fPsi functions for edges

I need to make a common module for mesh, many functions for elements are
shared.

Also, try to reduce the 'select type' statements, but I don't know
enough Fortran for it.

src/modules/mesh/1DCart/moduleMesh1DCart.f90

@@ -31,6 +31,7 @@ MODULE moduleMesh1DCart
       PROCEDURE, PASS::   getNodes     => getNodes1DCart
       PROCEDURE, PASS::   intersection => intersection1DCart
       PROCEDURE, PASS::   randPos      => randPosEdge
+      procedure, nopass:: fPsi         => fPsiPoint
 
   END TYPE meshEdge1DCart
 
@@ -172,7 +173,19 @@ MODULE moduleMesh1DCart
 
     END FUNCTION randPosEdge
 
-    !VOLUME FUNCTIONS
+    !Compute element functions at point Xi
+    pure function fPsiPoint(Xi, nNodes) RESULT(fPsi)
+      implicit none
+
+      real(8), intent(in):: Xi(1:3)
+      integer, intent(in):: nNodes
+      real(8):: fPsi(1:nNodes)
+
+      fPsi = (/ 1.D0 /)
+
+    end function fPsiPoint
+
+    !CELL FUNCTIONS
     !SEGMENT FUNCTIONS
     !Init element
     SUBROUTINE initCell1DCartSegm(self, n, p, nodes)
@@ -446,7 +459,7 @@ MODULE moduleMesh1DCart
 
     END SUBROUTINE volumeSegm
 
-    !COMMON FUNCTIONS FOR 1D VOLUME ELEMENTS
+    !COMMON FUNCTIONS FOR 1D CELL ELEMENTS
     !Compute element Jacobian determinant
     PURE FUNCTION detJ1DCart(pDer) RESULT(dJ)
       IMPLICIT NONE

src/modules/mesh/1DRad/moduleMesh1DRad.f90

@@ -31,6 +31,7 @@ MODULE moduleMesh1DRad
       PROCEDURE, PASS::   getNodes     => getNodes1DRad
       PROCEDURE, PASS::   intersection => intersection1DRad
       PROCEDURE, PASS::   randPos      => randPos1DRad
+      procedure, nopass:: fPsi         => fPsiPoint
 
   END TYPE meshEdge1DRad
 
@@ -172,7 +173,19 @@ MODULE moduleMesh1DRad
 
     END FUNCTION randPos1DRad
 
-    !VOLUME FUNCTIONS
+    !Compute element functions at point Xi
+    pure function fPsiPoint(Xi, nNodes) RESULT(fPsi)
+      implicit none
+
+      real(8), intent(in):: Xi(1:3)
+      integer, intent(in):: nNodes
+      real(8):: fPsi(1:nNodes)
+
+      fPsi = (/ 1.D0 /)
+
+    end function fPsiPoint
+
+    !CELL FUNCTIONS
     !SEGMENT FUNCTIONS
     !Init element
     SUBROUTINE initCell1DRadSegm(self, n, p, nodes)
@@ -461,7 +474,7 @@ MODULE moduleMesh1DRad
 
     END SUBROUTINE volumeSegm
 
-    !COMMON FUNCTIONS FOR 1D VOLUME ELEMENTS
+    !COMMON FUNCTIONS FOR 1D CELL ELEMENTS
     !Compute element Jacobian determinant
     PURE FUNCTION detJ1DRad(pDer) RESULT(dJ)
       IMPLICIT NONE

src/modules/mesh/2DCart/moduleMesh2DCart.f90

@@ -36,6 +36,7 @@ MODULE moduleMesh2DCart
       PROCEDURE, PASS::   getNodes     => getNodes2DCart
       PROCEDURE, PASS::   intersection => intersection2DCartEdge
       PROCEDURE, PASS::   randPos      => randPosEdge
+      procedure, nopass:: fPsi         => fPsiSegm
 
   END TYPE meshEdge2DCart
 
@@ -234,6 +235,21 @@ MODULE moduleMesh2DCart
 
     END FUNCTION randPosEdge
 
+    !Compute element functions at point Xi
+    pure function fPsiSegm(Xi, nNodes) RESULT(fPsi)
+      implicit none
+
+      real(8), intent(in):: Xi(1:3)
+      integer, intent(in):: nNodes
+      real(8):: fPsi(1:nNodes)
+
+      fPsi = (/ 1.D0 - Xi(1), &
+                1.D0 + Xi(1) /)
+
+      fPsi    = fPsi * 0.50D0
+
+    end function fPsiSegm
+
     !VOLUME FUNCTIONS
     !QUAD FUNCTIONS
     !Init element

src/modules/mesh/2DCyl/moduleMesh2DCyl.f90

@@ -36,6 +36,7 @@ MODULE moduleMesh2DCyl
       PROCEDURE, PASS::   getNodes     => getNodes2DCyl
       PROCEDURE, PASS::   intersection => intersection2DCylEdge
       PROCEDURE, PASS::   randPos      => randPosEdge
+      procedure, nopass:: fPsi         => fPsiSegm
 
