What is the advantage of symmetry in FEKO?

Altair Forum User

What is the advantage of symmetry in FEKO?

JIF

Electric and magnetic symmetry can be used to reduce runtime and memory requirements in FEKO. Symmetry can be taken advantage of in the solver for all models where the MoM is used, including all the hybrid methods (such as FEM/MoM and MoM/PO). The MLFMM and Higher Order Basis Functions (HOBF) for the MoM do not support symmetry, but symmetry is supported for higher order basis functions for the FEM.

It must be stressed that the user does not have to remember which solver supports symmetry as FEKO will internally decide whether to take advantage of symmetry or not. In all cases, the meshing of the model will be faster when symmetry is specified.

For the MoM, a metal sphere is made consisting of 4188 metallic triangles or 6282 unknowns.

The problem is solved in 5 different ways:

1. No symmetry
2. 1 plane of symmetry
3. 1 plane of symmetry but run in a scenario where the available memory is just less than that of (2)
4. 2 planes of symmetry
5. 2 planes of symmetry but run in a scenario where the available memory is just less than that of (4)

 

Model	symmetry	memory limit [MB]	memory used [MB]	runtime
MOM metal sphere	none	none	303	162
	1 plane	none	154	55
		130	79	450
	2 planes	none	77	34
		70	21	218

 

It is seen that symmetry introduces large savings in resources. Specifically, 1 plane of symmetry will use half of the memory used for the case of no symmetry, and 2 planes of symmetry will use half of the latter, but this applies only when efficient solving is used. When symmetry is used and FEKO is unable to allocate 1/2 of the memory (for 1 plane of symmetry) or 1/4 of the memory (for 2 planes of symmetry), it can use a different technique for storing the matrix. This alternate technique results in a further reduction of memory although the runtime will increase.

It is seen that when the alternate technique is used, then for 1 plane of symmetry FEKO can half the memory again compared to the efficient method - approximately 1/4 of the memory is then used compared to the no symmetry case. And for 2 planes of symmetry FEKO can use 1/4 of the memory used when solving the problem efficiently with 2 planes of symmetry -  approximately 1/16 of the memory is then used compared to the no symmetry case.

For the surface equivalence principle, a dielectric sphere is made with 2484 dielectric triangles or 7452 unknowns. The resources are shown below.

 

Model	symmetry	memory limit [MB]	memory used [MB]	runtime
SEP dielectric sphere	none	none	425	214
	1 plane	none	213	65
		200	107	927
	2 planes	none	108	35
		90	28	478

 

It is seen that savings in resources is very similar to metal sphere.

For the FEM/MoM, the same dielectric sphere is used but meshed with tetrahedra. The resources are shown below.
 

Model	symmetry	memory limit [MB]	memory used [MB]	runtime
FEM/MOM dielectric sphere	none	none	707	213
	1 plane	none	350	81
		320	223	84
	2 planes	none	161	48
		150	107	50

 

With the FEM/MoM, we see that the runtimes for efficient solving does not differ substantially from the inefficient (or memory limited method), but the memory reductions are still realised. There also may be differences depending on the number of tetrahedra compared to surface triangles.

Geometric symmetry also has some advantages, although not as much as electric and magnetic symmetry - geometric symmetry will speed up the setup of the triangle integrals. When meshes with a large number of elements are used, a slight reduction in memory will be obtained due to the reduced geometry that needs to be stored.