJac(Xi, dPsi)
fPsi = self%fPsi(Xii) CALL self%fPsi(Xi, fPsi)
r = DOT_PRODUCT(fPsi, self%r) r = DOT_PRODUCT(fPsi, self%r)
localK = localK + MATMUL(RESHAPE(MATMUL(invJ,dPsi), (/ 2, 1/)), & localK = localK + MATMUL(RESHAPE(MATMUL(invJ,dPsi), (/ 2, 1/)), &
RESHAPE(MATMUL(invJ,dPsi), (/ 1, 2/)))* & RESHAPE(MATMUL(invJ,dPsi), (/ 1, 2/)))* &
@ -357,17 +357,17 @@ MODULE moduleMesh1DRad
REAL(8), ALLOCATABLE:: localF(:) REAL(8), ALLOCATABLE:: localF(:)
REAL(8):: fPsi(1:2) REAL(8):: fPsi(1:2)
REAL(8):: detJ, f, r REAL(8):: detJ, f, r
REAL(8):: Xii(1:3) REAL(8):: Xi(1:3)
INTEGER:: l INTEGER:: l
ALLOCATE(localF(1:2)) ALLOCATE(localF(1:2))
localF = 0.D0 localF = 0.D0
Xii = 0.D0 Xi = 0.D0
DO l = 1, 3 DO l = 1, 3
xii(1) = corSeg(l) Xi(1) = corSeg(l)
detJ = self%detJac(Xii) detJ = self%detJac(Xi)
fPsi = self%fPsi(Xii) CALL self%fPsi(Xi, fPsi)
r = DOT_PRODUCT(fPsi, self%r) r = DOT_PRODUCT(fPsi, self%r)
f = DOT_PRODUCT(fPsi, source) f = DOT_PRODUCT(fPsi, source)
localF = localF + f*fPsi*r*wSeg(l)*detJ localF = localF + f*fPsi*r*wSeg(l)*detJ
@ -387,7 +387,7 @@ MODULE moduleMesh1DRad
END FUNCTION insideRad END FUNCTION insideRad
!Gathers EF at position Xii !Gathers EF at position Xi
PURE FUNCTION gatherEFRad(self, xi) RESULT(EF) PURE FUNCTION gatherEFRad(self, xi) RESULT(EF)
IMPLICIT NONE IMPLICIT NONE
@ -426,7 +426,7 @@ MODULE moduleMesh1DRad
MF_Nodes(1:2,3) = (/ self%n1%emData%B(3), & MF_Nodes(1:2,3) = (/ self%n1%emData%B(3), &
self%n2%emData%B(3) /) self%n2%emData%B(3) /)
fPsi = self%fPsi(xi) CALL self%fPsi(xi, fPsi)
MF = MATMUL(fPsi, MF_Nodes) MF = MATMUL(fPsi, MF_Nodes)
END FUNCTION gatherMFRad END FUNCTION gatherMFRad

323
src/modules/mesh/2DCart/moduleMesh2DCart.f90
View file

@ -11,8 +11,8 @@ MODULE moduleMesh2DCart
REAL(8), PARAMETER:: corQuad(1:3) = (/ -DSQRT(3.D0/5.D0), 0.D0, DSQRT(3.D0/5.D0) /) REAL(8), PARAMETER:: corQuad(1:3) = (/ -DSQRT(3.D0/5.D0), 0.D0, DSQRT(3.D0/5.D0) /)
REAL(8), PARAMETER:: wQuad(1:3) = (/ 5.D0/9.D0, 8.D0/9.D0, 5.D0/9.D0 /) REAL(8), PARAMETER:: wQuad(1:3) = (/ 5.D0/9.D0, 8.D0/9.D0, 5.D0/9.D0 /)
REAL(8), PARAMETER:: xi1Tria(1:4) = (/ 1.D0/3.D0, 1.D0/5.D0, 3.D0/5.D0, 1.D0/5.D0 /) REAL(8), PARAMETER:: Xi1Tria(1:4) = (/ 1.D0/3.D0, 1.D0/5.D0, 3.D0/5.D0, 1.D0/5.D0 /)
REAL(8), PARAMETER:: xi2Tria(1:4) = (/ 1.D0/3.D0, 1.D0/5.D0, 1.D0/5.D0, 3.D0/5.D0 /) REAL(8), PARAMETER:: Xi2Tria(1:4) = (/ 1.D0/3.D0, 1.D0/5.D0, 1.D0/5.D0, 3.D0/5.D0 /)
REAL(8), PARAMETER:: wTria(1:4) = (/ -27.D0/96.D0, 25.D0/96.D0, 25.D0/96.D0, 25.D0/96.D0 /) REAL(8), PARAMETER:: wTria(1:4) = (/ -27.D0/96.D0, 25.D0/96.D0, 25.D0/96.D0, 25.D0/96.D0 /)
TYPE, PUBLIC, EXTENDS(meshNode):: meshNode2DCart TYPE, PUBLIC, EXTENDS(meshNode):: meshNode2DCart
@ -47,8 +47,8 @@ MODULE moduleMesh2DCart
END TYPE meshVol2DCart END TYPE meshVol2DCart
ABSTRACT INTERFACE ABSTRACT INTERFACE
PURE FUNCTION dPsi_interface(xi) RESULT(dPsi) PURE FUNCTION dPsi_interface(Xi) RESULT(dPsi)
REAL(8), INTENT(in):: xi(1:3) REAL(8), INTENT(in):: Xi(1:3)
REAL(8), ALLOCATABLE:: dPsi(:,:) REAL(8), ALLOCATABLE:: dPsi(:,:)
END FUNCTION dPsi_interface END FUNCTION dPsi_interface
@ -210,14 +210,14 @@ MODULE moduleMesh2DCart
CLASS(meshVol2DCartQuad), INTENT(in):: self CLASS(meshVol2DCartQuad), INTENT(in):: self
REAL(8):: r(1:3) REAL(8):: r(1:3)
REAL(8):: xii(1:3) REAL(8):: Xi(1:3)
REAL(8), ALLOCATABLE:: fPsi(:) REAL(8), ALLOCATABLE:: fPsi(:)
xii(1) = random(-1.D0, 1.D0) Xi(1) = random(-1.D0, 1.D0)
xii(2) = random(-1.D0, 1.D0) Xi(2) = random(-1.D0, 1.D0)
xii(3) = 0.D0 Xi(3) = 0.D0
fPsi = self%fPsi(xii) CALL self%fPsi(Xi, fPsi)
r(1) = DOT_PRODUCT(fPsi, self%x) r(1) = DOT_PRODUCT(fPsi, self%x)
r(2) = DOT_PRODUCT(fPsi, self%y) r(2) = DOT_PRODUCT(fPsi, self%y)
@ -319,78 +319,77 @@ MODULE moduleMesh2DCart
IMPLICIT NONE IMPLICIT NONE
CLASS(meshVol2DCartQuad), INTENT(inout):: self CLASS(meshVol2DCartQuad), INTENT(inout):: self
REAL(8):: xi(1:3) REAL(8):: Xi(1:3)
REAL(8):: detJ REAL(8):: detJ
REAL(8):: fPsi(1:4) REAL(8):: fPsi(1:4)
self%volume = 0.D0 self%volume = 0.D0
self%arNodes = 0.D0 self%arNodes = 0.D0
!2D 1 point Gauss Quad Integral !2D 1 point Gauss Quad Integral
xi = 0.D0 Xi = 0.D0
detJ = self%detJac(xi)*4.D0 !4 detJ = self%detJac(Xi)*4.D0 !4
fPsi = self%fPsi(xi) CALL self%fPsi(Xi, fPsi)
self%volume = detJ self%volume = detJ
self%arNodes = fPsi*detJ self%arNodes = fPsi*detJ
END SUBROUTINE areaQuad END SUBROUTINE areaQuad
!Computes element functions in point xi !Computes element functions in point Xi
PURE FUNCTION fPsiQuad(xi) RESULT(fPsi) PURE SUBROUTINE fPsiQuad(Xi, fPsi)
IMPLICIT NONE IMPLICIT NONE
REAL(8),INTENT(in):: xi(1:3) REAL(8), INTENT(in):: Xi(1:3)
REAL(8), ALLOCATABLE:: fPsi(:) REAL(8), INTENT(out):: fPsi(:)
ALLOCATE(fPsi(1:4)) 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(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 fPsi = fPsi*0.25D0
END FUNCTION fPsiQuad END SUBROUTINE fPsiQuad
!Derivative element function at coordinates xi !Derivative element function at coordinates Xi
PURE FUNCTION dPsiQuad(xi) RESULT(dPsi) PURE FUNCTION dPsiQuad(Xi) RESULT(dPsi)
IMPLICIT NONE IMPLICIT NONE
REAL(8), INTENT(in):: xi(1:3) REAL(8), INTENT(in):: Xi(1:3)
REAL(8), ALLOCATABLE:: dPsi(:,:) REAL(8), ALLOCATABLE:: dPsi(:,:)
ALLOCATE(dPsi(1:2,1:4)) ALLOCATE(dPsi(1:2,1:4))
dPsi(1,:) = dPsiQuadXi1(xi(2)) dPsi(1,:) = dPsiQuadXi1(Xi(2))
dPsi(2,:) = dPsiQuadXi2(xi(1)) dPsi(2,:) = dPsiQuadXi2(Xi(1))
END FUNCTION dPsiQuad END FUNCTION dPsiQuad
!Derivative element function (xi1) !Derivative element function (Xi1)
PURE FUNCTION dPsiQuadXi1(xi2) RESULT(dPsiXi1) PURE FUNCTION dPsiQuadXi1(Xi2) RESULT(dPsiXi1)
IMPLICIT NONE IMPLICIT NONE
REAL(8),INTENT(in):: xi2 REAL(8),INTENT(in):: Xi2
REAL(8):: dPsiXi1(1:4) REAL(8):: dPsiXi1(1:4)
dPsiXi1(1) = -(1.D0-xi2) dPsiXi1(1) = -(1.D0-Xi2)
dPsiXi1(2) = (1.D0-xi2) dPsiXi1(2) = (1.D0-Xi2)
dPsiXi1(3) = (1.D0+xi2) dPsiXi1(3) = (1.D0+Xi2)
dPsiXi1(4) = -(1.D0+xi2) dPsiXi1(4) = -(1.D0+Xi2)
dPsiXi1 = dPsiXi1*0.25D0 dPsiXi1 = dPsiXi1*0.25D0
END FUNCTION dPsiQuadXi1 END FUNCTION dPsiQuadXi1
!Derivative element function (xi2) !Derivative element function (Xi2)
PURE FUNCTION dPsiQuadXi2(xi1) RESULT(dPsiXi2) PURE FUNCTION dPsiQuadXi2(Xi1) RESULT(dPsiXi2)
IMPLICIT NONE IMPLICIT NONE
REAL(8),INTENT(in):: xi1 REAL(8),INTENT(in):: Xi1
