3D MoM technique problem with triangular patches

3D MOM problem

Hi,

i am trying to solve EM scattering by a dielectric sphere using Method of Moment technique. Surface of the sphere is divided into triangular patches. How do i perform integration on the triangular patches? Which method should i use as the vertices of the patches have x-y-z co-ordinates? any suggestions ? i am following the papers by S. M. Rao, D. R. Wilton, and A. W. Glisson.

Thanks...

sar5

Re: 3D MOM problem

For non-singular integrations (non-overlapping triangles) you should use a N-point gaussian quadrature rule. 1, 4 and 7 point rules are very common.

For overlapping triangles (EFIE formulation) you should use singularity extraction. For the analytic part you can use the relationships in the following paper:

T. F. Eibert and V. Hansen, "On the Calculation of Potential Integrals for Linear Source Distributions on Triangular Domains," IEEE Trans. Antennas Propag., vol. 43, pp. 1499-1502, Dec. 1995.

Best of luck.

3D MOM problem

If you RWG basis functions, another way for overlapping triangles is to use Duffy transform.

Re: 3D MOM problem

Remember to verify your result with a 3D simulator as in HFSS

Re: 3D MOM problem

the RWG paper describe the scattering from a conducting bodies only. You can not use the algorithm in this paper in solving dielectric media. But if you speak about athe conducting sphere in this paper. you need to do the integrals as described in this paper. It uses the normalized area coordinate system of integration at the end of the paper.

it uses r=eta *r1+zeta*r2+(1-eta-zeta)*r3. if you integrate over eta and zeta it will be a double integral .i.e surface integral over the triangular patch.

regarding the dielectric bodies the techniques that attack this problem is divided into two categoris:
the first is based on the surface integral equation using triangular patches
the second category based on modeling the dielectric media into tetrahedrons.