Matrix-Free Method for Transient Maxwell-Thermal Cosimulation in Arbitrary Unstructured Meshes

Existing electrical-thermal cosimulation methods require solving a system matrix when handling inhomogeneous materials and irregular geometries discretized into unstructured meshes. In this paper, a matrix-free method is developed for cosimulating full-wave Maxwell's equations and the thermal diffusion equation in the time domain. The method is free of matrix solutions regardless of the shape of the element used for space discretization. A theoretical stability analysis is also developed for the coupled electrical and thermal analysis, which is nonlinear in nature. Numerical experiments on both unstructured tetrahedral and triangular prism element meshes have validated the accuracy and efficiency of the proposed method.