   END TYPE meshEdge2DCyl
 
@@ -243,7 +244,22 @@ MODULE moduleMesh2DCyl
 
     END FUNCTION randPosEdge
 
-    !VOLUME FUNCTIONS
+    !Compute element functions at point Xi
+    pure function fPsiSegm(Xi, nNodes) RESULT(fPsi)
+      implicit none
+
+      real(8), intent(in):: Xi(1:3)
+      integer, intent(in):: nNodes
+      real(8):: fPsi(1:nNodes)
+
+      fPsi = (/ 1.D0 - Xi(1), &
+                1.D0 + Xi(1) /)
+
+      fPsi    = fPsi * 0.50D0
+
+    end function fPsiSegm
+
+    !CELL FUNCTIONS
     !QUAD FUNCTIONS
     !Init element
     SUBROUTINE initCellQuad2DCyl(self, n, p, nodes)
@@ -929,7 +945,7 @@ MODULE moduleMesh2DCyl
 
     END SUBROUTINE volumeTria
 
-    !COMMON FUNCTIONS FOR CYLINDRICAL VOLUME ELEMENTS
+    !COMMON FUNCTIONS FOR CYLINDRICAL CELL ELEMENTS
     !Compute element Jacobian determinant
     PURE FUNCTION detJ2DCyl(pDer) RESULT(dJ)
       IMPLICIT NONE

src/modules/mesh/3DCart/moduleMesh3DCart.f90

@@ -30,7 +30,7 @@ MODULE moduleMesh3DCart
       PROCEDURE, PASS::   intersection => intersection3DCartTria
       PROCEDURE, PASS::   randPos      => randPosEdgeTria
       !PARTICULAR PROCEDURES
-      PROCEDURE, NOPASS, PRIVATE:: fPsi => fPsiEdgeTria
+      PROCEDURE, NOPASS:: fPsi => fPsiTria
 
   END TYPE meshEdge3DCartTria
 
@@ -204,7 +204,7 @@ MODULE moduleMesh3DCart
       Xi(2) = random( 0.D0, 1.D0 - Xi(1))
       Xi(3) = 0.D0
 
-      fPsi = self%fPsi(Xi)
+      fPsi = self%fPsi(Xi, 3)
       r = (/DOT_PRODUCT(fPsi, self%x), &
             DOT_PRODUCT(fPsi, self%y), &
             DOT_PRODUCT(fPsi, self%z)/)
@@ -212,17 +212,18 @@ MODULE moduleMesh3DCart
     END FUNCTION randPosEdgeTria
 
     !Shape functions for triangular surface
-    PURE FUNCTION fPsiEdgeTria(Xi) RESULT(fPsi)
+    PURE FUNCTION fPsiTria(Xi, nNodes) RESULT(fPsi)
       IMPLICIT NONE
 
       REAL(8), INTENT(in):: Xi(1:3)
-      REAL(8):: fPsi(1:3)
+      INTEGER, INTENT(in):: nNodes
+      REAL(8):: fPsi(1:nNodes)
 
       fPsi(1) = 1.D0 - Xi(1) - Xi(2)
       fPsi(2) =        Xi(1)
       fPsi(3) =                Xi(2)
 
-    END FUNCTION fPsiEdgeTria
+    END FUNCTION fPsiTria
 
     !VOLUME FUNCTIONS
     !TETRA FUNCTIONS

src/modules/mesh/moduleMesh.f90

@@ -97,6 +97,10 @@ MODULE moduleMesh
       PROCEDURE(getNodesEdge_interface),     DEFERRED, PASS:: getNodes
       PROCEDURE(intersectionEdge_interface), DEFERRED, PASS:: intersection
       PROCEDURE(randPosEdge_interface),      DEFERRED, PASS:: randPos
+      PROCEDURE(fPsi_interface),             DEFERRED, NOPASS:: fPsi
+      !Gather value and spatial derivative on the nodes at position Xi
+      PROCEDURE, PASS, PRIVATE:: gatherF_edge_scalar
+      GENERIC:: gatherF  => gatherF_edge_scalar
 
   END TYPE meshEdge
 
@@ -561,6 +565,22 @@ MODULE moduleMesh
 
     END FUNCTION gatherF_cell_scalar
 
+    ! Gather the value of valNodes at position Xi of an edge
+    pure function gatherF_edge_scalar(self, Xi, nNodes, valNodes) RESULT(f)
+      implicit none
+
+      class(meshEdge), intent(in):: self
+      real(8), intent(in):: Xi(1:3)
+      integer, intent(in):: nNodes
+      real(8), intent(in):: valNodes(1:nNodes)
+      real(8):: f
+      real(8):: fPsi(1:nNodes)
+
+      fPsi = self%fPsi(Xi, nNodes)
+      f = dot_product(fPsi, valNodes)
+
+    end function gatherF_edge_scalar
+
     !Gather the value of valNodes (array) at position Xi
     PURE FUNCTION gatherF_cell_array(self, Xi, nNodes, valNodes) RESULT(f)
       IMPLICIT NONE

src/modules/mesh/moduleMeshBoundary.f90

@@ -223,12 +223,19 @@ MODULE moduleMeshBoundary
 
       class(meshEdge), intent(inout):: edge
       class(particle), intent(inout):: part
+      real(8), allocatable:: density(:)
+      integer:: nNodes
+      integer, allocatable:: nodes(:)
+
 
       select type(bound => edge%boundary%bTypes(part%species%n)%obj)
       type is(boundaryQuasiNeutrality)
+        nNodes = edge%nNodes
+        nodes  = edge%getNodes(nNodes)
+
         bound%alpha = 1.0d-1
 
-        if (random() < bound%alpha) then
+        if (random() <= bound%alpha) then
           call reflection(edge, part)
 
         else