A HYBRID NUMERICAL BOUNDARY-CONDITION AND ITS APPROXIMATIONS FOR ELECTROMAGNETIC SCATTERING PROBLEMS

A hybrid numerical boundary condition (HNBC) with the same accuracy as surface integral methods, applicable to an absorbing boundary with an arbitrary shape, is proposed. The HNBC is a global boundary condition resulting in a dense submatrix due to the coupling of all boundary no des. In many cases, the HNBC can be approximated by another set of Bou ndary conditions where only a few boundary nodes are coupled together to preserve the sparsity of the resulting matrix equation. One special approximation will result in the measured equation of invariance (MEI ) method. Another approximation will result in a nonlocal numerical bo undary condition (NNBC), of which the MEI method is a subset. For the NNBC, the sparsity of the resulting finite element matrix is preserved , although the boundary condition is nonlocal. Numerical results for a class of 2-D problems are presented to illustrate the accuracy of the original global hybrid numerical boundary condition and the nonlocal numerical boundary condition.