REAL(8):: dPsiXi2(1:4) REAL(8):: dPsiXi2(1:4)
dPsiXi2(1) = -(1.D0-xi1) dPsiXi2(1) = -(1.D0-Xi1)
dPsiXi2(2) = -(1.D0+xi1) dPsiXi2(2) = -(1.D0+Xi1)
dPsiXi2(3) = (1.D0+xi1) dPsiXi2(3) = (1.D0+Xi1)
dPsiXi2(4) = (1.D0-xi1) dPsiXi2(4) = (1.D0-Xi1)
dPsiXi2 = dPsiXi2*0.25D0 dPsiXi2 = dPsiXi2*0.25D0
END FUNCTION dPsiQuadXi2 END FUNCTION dPsiQuadXi2
@ -415,24 +414,24 @@ MODULE moduleMesh2DCart
CLASS(meshVol2DCartQuad), INTENT(in):: self CLASS(meshVol2DCartQuad), INTENT(in):: self
REAL(8), ALLOCATABLE:: localK(:,:) REAL(8), ALLOCATABLE:: localK(:,:)
REAL(8):: xi(1:3) REAL(8):: Xi(1:3)
REAL(8):: fPsi(1:4), dPsi(1:2,1:4) REAL(8):: fPsi(1:4), dPsi(1:2,1:4)
REAL(8):: invJ(1:2,1:2), detJ REAL(8):: invJ(1:2,1:2), detJ
INTEGER:: l, m INTEGER:: l, m
ALLOCATE(localK(1:4, 1:4)) ALLOCATE(localK(1:4, 1:4))
localK=0.D0 localK=0.D0
xi=0.D0 Xi=0.D0
!Start 2D Gauss Quad Integral !Start 2D Gauss Quad Integral
DO l=1, 3 DO l=1, 3
xi(2) = corQuad(l) Xi(2) = corQuad(l)
dPsi(1,:) = self%dPsiXi1(xi(2)) dPsi(1,:) = self%dPsiXi1(Xi(2))
DO m = 1, 3 DO m = 1, 3
xi(1) = corQuad(m) Xi(1) = corQuad(m)
dPsi(2,:) = self%dPsiXi2(xi(1)) dPsi(2,:) = self%dPsiXi2(Xi(1))
fPsi = self%fPsi(xi) CALL self%fPsi(Xi, fPsi)
detJ = self%detJac(xi,dPsi) detJ = self%detJac(Xi,dPsi)
invJ = self%invJac(xi,dPsi) invJ = self%invJac(Xi,dPsi)
localK = localK + MATMUL(TRANSPOSE(MATMUL(invJ,dPsi)),MATMUL(invJ,dPsi))*wQuad(l)*wQuad(m)/detJ localK = localK + MATMUL(TRANSPOSE(MATMUL(invJ,dPsi)),MATMUL(invJ,dPsi))*wQuad(l)*wQuad(m)/detJ
END DO END DO
@ -447,20 +446,20 @@ MODULE moduleMesh2DCart
CLASS(meshVol2DCartQuad), INTENT(in):: self CLASS(meshVol2DCartQuad), INTENT(in):: self
REAL(8), INTENT(in):: source(1:) REAL(8), INTENT(in):: source(1:)
REAL(8), ALLOCATABLE:: localF(:) REAL(8), ALLOCATABLE:: localF(:)
REAL(8):: xi(1:3) REAL(8):: Xi(1:3)
REAL(8):: fPsi(1:4) REAL(8):: fPsi(1:4)
REAL(8):: detJ, f REAL(8):: detJ, f
INTEGER:: l, m INTEGER:: l, m
ALLOCATE(localF(1:4)) ALLOCATE(localF(1:4))
localF = 0.D0 localF = 0.D0
xi = 0.D0 Xi = 0.D0
DO l=1, 3 DO l=1, 3
xi(1) = corQuad(l) Xi(1) = corQuad(l)
DO m = 1, 3 DO m = 1, 3
xi(2) = corQuad(m) Xi(2) = corQuad(m)
detJ = self%detJac(xi) detJ = self%detJac(Xi)
fPsi = self%fPsi(xi) CALL self%fPsi(Xi, fPsi)
f = DOT_PRODUCT(fPsi,source) f = DOT_PRODUCT(fPsi,source)
localF = localF + f*fPsi*wQuad(l)*wQuad(m)*detJ localF = localF + f*fPsi*wQuad(l)*wQuad(m)*detJ
@ -470,23 +469,23 @@ MODULE moduleMesh2DCart
END FUNCTION elemFQuad END FUNCTION elemFQuad
!Checks if a particle is inside a quad element !Checks if a particle is inside a quad element
PURE FUNCTION insideQuad(xi) RESULT(ins) PURE FUNCTION insideQuad(Xi) RESULT(ins)
IMPLICIT NONE IMPLICIT NONE
REAL(8), INTENT(in):: xi(1:3) REAL(8), INTENT(in):: Xi(1:3)
LOGICAL:: ins LOGICAL:: ins
ins = (xi(1) >= -1.D0 .AND. xi(1) <= 1.D0) .AND. & ins = (Xi(1) >= -1.D0 .AND. Xi(1) <= 1.D0) .AND. &
(xi(2) >= -1.D0 .AND. xi(2) <= 1.D0) (Xi(2) >= -1.D0 .AND. Xi(2) <= 1.D0)
END FUNCTION insideQuad END FUNCTION insideQuad
!Gathers the electric field at position xi !Gathers the electric field at position Xi
PURE FUNCTION gatherEFQuad(self,xi) RESULT(EF) PURE FUNCTION gatherEFQuad(self,Xi) RESULT(EF)
IMPLICIT NONE IMPLICIT NONE
CLASS(meshVol2DCartQuad), INTENT(in):: self CLASS(meshVol2DCartQuad), INTENT(in):: self
REAL(8), INTENT(in):: xi(1:3) REAL(8), INTENT(in):: Xi(1:3)
REAL(8):: dPsi(1:2,1:4) REAL(8):: dPsi(1:2,1:4)
REAL(8):: dPsiR(1:2,1:4)!Derivative of shpae functions in global coordinates REAL(8):: dPsiR(1:2,1:4)!Derivative of shpae functions in global coordinates
REAL(8):: invJ(1:2,1:2), detJ REAL(8):: invJ(1:2,1:2), detJ
@ -498,9 +497,9 @@ MODULE moduleMesh2DCart
self%n3%emData%phi, & self%n3%emData%phi, &
self%n4%emData%phi /) self%n4%emData%phi /)
dPsi = self%dPsi(xi) dPsi = self%dPsi(Xi)
detJ = self%detJac(xi,dPsi) detJ = self%detJac(Xi,dPsi)
invJ = self%invJac(xi,dPsi) invJ = self%invJac(Xi,dPsi)
dPsiR = MATMUL(invJ, dPsi)/detJ dPsiR = MATMUL(invJ, dPsi)/detJ
EF(1) = -DOT_PRODUCT(dPsiR(1,:), phi) EF(1) = -DOT_PRODUCT(dPsiR(1,:), phi)
EF(2) = -DOT_PRODUCT(dPsiR(2,:), phi) EF(2) = -DOT_PRODUCT(dPsiR(2,:), phi)
@ -508,11 +507,11 @@ MODULE moduleMesh2DCart
END FUNCTION gatherEFQuad END FUNCTION gatherEFQuad
PURE FUNCTION gatherMFQuad(self,xi) RESULT(MF) PURE FUNCTION gatherMFQuad(self,Xi) RESULT(MF)
IMPLICIT NONE IMPLICIT NONE
CLASS(meshVol2DCartQuad), INTENT(in):: self CLASS(meshVol2DCartQuad), INTENT(in):: self
REAL(8), INTENT(in):: xi(1:3) REAL(8), INTENT(in):: Xi(1:3)
REAL(8):: fPsi(1:4) REAL(8):: fPsi(1:4)
REAL(8):: MF_Nodes(1:4,1:3) REAL(8):: MF_Nodes(1:4,1:3)
REAL(8):: MF(1:3) REAL(8):: MF(1:3)
@ -530,7 +529,7 @@ MODULE moduleMesh2DCart
self%n3%emData%B(3), & self%n3%emData%B(3), &
self%n4%emData%B(3) /) self%n4%emData%B(3) /)
fPsi = self%fPsi(xi) CALL self%fPsi(Xi, fPsi)
MF = MATMUL(fPsi(:), MF_Nodes) MF = MATMUL(fPsi(:), MF_Nodes)
END FUNCTION gatherMFQuad END FUNCTION gatherMFQuad
@ -548,47 +547,47 @@ MODULE moduleMesh2DCart
END FUNCTION getNodesQuad END FUNCTION getNodesQuad
!Transforms physical coordinates to element coordinates !Transforms physical coordinates to element coordinates
PURE FUNCTION phy2logQuad(self,r) RESULT(xN) PURE FUNCTION phy2logQuad(self,r) RESULT(XiN)
IMPLICIT NONE IMPLICIT NONE
CLASS(meshVol2DCartQuad), INTENT(in):: self CLASS(meshVol2DCartQuad), INTENT(in):: self
REAL(8), INTENT(in):: r(1:3) REAL(8), INTENT(in):: r(1:3)
REAL(8):: xN(1:3) REAL(8):: XiN(1:3)
REAL(8):: xO(1:3), detJ, invJ(1:2,1:2), f(1:2) REAL(8):: XiO(1:3), detJ, invJ(1:2,1:2), f(1:2)
REAL(8):: dPsi(1:2,1:4), fPsi(1:4) REAL(8):: dPsi(1:2,1:4), fPsi(1:4)
REAL(8):: conv REAL(8):: conv
!Iterative newton method to transform coordinates !Iterative newton method to transform coordinates
conv=1.D0 conv=1.D0
xO=0.D0 XiO=0.D0
DO WHILE(conv>1.D-4) DO WHILE(conv>1.D-4)
dPsi = self%dPsi(xO) dPsi = self%dPsi(XiO)
invJ = self%invJac(xO, dPsi) invJ = self%invJac(XiO, dPsi)
fPsi = self%fPsi(xO) CALL self%fPsi(XiO, fPsi)
f(1) = DOT_PRODUCT(fPsi,self%x)-r(1) f(1) = DOT_PRODUCT(fPsi,self%x)-r(1)
f(2) = DOT_PRODUCT(fPsi,self%y)-r(2) f(2) = DOT_PRODUCT(fPsi,self%y)-r(2)
detJ = self%detJac(xO,dPsi) detJ = self%detJac(XiO,dPsi)
xN(1:2)=xO(1:2) - MATMUL(invJ, f)/detJ XiN(1:2)=XiO(1:2) - MATMUL(invJ, f)/detJ
