Accuracy-controlled convergence criterion for full wave simulation

Abstract

Full wave electromagnetic (EM) simulations frequently encounter low-frequency breakdown: for decoupling of electric and magnetic fields in low frequency, the impedance matrix degenerates into near singular matrix and causes convergence problems. The iterative algorithms are currently the primary solvers of matrix equation for massive EM simulation. For absence of constraint between simulation accuracy and the convergence condition for iterative solver, excessively rigorous convergence condition has to be applied to ensure simulation accuracy, as a result, this way leads to over convergence, i.e., converge at unnecessarily high accuracy and simulation time doubly increases. By theoretically analyzing the impedance matrix, connection between simulation accuracy and the relative residual error which serves as the convergence condition in iterative solvers is established, and an accuracy-controlled convergence criterion is proposed. Numerical experiments are included to demonstrate that this convergence criterion effectively avoids the occurrence of over convergence yet insures simulation accuracy; therefore the simulation efficiency is visibly promoted.