5.4 Advanced Symmetries and Ghosts-Lower Layer

The geometric symmetry layer in the preceeding section is actually a thin wrapper around this lower, more difficult to use layer.

void FEM_Set_sym_nodes(const int *canon,const int *sym);
SUBROUTINE FEM_Set_sym_nodes(canon,sym)
INTEGER, INTENT(IN) :: canon(nNodes)
INTEGER, INTENT(IN) :: sym(nNodes)

This call describes all possible symmetries in an extremely terse format. It can only be called from init(). The ``canonicalization array'' canon maps nodes to their canonical representative--if canon()=canon(), nodes and are images of each other under some symmetry. The sym array has bits set for each symmetry boundary passing through a node.

For example, a 2d domain with 6 elements A, B, C, D, E, and F and 12 nodes numbered 1-12 that is mirror-symmetric on the horizontal boundaries but periodic in the vertical boundaries would look like:

   D^'|  D^ |  E^ |  F^ |  F^`
   -  1  -  2  -  3  -  4  -
   A' |  A  |  B  |  C  |  C`
   -  5  -  6  -  7  -  8  -
   D' |  D  |  E  |  F  |  F`
   -  9  - 10  -  11 -  12 -
   Av'|  Av |  Bv |  Cv |  Cv`

  v indicates the value has been shifted down (bottom boundary),
  ^ indicates the value has been shifted up (top boundary),
  ' indicates the value has been copied from the left (right boundary),
  ` indicates the value has been copied from the right (left boundary).

If we mark the left border with 1, the top with 2, the right with 4, and the bottom with 8, this situation is indicated by topologically pasting the top row to the bottom row by setting their canon entries equal, and marking each node with its symmetries.

Node	canon	sym
1	1	3 (left + top)
2	2	2 (top)
3	3	2 (top)
4	4	6 (top + right)
5	5	1 (left)
6	6	0 (none)
7	7	0 (none)
8	8	4 (right)
9	1	9 (left+bottom)
10	2	8 (bottom)
11	3	8 (bottom)
12	4	12 (bottom+right)

void FEM_Get_sym(int elTypeOrMinusOne,int *destSym);
void FEM_Get_sym(elTypeOrZero,destSym);
INTEGER, INTENT(IN) :: elTypeOrMinusOne
INTEGER, INTENT(OUT) :: destSym(nItems)

This call extracts the list of symmetry conditions that apply to an item type. If elType is an element type, it returns the symmetry conditions that apply to that element type; if elType is -1 (zero for Fortran), it returns the symmetry conditions that apply to the nodes. Symmetry conditions are normally only nonzero for ghost nodes and elements.

Mirror symmetry conditions are not yet supported, nor are multiple layers of symmetry ghosts, but both should be easy to add without changing this interface.