conv=MAXVAL(DABS(xN-xO),1) conv=MAXVAL(DABS(XiN-XiO),1)
xO=xN XiO=XiN
END DO END DO
END FUNCTION phy2logQuad END FUNCTION phy2logQuad
!Gets the next element for a logical position xi !Gets the next element for a logical position Xi
SUBROUTINE nextElementQuad(self, xi, nextElement) SUBROUTINE nextElementQuad(self, Xi, nextElement)
IMPLICIT NONE IMPLICIT NONE
CLASS(meshVol2DCartQuad), INTENT(in):: self CLASS(meshVol2DCartQuad), INTENT(in):: self
REAL(8), INTENT(in):: xi(1:3) REAL(8), INTENT(in):: Xi(1:3)
CLASS(meshElement), POINTER, INTENT(out):: nextElement CLASS(meshElement), POINTER, INTENT(out):: nextElement
REAL(8):: xiArray(1:4) REAL(8):: XiArray(1:4)
INTEGER:: nextInt INTEGER:: nextInt
xiArray = (/ -xi(2), xi(1), xi(2), -xi(1) /) XiArray = (/ -Xi(2), Xi(1), Xi(2), -Xi(1) /)
nextInt = MAXLOC(xiArray,1) nextInt = MAXLOC(XiArray,1)
!Selects the higher value of directions and searches in that direction !Selects the higher value of directions and searches in that direction
NULLIFY(nextElement) NULLIFY(nextElement)
SELECT CASE (nextInt) SELECT CASE (nextInt)
@ -649,14 +648,14 @@ MODULE moduleMesh2DCart
CLASS(meshVol2DCartTria), INTENT(in):: self CLASS(meshVol2DCartTria), INTENT(in):: self
REAL(8):: r(1:3) REAL(8):: r(1:3)
REAL(8):: xii(1:3) REAL(8):: Xi(1:3)
REAL(8), ALLOCATABLE:: fPsi(:) REAL(8):: fPsi(1:3)
xii(1) = random( 0.D0, 1.D0) Xi(1) = random( 0.D0, 1.D0)
xii(2) = random( 0.D0, 1.D0 - xii(1)) Xi(2) = random( 0.D0, 1.D0 - Xi(1))
xii(3) = 0.D0 Xi(3) = 0.D0
fPsi = self%fPsi(xii) CALL self%fPsi(Xi, fPsi)
r(1) = DOT_PRODUCT(fPsi, self%x) r(1) = DOT_PRODUCT(fPsi, self%x)
r(2) = DOT_PRODUCT(fPsi, self%y) r(2) = DOT_PRODUCT(fPsi, self%y)
@ -669,55 +668,53 @@ MODULE moduleMesh2DCart
IMPLICIT NONE IMPLICIT NONE
CLASS(meshVol2DCartTria), INTENT(inout):: self CLASS(meshVol2DCartTria), INTENT(inout):: self
REAL(8):: xi(1:3) REAL(8):: Xi(1:3)
REAL(8):: detJ REAL(8):: detJ
REAL(8):: fPsi(1:3) REAL(8):: fPsi(1:3)
self%volume = 0.D0 self%volume = 0.D0
self%arNodes = 0.D0 self%arNodes = 0.D0
!2D 1 point Gauss Quad Integral !2D 1 point Gauss Quad Integral
xi = (/1.D0/3.D0, 1.D0/3.D0, 0.D0 /) Xi = (/1.D0/3.D0, 1.D0/3.D0, 0.D0 /)
detJ = self%detJac(xi)/2.D0 detJ = self%detJac(Xi)/2.D0
fPsi = self%fPsi(xi) CALL self%fPsi(Xi, fPsi)
self%volume = detJ self%volume = detJ
self%arNodes = fPsi*detJ self%arNodes = fPsi*detJ
END SUBROUTINE areaTria END SUBROUTINE areaTria
!Shape functions for triangular element !Shape functions for triangular element
PURE FUNCTION fPsiTria(xi) RESULT(fPsi) PURE SUBROUTINE fPsiTria(Xi, fPsi)
IMPLICIT NONE IMPLICIT NONE
REAL(8), INTENT(in):: xi(1:3) REAL(8), INTENT(in):: Xi(1:3)
REAL(8), ALLOCATABLE:: fPsi(:) REAL(8), INTENT(out):: fPsi(:)
ALLOCATE(fPsi(1:3)) fPsi(1) = 1.D0 - Xi(1) - Xi(2)
fPsi(2) = Xi(1)
fPsi(3) = Xi(2)
fPsi(1) = 1.D0 - xi(1) - xi(2) END SUBROUTINE fPsiTria
fPsi(2) = xi(1)
fPsi(3) = xi(2)
END FUNCTION fPsiTria !Derivative element function at coordinates Xi
PURE FUNCTION dPsiTria(Xi) RESULT(dPsi)
!Derivative element function at coordinates xi
PURE FUNCTION dPsiTria(xi) RESULT(dPsi)
IMPLICIT NONE IMPLICIT NONE
REAL(8), INTENT(in):: xi(1:3) REAL(8), INTENT(in):: Xi(1:3)
REAL(8), ALLOCATABLE:: dPsi(:,:) REAL(8), ALLOCATABLE:: dPsi(:,:)
ALLOCATE(dPsi(1:2,1:3)) ALLOCATE(dPsi(1:2,1:3))
dPsi(1,:) = dPsiTriaXi1(xi(2)) dPsi(1,:) = dPsiTriaXi1(Xi(2))
dPsi(2,:) = dPsiTriaXi2(xi(1)) dPsi(2,:) = dPsiTriaXi2(Xi(1))
END FUNCTION dPsiTria END FUNCTION dPsiTria
!Derivative element function (xi1) !Derivative element function (Xi1)
PURE FUNCTION dPsiTriaXi1(xi2) RESULT(dPsiXi1) PURE FUNCTION dPsiTriaXi1(Xi2) RESULT(dPsiXi1)
IMPLICIT NONE IMPLICIT NONE
REAL(8), INTENT(in):: xi2 REAL(8), INTENT(in):: Xi2
REAL(8):: dPsiXi1(1:3) REAL(8):: dPsiXi1(1:3)
dPsiXi1(1) = -1.D0 dPsiXi1(1) = -1.D0
@ -726,11 +723,11 @@ MODULE moduleMesh2DCart
END FUNCTION dPsiTriaXi1 END FUNCTION dPsiTriaXi1
!Derivative element function (xi1) !Derivative element function (Xi1)
PURE FUNCTION dPsiTriaXi2(xi1) RESULT(dPsiXi2) PURE FUNCTION dPsiTriaXi2(Xi1) RESULT(dPsiXi2)
IMPLICIT NONE IMPLICIT NONE
REAL(8), INTENT(in):: xi1 REAL(8), INTENT(in):: Xi1
REAL(8):: dPsiXi2(1:3) REAL(8):: dPsiXi2(1:3)
dPsiXi2(1) = -1.D0 dPsiXi2(1) = -1.D0
@ -759,22 +756,22 @@ MODULE moduleMesh2DCart
CLASS(meshVol2DCartTria), INTENT(in):: self CLASS(meshVol2DCartTria), INTENT(in):: self
REAL(8), ALLOCATABLE:: localK(:,:) REAL(8), ALLOCATABLE:: localK(:,:)
REAL(8):: xi(1:3) REAL(8):: Xi(1:3)
REAL(8):: fPsi(1:3), dPsi(1:2,1:3) REAL(8):: fPsi(1:3), dPsi(1:2,1:3)
REAL(8):: invJ(1:2,1:2), detJ REAL(8):: invJ(1:2,1:2), detJ
INTEGER:: l INTEGER:: l
ALLOCATE(localK(1:4, 1:4)) ALLOCATE(localK(1:4, 1:4))
localK=0.D0 localK=0.D0
xi=0.D0 Xi=0.D0
!Start 2D Gauss Quad Integral !Start 2D Gauss Quad Integral
DO l=1, 4 DO l=1, 4
xi(1) = xi1Tria(l) Xi(1) = Xi1Tria(l)
xi(2) = xi2Tria(l) Xi(2) = Xi2Tria(l)
dPsi = self%dPsi(xi) dPsi = self%dPsi(Xi)
detJ = self%detJac(xi,dPsi) detJ = self%detJac(Xi,dPsi)
invJ = self%invJac(xi,dPsi) invJ = self%invJac(Xi,dPsi)
fPsi = self%fPsi(xi) CALL self%fPsi(Xi, fPsi)
localK = localK + MATMUL(TRANSPOSE(MATMUL(invJ,dPsi)),MATMUL(invJ,dPsi))*wTria(l)/detJ localK = localK + MATMUL(TRANSPOSE(MATMUL(invJ,dPsi)),MATMUL(invJ,dPsi))*wTria(l)/detJ
END DO END DO
@ -789,19 +786,19 @@ MODULE moduleMesh2DCart
REAL(8), INTENT(in):: source(1:) REAL(8), INTENT(in):: source(1:)
REAL(8), ALLOCATABLE:: localF(:) REAL(8), ALLOCATABLE:: localF(:)
REAL(8):: fPsi(1:3) REAL(8):: fPsi(1:3)
REAL(8):: xi(1:3) REAL(8):: Xi(1:3)
REAL(8):: detJ, f REAL(8):: detJ, f
INTEGER:: l INTEGER:: l
ALLOCATE(localF(1:3)) ALLOCATE(localF(1:3))
localF = 0.D0 localF = 0.D0
xi = 0.D0 Xi = 0.D0
!Start 2D Gauss Quad Integral !Start 2D Gauss Quad Integral
DO l=1, 4 DO l=1, 4
xi(1) = xi1Tria(l) Xi(1) = Xi1Tria(l)
xi(2) = xi2Tria(l) Xi(2) = Xi2Tria(l)
detJ = self%detJac(xi) detJ = self%detJac(Xi)
fPsi = self%fPsi(xi) CALL self%fPsi(Xi, fPsi)
f = DOT_PRODUCT(fPsi,source) f = DOT_PRODUCT(fPsi,source)
localF = localF + f*fPsi*wTria(l)*detJ localF = localF + f*fPsi*wTria(l)*detJ
@ -809,24 +806,24 @@ MODULE moduleMesh2DCart
END FUNCTION elemFTria END FUNCTION elemFTria
PURE FUNCTION insideTria(xi) RESULT(ins) PURE FUNCTION insideTria(Xi) RESULT(ins)
IMPLICIT NONE IMPLICIT NONE
