Simulation of multiscale problems using equivalence principle algorithm

Computational electromagnetic (CEM) simulations have become an indispensable tool in analyzing and designing modern electromagnetic system. However, many challenges arise when applying CEM solvers to real world problems. Multiscale phenomena are one of them. The existence of both wave and circuit physics in such problems introduces large and small eigenvalues simultaneously that causes the resulting matrix equation ill-conditioned. Equivalence principle algorithm (EPA) is essentially a domain decomposition scheme to solve multiscale problems. It is based on equivalence principle and integral equations [1]. By the introduction of virtual equivalence surfaces to enclose the regions with fine features, low frequency physics is isolated from high frequency physics. This results in a better conditioned matrix equation with fewer unknowns. To model continuous current flow in and out of the equivalence surface, a tap basis scheme was introduced. This scheme avoids the computation of current singularities at the cut and can be incorporated with EPA naturally. Moreover, to improve the accuracy of field projections, a high-order quadrature point-sampling scheme was used to describe the currents on equivalence surfaces. This scheme samples the currents directly at points on the equivalence surfaces and integrates using high-order quadrature rules. By using this, EPA is shown to be accurate.