LaGriT Mesh Object Connectivity

The Mesh Object attributes itettyp, itetoff, jtetoff, itet, and jtet along with the variables contained in the include files local_element.h and blockcom.h completely describe the mesh connectivity. The following discussion is based on the concept of local facets and local edges for an element. The nodes comprising a given element are always specified in a well-defined order; hence when one references the ‘second facet’ of an element, one references a pre-defined set of points.

For element ordering of nodes, faces, and edges see LaGriT Supported Element Types)

The following describes a LaGriT tetrahedral element, with nodes I1-I4 labeled as in the diagram:

The 3D face ordering is such that the right-hand-normals of all facets point outward. For this tetrahedral, the points are oriented so that the triple product  I1I2 x I2I3 x I2I4  is positive, and the volume of the tetrahedral is one-sixth of the triple product and the right-hand-normals of the facets point outward.

The local facets for this tetrahedral are defined as follows:

The local edges for this tetrahedral are defined as follows:

Similarly, local facets and local edges are defined for all element types.  (see LaGriT Supported Element Types)

itettyp(it) gives the element type of element it.

itetoff(it) gives the offset to the first node in element it.

itet(itetoff(it)+j) gives the jth node of element it.

nelmnen(itettyp(it)) gives the number of nodes of element it.

To loop through all the nodes of all elements in the mesh:

    do it=1,ntets
        do j=1,nelmnen(itettyp(it))
            k=itet(itetoff(it)+j)
        enddo
      enddo

nelmnef(itettyp(it)) gives the number of facets of element it. ielmface0(iface,itettyp(it)) gives the number of nodes on facet iface of element it. ielmface1(local_node,iface,itettyp(it)) gives the increment to the node number (local_node) on facet iface of element it.

To loop through all the nodes, k, of all elements in the mesh by facets:

      do it=1,ntets
        do i=1,nelmnef(itettyp(it))
          do j=1,ielmface0(i,itettyp(it))
             k=itet(itetoff(it)+
             ielmface1(j,i,itettyp(it)))
          enddo
        enddo
      enddo

nelmnee(itettyp(it)) gives the number of edges of element it. ielmface2(inode,iface,itettyp(it)) gives the edge number associated with inode on facet iface of element it.

ielmedge1(12,iedge,itettyp(it)) gives the node offset associated with edge iedge of element it.

To loop through all pairs of edge nodes (i1,i2) of all elements in the mesh :

       do it=1,ntets
     do i=1,nelmnee(itettyp(it))
          i1=itet(itetoff(it)+
          ielmedge1(1,i,itettyp(it)))
          i2=itet(itetoff(it)+
          ielmedge1(2,i,itettyp(it))
      enddo
      enddo

To loop through all pairs of edge nodes (i1,i2) of all elements in the mesh by facets:

       do it=1,ntets
          do i=1,nelmnef(itettyp(it))
            do j=1,ielmface0(i,itettyp(it))
              ie=ielmface2(j,i,itettype(it))
              i1=itet(itetoff(it)+
              ielmedge1(1,ie,itettyp(it)))
              i2=itet(itetoff(it)+
              ielmedge1(2,ie,itettyp(it)))
            enddo
          enddo
        enddo

jtetjtet(jtetoff(it)+j) gives the element number and local facet number of the neighbor to element it, facet j.

To loop to find all face neighbors of elements ** ** ( jt is the neighbor element number, jf is the local facet of the neighboring element) if jt is a neighbor of element it and local face if of it is the shared face jf of jt then jtet (jtetoff(it) + if) = nef_cmo* (jt-1)+jf, where nef_cmo is the number of faces per element. Similarily, jtet (jtetoff(jt) + jf) = nef_cmo* (it -1) ** ** + if mbndry is the value added to jtet if element it is on a boundary or interface; the jtet value of an element it with facet j on an exterior boundary will be exactly mbndry; the jtet value of an element it with facet j on an interior interface will be mbndry + the jtet value calculated from the neighboring element number and neighbor element local_facet number):

   c get number of faces per element for this mesh object
   call cmo_get_info(`faces_per_element',cmo_name,
    nef_cmo,ilen,ity,ics)
    do it=1,ntets
     do i=1,nelmnef(itettyp(it))
    c check if element face is on an external boundry
        if(jtet(jtetoff(it)+i).eq.mbndry) then
          jt=0
          jf=0
    c check if element face is on an internal boundry
          elseif(jtet(jtetoff(it)+i).gt.mbndry)then
         jt=1+(jtet(jtetoff(it)+i)-mbndry-1)/nef_cmo
         jf=jtet(jtetoff(it)+i)-mbndry-nef_cmo*(jt-1)
    C Volume element
            else
         jt=1+(jtet(jtetoff(it)+i)-1)/nef_cmo
         jf=jtet(jtetoff(it)+i)-nef_cmo*(jt-1)
       endif
     enddo
    enddo