REAL(8), INTENT(in):: xi(1:3) REAL(8), INTENT(in):: Xi(1:3)
LOGICAL:: ins LOGICAL:: ins
ins = xi(1) >= 0.D0 .AND. & ins = Xi(1) >= 0.D0 .AND. &
xi(2) >= 0.D0 .AND. & Xi(2) >= 0.D0 .AND. &
1.D0 - xi(1) - xi(2) >= 0.D0 1.D0 - Xi(1) - Xi(2) >= 0.D0
END FUNCTION insideTria END FUNCTION insideTria
!Gathers the electric field at position xi !Gathers the electric field at position Xi
PURE FUNCTION gatherEFTria(self,xi) RESULT(EF) PURE FUNCTION gatherEFTria(self,Xi) RESULT(EF)
IMPLICIT NONE IMPLICIT NONE
CLASS(meshVol2DCartTria), INTENT(in):: self CLASS(meshVol2DCartTria), INTENT(in):: self
REAL(8), INTENT(in):: xi(1:3) REAL(8), INTENT(in):: Xi(1:3)
REAL(8):: dPsi(1:2,1:3) REAL(8):: dPsi(1:2,1:3)
REAL(8):: dPsiR(1:2,1:3)!Derivative of shpae functions in global coordinates REAL(8):: dPsiR(1:2,1:3)!Derivative of shpae functions in global coordinates
REAL(8):: invJ(1:2,1:2), detJ REAL(8):: invJ(1:2,1:2), detJ
@ -837,9 +834,9 @@ MODULE moduleMesh2DCart
self%n2%emData%phi, & self%n2%emData%phi, &
self%n3%emData%phi /) self%n3%emData%phi /)
dPsi = self%dPsi(xi) dPsi = self%dPsi(Xi)
detJ = self%detJac(xi,dPsi) detJ = self%detJac(Xi,dPsi)
invJ = self%invJac(xi,dPsi) invJ = self%invJac(Xi,dPsi)
dPsiR = MATMUL(invJ, dPsi)/detJ dPsiR = MATMUL(invJ, dPsi)/detJ
EF(1) = -DOT_PRODUCT(dPsiR(1,:), phi) EF(1) = -DOT_PRODUCT(dPsiR(1,:), phi)
EF(2) = -DOT_PRODUCT(dPsiR(2,:), phi) EF(2) = -DOT_PRODUCT(dPsiR(2,:), phi)
@ -847,11 +844,11 @@ MODULE moduleMesh2DCart
END FUNCTION gatherEFTria END FUNCTION gatherEFTria
PURE FUNCTION gatherMFTria(self,xi) RESULT(MF) PURE FUNCTION gatherMFTria(self,Xi) RESULT(MF)
IMPLICIT NONE IMPLICIT NONE
CLASS(meshVol2DCartTria), INTENT(in):: self CLASS(meshVol2DCartTria), INTENT(in):: self
REAL(8), INTENT(in):: xi(1:3) REAL(8), INTENT(in):: Xi(1:3)
REAL(8):: fPsi(1:3) REAL(8):: fPsi(1:3)
REAL(8):: MF_Nodes(1:3,1:3) REAL(8):: MF_Nodes(1:3,1:3)
REAL(8):: MF(1:3) REAL(8):: MF(1:3)
@ -866,7 +863,7 @@ MODULE moduleMesh2DCart
self%n2%emData%B(3), & self%n2%emData%B(3), &
self%n3%emData%B(3) /) self%n3%emData%B(3) /)
fPsi = self%fPsi(xi) CALL self%fPsi(Xi, fPsi)
MF = MATMUL(fPsi, MF_Nodes) MF = MATMUL(fPsi, MF_Nodes)
END FUNCTION gatherMFTria END FUNCTION gatherMFTria
@ -884,37 +881,37 @@ MODULE moduleMesh2DCart
END FUNCTION getNodesTria END FUNCTION getNodesTria
!Transforms physical coordinates to element coordinates !Transforms physical coordinates to element coordinates
PURE FUNCTION phy2logTria(self,r) RESULT(xi) PURE FUNCTION phy2logTria(self,r) RESULT(Xi)
IMPLICIT NONE IMPLICIT NONE
CLASS(meshVol2DCartTria), INTENT(in):: self CLASS(meshVol2DCartTria), INTENT(in):: self
REAL(8), INTENT(in):: r(1:3) REAL(8), INTENT(in):: r(1:3)
REAL(8):: xi(1:3) REAL(8):: Xi(1:3)
REAL(8):: invJ(1:2,1:2), detJ REAL(8):: invJ(1:2,1:2), detJ
REAL(8):: deltaR(1:2) REAL(8):: deltaR(1:2)
REAL(8):: dPsi(1:2,1:3) REAL(8):: dPsi(1:2,1:3)
!Direct method to convert coordinates !Direct method to convert coordinates
xi = 0.D0 !Irrelevant, required for input Xi = 0.D0 !Irrelevant, required for input
deltaR = (/ r(1) - self%x(1), r(2) - self%y(1) /) deltaR = (/ r(1) - self%x(1), r(2) - self%y(1) /)
dPsi = self%dPsi(xi) dPsi = self%dPsi(Xi)
invJ = self%invJac(xi, dPsi) invJ = self%invJac(Xi, dPsi)
detJ = self%detJac(xi, dPsi) detJ = self%detJac(Xi, dPsi)
xi(1:2) = MATMUL(invJ,deltaR)/detJ Xi(1:2) = MATMUL(invJ,deltaR)/detJ
END FUNCTION phy2logTria END FUNCTION phy2logTria
SUBROUTINE nextElementTria(self, xi, nextElement) SUBROUTINE nextElementTria(self, Xi, nextElement)
IMPLICIT NONE IMPLICIT NONE
CLASS(meshVol2DCartTria), INTENT(in):: self CLASS(meshVol2DCartTria), INTENT(in):: self
REAL(8), INTENT(in):: xi(1:3) REAL(8), INTENT(in):: Xi(1:3)
CLASS(meshElement), POINTER, INTENT(out):: nextElement CLASS(meshElement), POINTER, INTENT(out):: nextElement
REAL(8):: xiArray(1:3) REAL(8):: XiArray(1:3)
INTEGER:: nextInt INTEGER:: nextInt
xiArray = (/ xi(2), 1.D0-xi(1)-xi(2), xi(1) /) XiArray = (/ Xi(2), 1.D0-Xi(1)-Xi(2), Xi(1) /)
nextInt = MINLOC(xiArray,1) nextInt = MINLOC(XiArray,1)
NULLIFY(nextElement) NULLIFY(nextElement)
SELECT CASE (nextInt) SELECT CASE (nextInt)
CASE (1) CASE (1)
@ -929,11 +926,11 @@ MODULE moduleMesh2DCart
!COMMON FUNCTIONS FOR CARTESIAN VOLUME ELEMENTS IN 2D !COMMON FUNCTIONS FOR CARTESIAN VOLUME ELEMENTS IN 2D
!Computes element Jacobian determinant !Computes element Jacobian determinant
PURE FUNCTION detJ2DCart(self, xi, dPsi_in) RESULT(dJ) PURE FUNCTION detJ2DCart(self, Xi, dPsi_in) RESULT(dJ)
IMPLICIT NONE IMPLICIT NONE
CLASS(meshVol2DCart), INTENT(in):: self CLASS(meshVol2DCart), INTENT(in):: self
REAL(8), INTENT(in):: xi(1:3) REAL(8), INTENT(in):: Xi(1:3)
REAL(8), INTENT(in), OPTIONAL:: dPsi_in(1:,1:) REAL(8), INTENT(in), OPTIONAL:: dPsi_in(1:,1:)
REAL(8), ALLOCATABLE:: dPsi(:,:) REAL(8), ALLOCATABLE:: dPsi(:,:)
REAL(8):: dJ REAL(8):: dJ
@ -943,7 +940,7 @@ MODULE moduleMesh2DCart
dPsi = dPsi_in dPsi = dPsi_in
ELSE ELSE
dPsi = self%dPsi(xi) dPsi = self%dPsi(Xi)
END IF END IF
@ -953,11 +950,11 @@ MODULE moduleMesh2DCart
END FUNCTION detJ2DCart END FUNCTION detJ2DCart
!Computes element Jacobian inverse matrix (without determinant) !Computes element Jacobian inverse matrix (without determinant)
PURE FUNCTION invJ2DCart(self,xi,dPsi_in) RESULT(invJ) PURE FUNCTION invJ2DCart(self,Xi,dPsi_in) RESULT(invJ)
IMPLICIT NONE IMPLICIT NONE
CLASS(meshVol2DCart), INTENT(in):: self CLASS(meshVol2DCart), INTENT(in):: self
REAL(8), INTENT(in):: xi(1:3) REAL(8), INTENT(in):: Xi(1:3)
REAL(8), INTENT(in), OPTIONAL:: dPsi_in(1:,1:) REAL(8), INTENT(in), OPTIONAL:: dPsi_in(1:,1:)
REAL(8), ALLOCATABLE:: dPsi(:,:) REAL(8), ALLOCATABLE:: dPsi(:,:)
REAL(8):: dx(1:2), dy(1:2) REAL(8):: dx(1:2), dy(1:2)
@ -967,7 +964,7 @@ MODULE moduleMesh2DCart
dPsi=dPsi_in dPsi=dPsi_in
ELSE ELSE
dPsi = self%dPsi(xi) dPsi = self%dPsi(Xi)
END IF END IF

107
src/modules/mesh/2DCyl/moduleMesh2DCyl.f90
View file

@ -310,49 +310,52 @@ MODULE moduleMesh2DCyl
CLASS(meshVol2DCylQuad), INTENT(inout):: self CLASS(meshVol2DCylQuad), INTENT(inout):: self
REAL(8):: r, xi(1:3) REAL(8):: r, xi(1:3)
REAL(8):: detJ REAL(8):: detJ
REAL(8):: fPsi(1:4) REAL(8):: fPsi(1:4), fPsi_node(1:4)
self%volume = 0.D0 self%volume = 0.D0
self%arNodes = 0.D0 self%arNodes = 0.D0
