HomerReid
commented
8 years ago Thanks for your interest. The conversion factor here is 4*pi*(4*A*A') where A, A' are the triangle areas. In this case the areas are A=A'=0.005 so the conversion factor is 4*pi*4*0.005*0.005 ~= 0.00125, which explains your findings.
In other words, when you combine TD_UNITY with TD_RP, the actual integral you are getting is
\int dx \int dx' r^p / (4*pi*4*A*A')
I just checked and realized the online documentation is not quite right---the TD_RP kernel should read r^p/(4\pi) instead of r^p, while the TD_UNITY polynomial should read 1/(4AA^\prime) instead of 1. The former convention is designed in anticipation of using r^p integrals to desingularize the Helmholtz kernel, which has the 1/4\pi factor built in. The latter convention anticipates the use of RWG basis functions, for which the 1/(4AA^\prime) factor is always present by definition. I will update the documentation.
urp1
Thanks of uploading this very useful code! I am having an issue using the standalone singularity program that I downloaded from (http://homerreid.dyndns.org/scuff-EM/SingularIntegrals/).
I am integrating 1/R over triangles T and T' using the code for T = T'. The results I obtain do not agree with the analytic solution - See the first entry in Table 1 in "On the Evaluation of the Double Surface Integrals Arising in the Application of the Boundary Integral Method to 3-D Problems, " Arcioni, Bressan, Perregrin, 1997 IEEE Transactions on MTT.
Scuff-EM works very well for all the cases I have tried so far, so I am not sure what is the reason for the mismatch. Test parameters I use with the code and the output are given below along with expected analytic solution.
I have set : int WhichCase = 3 double V1[3] = {0.0, 0.0, 0.0}; double V2[3] = {0.1, 0.0, 0.0}; double V3[3] = {0.05, 0.1, 0.0}; int NumPKs = 1; PIndex[1] = {TD_UNITY}; PIndex[1] = {TD_RP}; cdouble KParam[1] = {-1.0};
Result with code: 8.12533971e-1 Result with Analytic Formula: 1.0210603e-3