Abstract
The analysis of a multiphysics problem typically requires an efficient simulation of many types of partial differential equations (PDEs). In this paper, we demonstrate that the matrix-free time-domain method [1] recently developed for solving vector-based Maxwell's equations is equally applicable to solving the scalar thermal diffusion equation, in a matrix-solution free manner in arbitrary unstructured meshes. This is achieved by appending a direction to the original scalar-based temperature, and transforming the thermal equation to two equivalent vector equations to solve. Both 2- and 3-D thermal simulations have validated the correctness of the proposed method. The flexible framework of the matrix-free method also allows for an efficient solution of other types of PDEs.
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