!2D 1 point Gauss Quad Integral !2D 1 point Gauss Quad Integral
xi = 0.D0 xi = 0.D0
detJ = self%detJac(xi)*PI8 !4*2*pi detJ = self%detJac(xi)*PI8 !4*2*pi
fPsi = self%fPsi(xi) CALL self%fPsi(xi, fPsi)
!Computes total volume of the cell !Computes total volume of the cell
r = DOT_PRODUCT(fPsi,self%r) r = DOT_PRODUCT(fPsi,self%r)
self%volume = r*detJ self%volume = r*detJ
!Computes volume per node !Computes volume per node
xi = (/-5.D-1, -5.D-1, 0.D0/) xi = (/-5.D-1, -5.D-1, 0.D0/)
r = DOT_PRODUCT(self%fPsi(xi),self%r) CALL self%fPsi(xi, fPsi_node)
r = DOT_PRODUCT(fPsi_node,self%r)
self%arNodes(1) = fPsi(1)*r*detJ self%arNodes(1) = fPsi(1)*r*detJ
xi = (/ 5.D-1, -5.D-1, 0.D0/) xi = (/ 5.D-1, -5.D-1, 0.D0/)
r = DOT_PRODUCT(self%fPsi(xi),self%r) CALL self%fPsi(xi, fPsi_node)
r = DOT_PRODUCT(fPsi_node,self%r)
self%arNodes(2) = fPsi(2)*r*detJ self%arNodes(2) = fPsi(2)*r*detJ
xi = (/ 5.D-1, 5.D-1, 0.D0/) xi = (/ 5.D-1, 5.D-1, 0.D0/)
r = DOT_PRODUCT(self%fPsi(xi),self%r) CALL self%fPsi(xi, fPsi_node)
r = DOT_PRODUCT(fPsi_node,self%r)
self%arNodes(3) = fPsi(3)*r*detJ self%arNodes(3) = fPsi(3)*r*detJ
xi = (/-5.D-1, 5.D-1, 0.D0/) xi = (/-5.D-1, 5.D-1, 0.D0/)
r = DOT_PRODUCT(self%fPsi(xi),self%r) CALL self%fPsi(xi, fPsi_node)
r = DOT_PRODUCT(fPsi_node,self%r)
self%arNodes(4) = fPsi(4)*r*detJ self%arNodes(4) = fPsi(4)*r*detJ
END SUBROUTINE areaQuad END SUBROUTINE areaQuad
!Computes element functions in point xi !Computes element functions in point xi
PURE FUNCTION fPsiQuad(xi) RESULT(fPsi) PURE SUBROUTINE fPsiQuad(xi, fPsi)
IMPLICIT NONE IMPLICIT NONE
REAL(8),INTENT(in):: xi(1:3) REAL(8), INTENT(in):: xi(1:3)
REAL(8), ALLOCATABLE:: fPsi(:) REAL(8), INTENT(out):: fPsi(:)
ALLOCATE(fPsi(1:4)) 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(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 fPsi = fPsi*0.25D0
END FUNCTION fPsiQuad END SUBROUTINE fPsiQuad
!Derivative element function at coordinates xi !Derivative element function at coordinates xi
PURE FUNCTION dPsiQuad(xi) RESULT(dPsi) PURE FUNCTION dPsiQuad(xi) RESULT(dPsi)
@ -375,10 +378,11 @@ MODULE moduleMesh2DCyl
REAL(8),INTENT(in):: xi2 REAL(8),INTENT(in):: xi2
REAL(8):: dPsiXi1(1:4) REAL(8):: dPsiXi1(1:4)
dPsiXi1(1) = -(1.D0-xi2) dPsiXi1(1) = -(1.D0 - xi2)
dPsiXi1(2) = (1.D0-xi2) dPsiXi1(2) = (1.D0 - xi2)
dPsiXi1(3) = (1.D0+xi2) dPsiXi1(3) = (1.D0 + xi2)
dPsiXi1(4) = -(1.D0+xi2) dPsiXi1(4) = -(1.D0 + xi2)
dPsiXi1 = dPsiXi1*0.25D0 dPsiXi1 = dPsiXi1*0.25D0
END FUNCTION dPsiQuadXi1 END FUNCTION dPsiQuadXi1
@ -390,11 +394,12 @@ MODULE moduleMesh2DCyl
REAL(8),INTENT(in):: xi1 REAL(8),INTENT(in):: xi1
REAL(8):: dPsiXi2(1:4) REAL(8):: dPsiXi2(1:4)
dPsiXi2(1) = -(1.D0-xi1) dPsiXi2(1) = -(1.D0 - xi1)
dPsiXi2(2) = -(1.D0+xi1) dPsiXi2(2) = -(1.D0 + xi1)
dPsiXi2(3) = (1.D0+xi1) dPsiXi2(3) = (1.D0 + xi1)
dPsiXi2(4) = (1.D0-xi1) dPsiXi2(4) = (1.D0 - xi1)
dPsiXi2 = dPsiXi2*0.25D0
dPsiXi2 = dPsiXi2 * 0.25D0
END FUNCTION dPsiQuadXi2 END FUNCTION dPsiQuadXi2
@ -427,7 +432,7 @@ MODULE moduleMesh2DCyl
xii(2) = random(-1.D0, 1.D0) xii(2) = random(-1.D0, 1.D0)
xii(3) = 0.D0 xii(3) = 0.D0
fPsi = self%fPsi(xii) CALL self%fPsi(xii, fPsi)
r(1) = DOT_PRODUCT(fPsi, self%z) r(1) = DOT_PRODUCT(fPsi, self%z)
r(2) = DOT_PRODUCT(fPsi, self%r) r(2) = DOT_PRODUCT(fPsi, self%r)
@ -457,7 +462,7 @@ MODULE moduleMesh2DCyl
DO m = 1, 3 DO m = 1, 3
xi(1) = corQuad(m) xi(1) = corQuad(m)
dPsi(2,:) = self%dPsiXi2(xi(1)) dPsi(2,:) = self%dPsiXi2(xi(1))
fPsi = self%fPsi(xi) CALL self%fPsi(xi, fPsi)
detJ = self%detJac(xi,dPsi) detJ = self%detJac(xi,dPsi)
invJ = self%invJac(xi,dPsi) invJ = self%invJac(xi,dPsi)
r = DOT_PRODUCT(fPsi,self%r) r = DOT_PRODUCT(fPsi,self%r)
@ -492,7 +497,7 @@ MODULE moduleMesh2DCyl
DO m = 1, 3 DO m = 1, 3
xi(2) = corQuad(m) xi(2) = corQuad(m)
detJ = self%detJac(xi) detJ = self%detJac(xi)
fPsi = self%fPsi(xi) CALL self%fPsi(xi, fPsi)
r = DOT_PRODUCT(fPsi,self%r) r = DOT_PRODUCT(fPsi,self%r)
f = DOT_PRODUCT(fPsi,source) f = DOT_PRODUCT(fPsi,source)
localF = localF + r*f*fPsi*wQuad(l)*wQuad(m)*detJ localF = localF + r*f*fPsi*wQuad(l)*wQuad(m)*detJ
@ -564,7 +569,7 @@ MODULE moduleMesh2DCyl
self%n3%emData%B(3), & self%n3%emData%B(3), &
self%n4%emData%B(3) /) self%n4%emData%B(3) /)
fPsi = self%fPsi(xi) CALL self%fPsi(xi, fPsi)
MF = MATMUL(fPsi(:), MF_Nodes) MF = MATMUL(fPsi(:), MF_Nodes)
END FUNCTION gatherMFQuad END FUNCTION gatherMFQuad
@ -582,30 +587,30 @@ MODULE moduleMesh2DCyl
END FUNCTION getNodesQuad END FUNCTION getNodesQuad
!Transforms physical coordinates to element coordinates !Transforms physical coordinates to element coordinates
PURE FUNCTION phy2logQuad(self,r) RESULT(xN) PURE FUNCTION phy2logQuad(self,r) RESULT(XiN)
IMPLICIT NONE IMPLICIT NONE
CLASS(meshVol2DCylQuad), INTENT(in):: self CLASS(meshVol2DCylQuad), INTENT(in):: self
REAL(8), INTENT(in):: r(1:3) REAL(8), INTENT(in):: r(1:3)
REAL(8):: xN(1:3) REAL(8):: XiN(1:3)
REAL(8):: xO(1:3), detJ, invJ(1:2,1:2), f(1:2) REAL(8):: XiO(1:3), detJ, invJ(1:2,1:2), f(1:2)
REAL(8):: dPsi(1:2,1:4), fPsi(1:4) REAL(8):: dPsi(1:2,1:4), fPsi(1:4)
REAL(8):: conv REAL(8):: conv
!Iterative newton method to transform coordinates !Iterative newton method to transform coordinates
conv=1.D0 conv=1.D0
xO=0.D0 XiO=0.D0
DO WHILE(conv>1.D-4) DO WHILE(conv>1.D-3)
dPsi = self%dPsi(xO) CALL self%fPsi(XiO, fPsi)
invJ = self%invJac(xO, dPsi) f = (/ DOT_PRODUCT(fPsi,self%z)-r(1), &
fPsi = self%fPsi(xO) DOT_PRODUCT(fPsi,self%r)-r(2) /)
f(1) = DOT_PRODUCT(fPsi,self%z)-r(1) dPsi = self%dPsi(XiO)
f(2) = DOT_PRODUCT(fPsi,self%r)-r(2) invJ = self%invJac(XiO, dPsi)
detJ = self%detJac(xO,dPsi) detJ = self%detJac(XiO,dPsi)
xN(1:2)=xO(1:2) - MATMUL(invJ, f)/detJ XiN(1:2)=XiO(1:2) - MATMUL(invJ, f)/detJ
conv=MAXVAL(DABS(xN-xO),1) conv=MAXVAL(DABS(XiN-XiO),1)
xO=xN XiO=XiN
END DO END DO
@ -690,7 +695,7 @@ MODULE moduleMesh2DCyl
xii(2) = random( 0.D0, 1.D0 - xii(1)) xii(2) = random( 0.D0, 1.D0 - xii(1))
xii(3) = 0.D0 xii(3) = 0.D0
fPsi = self%fPsi(xii) CALL self%fPsi(xii, fPsi)
r(1) = DOT_PRODUCT(fPsi, self%z) r(1) = DOT_PRODUCT(fPsi, self%z)
r(2) = DOT_PRODUCT(fPsi, self%r) r(2) = DOT_PRODUCT(fPsi, self%r)
@ -713,7 +718,7 @@ MODULE moduleMesh2DCyl
!2D 1 point Gauss Quad Integral !2D 1 point Gauss Quad Integral
xi = (/1.D0/3.D0, 1.D0/3.D0, 0.D0 /) xi = (/1.D0/3.D0, 1.D0/3.D0, 0.D0 /)
