An exclusive raffle opportunity for active members like you! Complete your profile, answer questions and get your first accepted badge to enter the raffle.
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:
No symmetry
1 plane of symmetry
1 plane of symmetry but run in a scenario where the available memory is just less than that of (2)
2 planes of symmetry
2 planes of symmetry but run in a scenario where the available memory is just less than that of (4)
Model
Model
symmetry
symmetry
memory limit [MB]
memory limit [MB]
memory used [MB]
memory used [MB]
runtime
runtime
Model
MOM metal sphere
symmetry
none
memory limit [MB]
none
memory used [MB]
303
runtime
162
Model
1 plane
symmetry
none
memory limit [MB]
154
memory used [MB]
55
Model
130
symmetry
79
memory limit [MB]
450
Model
2 planes
symmetry
none
memory limit [MB]
77
memory used [MB]
34
Model
70
symmetry
21
memory limit [MB]
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
Model
symmetry
symmetry
memory limit [MB]
memory limit [MB]
memory used [MB]
memory used [MB]
runtime
runtime
Model
SEP dielectric sphere
symmetry
none
memory limit [MB]
none
memory used [MB]
425
runtime
214
Model
1 plane
symmetry
none
memory limit [MB]
213
memory used [MB]
65
Model
200
symmetry
107
memory limit [MB]
927
Model
2 planes
symmetry
none
memory limit [MB]
108
memory used [MB]
35
Model
90
symmetry
28
memory limit [MB]
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
Model
symmetry
symmetry
memory limit [MB]
memory limit [MB]
memory used [MB]
memory used [MB]
runtime
runtime
Model
FEM/MOM dielectric sphere
symmetry
none
memory limit [MB]
none
memory used [MB]
707
runtime
213
Model
1 plane
symmetry
none
memory limit [MB]
350
memory used [MB]
81
Model
320
symmetry
223
memory limit [MB]
84
Model
2 planes
symmetry
none
memory limit [MB]
161
memory used [MB]
48
Model
150
symmetry
107
memory limit [MB]
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.
Altair Employee
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:
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.
For the FEM/MoM, the same dielectric sphere is used but meshed with tetrahedra. The resources are shown below.
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.