detJ = self%detJac(xi)*PI !2PI*1/2 detJ = self%detJac(xi)*PI !2PI*1/2
fPsi = self%fPsi(xi) CALL self%fPsi(xi, fPsi)
!Computes total volume of the cell !Computes total volume of the cell
r = DOT_PRODUCT(fPsi,self%r) r = DOT_PRODUCT(fPsi,self%r)
self%volume = r*detJ self%volume = r*detJ
@ -723,19 +728,17 @@ MODULE moduleMesh2DCyl
END SUBROUTINE areaTria END SUBROUTINE areaTria
!Shape functions for triangular element !Shape functions for triangular element
PURE FUNCTION fPsiTria(xi) RESULT(fPsi) PURE SUBROUTINE fPsiTria(xi, fPsi)
IMPLICIT NONE IMPLICIT NONE
REAL(8), INTENT(in):: xi(1:3) REAL(8), INTENT(in):: xi(1:3)
REAL(8), ALLOCATABLE:: fPsi(:) REAL(8), INTENT(out):: fPsi(:)
ALLOCATE(fPsi(1:3))
fPsi(1) = 1.D0 - xi(1) - xi(2) fPsi(1) = 1.D0 - xi(1) - xi(2)
fPsi(2) = xi(1) fPsi(2) = xi(1)
fPsi(3) = xi(2) fPsi(3) = xi(2)
END FUNCTION fPsiTria END SUBROUTINE fPsiTria
!Derivative element function at coordinates xi !Derivative element function at coordinates xi
PURE FUNCTION dPsiTria(xi) RESULT(dPsi) PURE FUNCTION dPsiTria(xi) RESULT(dPsi)
@ -813,7 +816,7 @@ MODULE moduleMesh2DCyl
dPsi = self%dPsi(xi) dPsi = self%dPsi(xi)
detJ = self%detJac(xi,dPsi) detJ = self%detJac(xi,dPsi)
invJ = self%invJac(xi,dPsi) invJ = self%invJac(xi,dPsi)
fPsi = self%fPsi(xi) CALL self%fPsi(xi, fPsi)
r = DOT_PRODUCT(fPsi,self%r) r = DOT_PRODUCT(fPsi,self%r)
localK = localK + MATMUL(TRANSPOSE(MATMUL(invJ,dPsi)),MATMUL(invJ,dPsi))*r*wTria(l)/detJ localK = localK + MATMUL(TRANSPOSE(MATMUL(invJ,dPsi)),MATMUL(invJ,dPsi))*r*wTria(l)/detJ
@ -843,7 +846,7 @@ MODULE moduleMesh2DCyl
xi(1) = xi1Tria(l) xi(1) = xi1Tria(l)
xi(2) = xi2Tria(l) xi(2) = xi2Tria(l)
detJ = self%detJac(xi) detJ = self%detJac(xi)
fPsi = self%fPsi(xi) CALL self%fPsi(xi, fPsi)
r = DOT_PRODUCT(fPsi,self%r) r = DOT_PRODUCT(fPsi,self%r)
f = DOT_PRODUCT(fPsi,source) f = DOT_PRODUCT(fPsi,source)
localF = localF + r*f*fPsi*wTria(l)*detJ localF = localF + r*f*fPsi*wTria(l)*detJ
@ -910,7 +913,7 @@ MODULE moduleMesh2DCyl
self%n2%emData%B(3), & self%n2%emData%B(3), &
self%n3%emData%B(3) /) self%n3%emData%B(3) /)
fPsi = self%fPsi(xi) CALL self%fPsi(xi, fPsi)
MF = MATMUL(fPsi, MF_Nodes) MF = MATMUL(fPsi, MF_Nodes)
END FUNCTION gatherMFTria END FUNCTION gatherMFTria

237
src/modules/mesh/3DCart/moduleMesh3DCart.f90
View file

@ -41,8 +41,8 @@ MODULE moduleMesh3DCart
END TYPE meshVol3DCart END TYPE meshVol3DCart
ABSTRACT INTERFACE ABSTRACT INTERFACE
PURE FUNCTION dPsi_interface(xii) RESULT(dPsi) PURE FUNCTION dPsi_interface(Xi) RESULT(dPsi)
REAL(8), INTENT(in):: xii(1:3) REAL(8), INTENT(in):: Xi(1:3)
REAL(8), ALLOCATABLE:: dPsi(:,:) REAL(8), ALLOCATABLE:: dPsi(:,:)
END FUNCTION dPsi_interface END FUNCTION dPsi_interface
@ -71,8 +71,8 @@ MODULE moduleMesh3DCart
PROCEDURE, PASS:: calcVol => volumeTetra PROCEDURE, PASS:: calcVol => volumeTetra
PROCEDURE, NOPASS:: fPsi => fPsiTetra PROCEDURE, NOPASS:: fPsi => fPsiTetra
PROCEDURE, NOPASS:: dPsi => dPsiTetra PROCEDURE, NOPASS:: dPsi => dPsiTetra
PROCEDURE, NOPASS:: dPsiXi1 => dPsiTetraXii1 PROCEDURE, NOPASS:: dPsiXi1 => dPsiTetraXi1
PROCEDURE, NOPASS:: dPsiXi2 => dPsiTetraXii2 PROCEDURE, NOPASS:: dPsiXi2 => dPsiTetraXi2
PROCEDURE, PASS:: partialDer => partialDerTetra PROCEDURE, PASS:: partialDer => partialDerTetra
PROCEDURE, PASS:: elemK => elemKTetra PROCEDURE, PASS:: elemK => elemKTetra
PROCEDURE, PASS:: elemF => elemFTetra PROCEDURE, PASS:: elemF => elemFTetra
@ -213,14 +213,14 @@ MODULE moduleMesh3DCart
CLASS(meshEdge3DCartTria), INTENT(in):: self CLASS(meshEdge3DCartTria), INTENT(in):: self
REAL(8):: r(1:3) REAL(8):: r(1:3)
REAL(8):: xii(1:3) REAL(8):: Xi(1:3)
REAL(8):: fPsi(1:3) REAL(8):: fPsi(1:3)
xii(1) = random( 0.D0, 1.D0) Xi(1) = random( 0.D0, 1.D0)
xii(2) = random( 0.D0, 1.D0 - xii(1)) Xi(2) = random( 0.D0, 1.D0 - Xi(1))
xii(3) = 0.D0 Xi(3) = 0.D0
fPsi = self%fPsi(xii) fPsi = self%fPsi(Xi)
r = (/DOT_PRODUCT(fPsi, self%x), & r = (/DOT_PRODUCT(fPsi, self%x), &
DOT_PRODUCT(fPsi, self%y), & DOT_PRODUCT(fPsi, self%y), &
DOT_PRODUCT(fPsi, self%z)/) DOT_PRODUCT(fPsi, self%z)/)
@ -228,17 +228,17 @@ MODULE moduleMesh3DCart
END FUNCTION randPosEdgeTria END FUNCTION randPosEdgeTria
!Shape functions for triangular surface !Shape functions for triangular surface
PURE FUNCTION fPsiEdgeTria(xii) RESULT(fPsi) PURE FUNCTION fPsiEdgeTria(Xi) RESULT(fPsi)
IMPLICIT NONE IMPLICIT NONE
REAL(8), INTENT(in):: xii(1:3) REAL(8), INTENT(in):: Xi(1:3)
REAL(8), ALLOCATABLE:: fPsi(:) REAL(8), ALLOCATABLE:: fPsi(:)
ALLOCATE(fPsi(1:3)) ALLOCATE(fPsi(1:3))
fPsi(1) = 1.D0 - xii(1) - xii(2) fPsi(1) = 1.D0 - Xi(1) - Xi(2)
fPsi(2) = xii(1) fPsi(2) = Xi(1)
fPsi(3) = xii(2) fPsi(3) = Xi(2)
END FUNCTION fPsiEdgeTria END FUNCTION fPsiEdgeTria
@ -254,6 +254,7 @@ MODULE moduleMesh3DCart
INTEGER, INTENT(in):: p(:) INTEGER, INTENT(in):: p(:)
TYPE(meshNodeCont), INTENT(in), TARGET:: nodes(:) TYPE(meshNodeCont), INTENT(in), TARGET:: nodes(:)
REAL(8), DIMENSION(1:3):: r1, r2, r3, r4 !Positions of each node REAL(8), DIMENSION(1:3):: r1, r2, r3, r4 !Positions of each node
REAL(8):: Xi(1:3), fPsi(1:4)
REAL(8):: volNodes(1:4) !Volume of each node REAL(8):: volNodes(1:4) !Volume of each node
self%n = n self%n = n
@ -274,8 +275,9 @@ MODULE moduleMesh3DCart
CALL self%calcVol() CALL self%calcVol()
!Assign proportional volume to each node !Assign proportional volume to each node
!TODO: Review this to apply to all elements in the future Xi = (/0.25D0, 0.25D0, 0.25D0/)
volNodes = self%fPsi((/0.25D0, 0.25D0, 0.25D0/))*self%volume CALL self%fPsi(Xi, fPsi)
volNodes = fPsi*self%volume
self%n1%v = self%n1%v + volNodes(1) self%n1%v = self%n1%v + volNodes(1)
self%n2%v = self%n2%v + volNodes(2) self%n2%v = self%n2%v + volNodes(2)
self%n3%v = self%n3%v + volNodes(3) self%n3%v = self%n3%v + volNodes(3)
@ -295,19 +297,18 @@ MODULE moduleMesh3DCart
CLASS(meshVol3DCartTetra), INTENT(in):: self CLASS(meshVol3DCartTetra), INTENT(in):: self
REAL(8):: r(1:3) REAL(8):: r(1:3)
REAL(8):: xii(1:3) REAL(8):: Xi(1:3)
REAL(8), ALLOCATABLE:: fPsi(:) REAL(8):: fPsi(1:4)
xii(1) = random( 0.D0, 1.D0) Xi(1) = random( 0.D0, 1.D0)
xii(2) = random( 0.D0, 1.D0 - xii(1)) Xi(2) = random( 0.D0, 1.D0 - Xi(1))
xii(3) = random( 0.D0, 1.D0 - xii(1) - xii(2)) Xi(3) = random( 0.D0, 1.D0 - Xi(1) - Xi(2))
ALLOCATE(fPsi(1:4)) CALL self%fPsi(Xi, fPsi)
fPsi = self%fPsi(xii)
r(1) = DOT_PRODUCT(fPsi, self%x) r = (/ DOT_PRODUCT(fPsi, self%x), &
r(2) = DOT_PRODUCT(fPsi, self%y) DOT_PRODUCT(fPsi, self%y), &
r(3) = DOT_PRODUCT(fPsi, self%z) DOT_PRODUCT(fPsi, self%z) /)
END FUNCTION randPosVolTetra END FUNCTION randPosVolTetra
@ -316,83 +317,81 @@ MODULE moduleMesh3DCart
IMPLICIT NONE IMPLICIT NONE
CLASS(meshVol3DCartTetra), INTENT(inout):: self CLASS(meshVol3DCartTetra), INTENT(inout):: self
REAL(8):: xii(1:3) REAL(8):: Xi(1:3)
self%volume = 0.D0 self%volume = 0.D0
xii = (/0.25D0, 0.25D0, 0.25D0/) Xi = (/0.25D0, 0.25D0, 0.25D0/)
self%volume = self%detJac(xii) self%volume = self%detJac(Xi)
END SUBROUTINE volumeTetra END SUBROUTINE volumeTetra
!Computes element functions in point xii !Computes element functions in point Xi
PURE FUNCTION fPsiTetra(xi) RESULT(fPsi) PURE SUBROUTINE fPsiTetra(Xi, fPsi)
IMPLICIT NONE IMPLICIT NONE
REAL(8), INTENT(in):: xi(1:3) REAL(8), INTENT(in):: Xi(1:3)
REAL(8), ALLOCATABLE:: fPsi(:) REAL(8), INTENT(out):: fPsi(:)
ALLOCATE(fPsi(1:4)) fPsi(1) = 1.D0 - Xi(1) - Xi(2) - Xi(3)
fPsi(2) = Xi(1)
fPsi(3) = Xi(2)
fPsi(4) = Xi(3)
fPsi(1) = 1.D0 - xi(1) - xi(2) - xi(3) END SUBROUTINE fPsiTetra
fPsi(2) = xi(1)
fPsi(3) = xi(2)
fPsi(4) = xi(3)
END FUNCTION fPsiTetra !Derivative element function at coordinates Xi
PURE FUNCTION dPsiTetra(Xi) RESULT(dPsi)
!Derivative element function at coordinates xii
PURE FUNCTION dPsiTetra(xii) RESULT(dPsi)
IMPLICIT NONE IMPLICIT NONE
REAL(8), INTENT(in):: xii(1:3) REAL(8), INTENT(in):: Xi(1:3)
REAL(8), ALLOCATABLE:: dPsi(:,:) REAL(8), ALLOCATABLE:: dPsi(:,:)
ALLOCATE(dPsi(1:3,1:4)) ALLOCATE(dPsi(1:3,1:4))
dPsi(1,:) = dPsiTetraXii1(xii(2), xii(3)) dPsi(1,:) = dPsiTetraXi1(Xi(2), Xi(3))
dPsi(2,:) = dPsiTetraXii2(xii(1), xii(3)) dPsi(2,:) = dPsiTetraXi2(Xi(1), Xi(3))
dPsi(3,:) = dPsiTetraXii3(xii(1), xii(2)) dPsi(3,:) = dPsiTetraXi3(Xi(1), Xi(2))
END FUNCTION dPsiTetra END FUNCTION dPsiTetra
!Derivative element function respect to xii1 !Derivative element function respect to Xi1
PURE FUNCTION dPsiTetraXii1(xii2, xii3) RESULT(dPsiXii1) PURE FUNCTION dPsiTetraXi1(Xi2, Xi3) RESULT(dPsiXi1)
IMPLICIT NONE IMPLICIT NONE
REAL(8), INTENT(in):: xii2, xii3 REAL(8), INTENT(in):: Xi2, Xi3
REAL(8):: dPsiXii1(1:4) REAL(8):: dPsiXi1(1:4)
dPsiXii1(1) = -1.D0 dPsiXi1(1) = -1.D0
dPsiXii1(2) = 1.D0 dPsiXi1(2) = 1.D0
dPsiXii1(3) = 0.D0 dPsiXi1(3) = 0.D0
dPsiXii1(4) = 0.D0 dPsiXi1(4) = 0.D0
END FUNCTION dPsiTetraXii1 END FUNCTION dPsiTetraXi1
!Derivative element function respect to xii2 !Derivative element function respect to Xi2
PURE FUNCTION dPsiTetraXii2(xii1, xii3) RESULT(dPsiXii2) PURE FUNCTION dPsiTetraXi2(Xi1, Xi3) RESULT(dPsiXi2)
IMPLICIT NONE IMPLICIT NONE
REAL(8), INTENT(in):: xii1, xii3 REAL(8), INTENT(in):: Xi1, Xi3
REAL(8):: dPsiXii2(1:4) REAL(8):: dPsiXi2(1:4)
dPsiXii2(1) = -1.D0 dPsiXi2(1) = -1.D0
dPsiXii2(2) = 0.D0 dPsiXi2(2) = 0.D0
dPsiXii2(3) = 1.D0 dPsiXi2(3) = 1.D0
dPsiXii2(4) = 0.D0 dPsiXi2(4) = 0.D0
END FUNCTION dPsiTetraXii2 END FUNCTION dPsiTetraXi2
!Derivative element function respect to xii3 !Derivative element function respect to Xi3
PURE FUNCTION dPsiTetraXii3(xii1, xii2) RESULT(dPsiXii3) PURE FUNCTION dPsiTetraXi3(Xi1, Xi2) RESULT(dPsiXi3)
IMPLICIT NONE IMPLICIT NONE
REAL(8), INTENT(in):: xii1, xii2 REAL(8), INTENT(in):: Xi1, Xi2
REAL(8):: dPsiXii3(1:4) REAL(8):: dPsiXi3(1:4)
dPsiXii3(1) = -1.D0 dPsiXi3(1) = -1.D0
dPsiXii3(2) = 0.D0 dPsiXi3(2) = 0.D0
dPsiXii3(3) = 0.D0 dPsiXi3(3) = 0.D0
dPsiXii3(4) = 1.D0 dPsiXi3(4) = 1.D0
END FUNCTION dPsiTetraXii3 END FUNCTION dPsiTetraXi3
!Computes the derivatives in global coordinates !Computes the derivatives in global coordinates
PURE SUBROUTINE partialDerTetra(self, dPsi, dx, dy, dz) PURE SUBROUTINE partialDerTetra(self, dPsi, dx, dy, dz)
@ -421,19 +420,19 @@ MODULE moduleMesh3DCart
CLASS(meshVol3DCartTetra), INTENT(in):: self CLASS(meshVol3DCartTetra), INTENT(in):: self
REAL(8), ALLOCATABLE:: localK(:,:) REAL(8), ALLOCATABLE:: localK(:,:)
REAL(8):: xii(1:3) REAL(8):: Xi(1:3)
REAL(8):: fPsi(1:4), dPsi(1:3, 1:4) REAL(8):: fPsi(1:4), dPsi(1:3, 1:4)
REAL(8):: invJ(1:3,1:3), detJ REAL(8):: invJ(1:3,1:3), detJ
ALLOCATE(localK(1:4,1:4)) ALLOCATE(localK(1:4,1:4))
localK = 0.D0 localK = 0.D0
xii = 0.D0 Xi = 0.D0
!TODO: One point Gauss integral. Upgrade when possible !TODO: One point Gauss integral. Upgrade when possible
xii = (/ 0.25D0, 0.25D0, 0.25D0 /) Xi = (/ 0.25D0, 0.25D0, 0.25D0 /)
dPsi = self%dPsi(xii) dPsi = self%dPsi(Xi)
detJ = self%detJac(xii, dPsi) detJ = self%detJac(Xi, dPsi)
invJ = self%invJac(xii, dPsi) invJ = self%invJac(Xi, dPsi)
fPsi = self%fPsi(xii) CALL self%fPsi(Xi, fPsi)
localK = MATMUL(TRANSPOSE(MATMUL(invJ,dPsi)),MATMUL(invJ,dPsi))*1.D0/detJ localK = MATMUL(TRANSPOSE(MATMUL(invJ,dPsi)),MATMUL(invJ,dPsi))*1.D0/detJ
END FUNCTION elemKTetra END FUNCTION elemKTetra
@ -445,40 +444,40 @@ MODULE moduleMesh3DCart
REAL(8), INTENT(in):: source(1:) REAL(8), INTENT(in):: source(1:)
REAL(8), ALLOCATABLE:: localF(:) REAL(8), ALLOCATABLE:: localF(:)
REAL(8):: fPsi(1:4), dPsi(1:3, 1:4) REAL(8):: fPsi(1:4), dPsi(1:3, 1:4)
REAL(8):: xii(1:3) REAL(8):: Xi(1:3)
REAL(8):: detJ, f REAL(8):: detJ, f
ALLOCATE(localF(1:4)) ALLOCATE(localF(1:4))
localF = 0.D0 localF = 0.D0
xii = 0.D0 Xi = 0.D0
!TODO: One point Gauss integral. Upgrade when possible Xi = (/ 0.25D0, 0.25D0, 0.25D0 /)
xii = (/ 0.25D0, 0.25D0, 0.25D0 /) dPsi = self%dPsi(Xi)
dPsi = self%dPsi(xii) detJ = self%detJac(Xi, dPsi)
detJ = self%detJac(xii, dPsi) CALL self%fPsi(Xi, fPsi)
fPsi = self%fPsi(xii)
f = DOT_PRODUCT(fPsi, source) f = DOT_PRODUCT(fPsi, source)
localF = f*fPsi*1.D0*detJ localF = f*fPsi*1.D0*detJ
END FUNCTION elemFTetra END FUNCTION elemFTetra
PURE FUNCTION insideTetra(xi) RESULT(ins) PURE FUNCTION insideTetra(Xi) RESULT(ins)
IMPLICIT NONE IMPLICIT NONE
REAL(8), INTENT(in):: xi(1:3) REAL(8), INTENT(in):: Xi(1:3)
LOGICAL:: ins LOGICAL:: ins
ins = xi(1) >= 0.D0 .AND. & ins = Xi(1) >= 0.D0 .AND. &
xi(2) >= 0.D0 .AND. & Xi(2) >= 0.D0 .AND. &
xi(3) >= 0.D0 .AND. & Xi(3) >= 0.D0 .AND. &
1.D0 - xi(1) - xi(2) - xi(3) >= 0.D0 1.D0 - Xi(1) - Xi(2) - Xi(3) >= 0.D0
END FUNCTION insideTetra END FUNCTION insideTetra
PURE FUNCTION gatherEFTetra(self, xi) RESULT(EF) PURE FUNCTION gatherEFTetra(self, Xi) RESULT(EF)
IMPLICIT NONE IMPLICIT NONE
CLASS(meshVol3DCartTetra), INTENT(in):: self CLASS(meshVol3DCartTetra), INTENT(in):: self
REAL(8), INTENT(in):: xi(1:3) REAL(8), INTENT(in):: Xi(1:3)
REAL(8):: dPsi(1:3, 1:4) REAL(8):: dPsi(1:3, 1:4)
REAL(8):: dPsiR(1:3, 1:4) REAL(8):: dPsiR(1:3, 1:4)
REAL(8):: invJ(1:3, 1:3), detJ REAL(8):: invJ(1:3, 1:3), detJ
@ -490,9 +489,9 @@ MODULE moduleMesh3DCart
self%n3%emData%phi, & self%n3%emData%phi, &
self%n4%emData%phi /) self%n4%emData%phi /)
dPsi = self%dPsi(xi) dPsi = self%dPsi(Xi)
detJ = self%detJac(xi, dPsi) detJ = self%detJac(Xi, dPsi)
invJ = self%invJac(xi, dPsi) invJ = self%invJac(Xi, dPsi)
dPsiR = MATMUL(invJ, dPsi)/detJ dPsiR = MATMUL(invJ, dPsi)/detJ
EF(1) = -DOT_PRODUCT(dPsiR(1,:), phi) EF(1) = -DOT_PRODUCT(dPsiR(1,:), phi)
EF(2) = -DOT_PRODUCT(dPsiR(2,:), phi) EF(2) = -DOT_PRODUCT(dPsiR(2,:), phi)
@ -500,11 +499,11 @@ MODULE moduleMesh3DCart
END FUNCTION gatherEFTetra END FUNCTION gatherEFTetra
PURE FUNCTION gatherMFTetra(self, xi) RESULT(MF) PURE FUNCTION gatherMFTetra(self, Xi) RESULT(MF)
IMPLICIT NONE IMPLICIT NONE
CLASS(meshVol3DCartTetra), INTENT(in):: self CLASS(meshVol3DCartTetra), INTENT(in):: self
REAL(8), INTENT(in):: xi(1:3) REAL(8), INTENT(in):: Xi(1:3)
REAL(8):: fPsi(1:4) REAL(8):: fPsi(1:4)
REAL(8):: MF_Nodes(1:4,1:3) REAL(8):: MF_Nodes(1:4,1:3)
REAL(8):: MF(1:3) REAL(8):: MF(1:3)
@ -522,7 +521,7 @@ MODULE moduleMesh3DCart
self%n3%emData%B(3), & self%n3%emData%B(3), &
self%n4%emData%B(3) /) self%n4%emData%B(3) /)
fPsi = self%fPsi(xi) CALL self%fPsi(Xi, fPsi)
MF = MATMUL(fPsi, MF_Nodes) MF = MATMUL(fPsi, MF_Nodes)
END FUNCTION gatherMFTetra END FUNCTION gatherMFTetra
@ -538,37 +537,37 @@ MODULE moduleMesh3DCart
END FUNCTION getNodesTetra END FUNCTION getNodesTetra
PURE FUNCTION phy2logTetra(self,r) RESULT(xi) PURE FUNCTION phy2logTetra(self,r) RESULT(Xi)
IMPLICIT NONE IMPLICIT NONE
CLASS(meshVol3DCartTetra), INTENT(in):: self CLASS(meshVol3DCartTetra), INTENT(in):: self
REAL(8), INTENT(in):: r(1:3) REAL(8), INTENT(in):: r(1:3)
REAL(8):: xi(1:3) REAL(8):: Xi(1:3)
REAL(8):: invJ(1:3, 1:3), detJ REAL(8):: invJ(1:3, 1:3), detJ
REAL(8):: deltaR(1:3) REAL(8):: deltaR(1:3)
REAL(8):: dPsi(1:3, 1:4) REAL(8):: dPsi(1:3, 1:4)
xi = 0.D0 Xi = 0.D0
deltaR = (/r(1) - self%x(1), r(2) - self%y(1), r(3) - self%z(1) /) deltaR = (/r(1) - self%x(1), r(2) - self%y(1), r(3) - self%z(1) /)
dPsi = self%dPsi(xi) dPsi = self%dPsi(Xi)
invJ = self%invJac(xi, dPsi) invJ = self%invJac(Xi, dPsi)
detJ = self%detJac(xi, dPsi) detJ = self%detJac(Xi, dPsi)
xi = MATMUL(invJ, deltaR)/detJ Xi = MATMUL(invJ, deltaR)/detJ
END FUNCTION phy2logTetra END FUNCTION phy2logTetra
SUBROUTINE nextElementTetra(self, xi, nextElement) SUBROUTINE nextElementTetra(self, Xi, nextElement)
IMPLICIT NONE IMPLICIT NONE
CLASS(meshVol3DCartTetra), INTENT(in):: self CLASS(meshVol3DCartTetra), INTENT(in):: self
REAL(8), INTENT(in):: xi(1:3) REAL(8), INTENT(in):: Xi(1:3)
CLASS(meshElement), POINTER, INTENT(out):: nextElement CLASS(meshElement), POINTER, INTENT(out):: nextElement
REAL(8):: xiArray(1:4) REAL(8):: XiArray(1:4)
INTEGER:: nextInt INTEGER:: nextInt
!TODO: Review when connectivity !TODO: Review when connectivity
xiArray = (/ xi(3), 1.D0 - xi(1) - xi(2) - xi(3), xi(2), xi(1) /) XiArray = (/ Xi(3), 1.D0 - Xi(1) - Xi(2) - Xi(3), Xi(2), Xi(1) /)
nextInt = MINLOC(xiArray, 1) nextInt = MINLOC(XiArray, 1)
NULLIFY(nextElement) NULLIFY(nextElement)
SELECT CASE(nextInt) SELECT CASE(nextInt)
CASE (1) CASE (1)
@ -585,11 +584,11 @@ MODULE moduleMesh3DCart
!COMMON FUNCTIONS FOR CARTESIAN VOLUME ELEMENTS IN 3D !COMMON FUNCTIONS FOR CARTESIAN VOLUME ELEMENTS IN 3D
!Computes element Jacobian determinant !Computes element Jacobian determinant
PURE FUNCTION detJ3DCart(self, xi, dPsi_in) RESULT(dJ) PURE FUNCTION detJ3DCart(self, Xi, dPsi_in) RESULT(dJ)
IMPLICIT NONE IMPLICIT NONE
CLASS(meshVol3DCart), INTENT(in)::self CLASS(meshVol3DCart), INTENT(in)::self
REAL(8), INTENT(in):: xi(1:3) REAL(8), INTENT(in):: Xi(1:3)
REAL(8), INTENT(in), OPTIONAL:: dPsi_in(1:, 1:) REAL(8), INTENT(in), OPTIONAL:: dPsi_in(1:, 1:)
REAL(8):: dJ REAL(8):: dJ
REAL(8), ALLOCATABLE:: dPsi(:,:) REAL(8), ALLOCATABLE:: dPsi(:,:)
@ -599,7 +598,7 @@ MODULE moduleMesh3DCart
dPsi = dPsi_in dPsi = dPsi_in
ELSE ELSE
dPsi = self%dPsi(xi) dPsi = self%dPsi(Xi)
END IF END IF
@ -610,11 +609,11 @@ MODULE moduleMesh3DCart
END FUNCTION detJ3DCart END FUNCTION detJ3DCart
PURE FUNCTION invJ3DCart(self,xi,dPsi_in) RESULT(invJ) PURE FUNCTION invJ3DCart(self,Xi,dPsi_in) RESULT(invJ)
IMPLICIT NONE IMPLICIT NONE
CLASS(meshVol3DCart), INTENT(in):: self CLASS(meshVol3DCart), INTENT(in):: self
REAL(8), INTENT(in):: xi(1:3) REAL(8), INTENT(in):: Xi(1:3)
REAL(8), INTENT(in), OPTIONAL:: dPsi_in(1:,1:) REAL(8), INTENT(in), OPTIONAL:: dPsi_in(1:,1:)
REAL(8), ALLOCATABLE:: dPsi(:,:) REAL(8), ALLOCATABLE:: dPsi(:,:)
REAL(8), DIMENSION(1:3):: dx, dy, dz REAL(8), DIMENSION(1:3):: dx, dy, dz
@ -624,7 +623,7 @@ MODULE moduleMesh3DCart
dPsi=dPsi_in dPsi=dPsi_in
ELSE ELSE
dPsi = self%dPsi(xi) dPsi = self%dPsi(Xi)
END IF END IF

15
src/modules/mesh/moduleMesh.f90
View file

@ -211,11 +211,11 @@ MODULE moduleMesh
END FUNCTION getNodesVol_interface END FUNCTION getNodesVol_interface
PURE FUNCTION fPsi_interface(xi) RESULT(fPsi) PURE SUBROUTINE fPsi_interface(xi, fPsi)
REAL(8), INTENT(in):: xi(1:3) REAL(8), INTENT(in):: xi(1:3)
REAL(8), ALLOCATABLE:: fPsi(:) REAL(8), INTENT(out):: fPsi(:)
END FUNCTION fPsi_interface END SUBROUTINE fPsi_interface
PURE FUNCTION elemK_interface(self) RESULT(localK) PURE FUNCTION elemK_interface(self) RESULT(localK)
IMPORT:: meshVol IMPORT:: meshVol
@ -496,11 +496,14 @@ MODULE moduleMesh
INTEGER:: i, nNodes INTEGER:: i, nNodes
CLASS(meshNode), POINTER:: node CLASS(meshNode), POINTER:: node
fPsi = self%fPsi(part%xi)
tensorS = outerProduct(part%v, part%v)
sp = part%species%n
volNodes = self%getNodes() volNodes = self%getNodes()
nNodes = SIZE(volNodes) nNodes = SIZE(volNodes)
ALLOCATE(fPsi(1:nNodes))
CALL self%fPsi(part%xi, fPsi)
tensorS = outerProduct(part%v, part%v)
sp = part%species%n
DO i = 1, nNodes DO i = 1, nNodes
node => mesh%nodes(volNodes(i))%obj node => mesh%nodes(volNodes(i))%obj