Patch-Based Matrix-Free Time-Domain Method in 3D Unstructured Meshes

In this work, we propose a new time-domain method for solving Maxwell’s equations: Patch-based Matrix-Free Time Domain (P-MFTD) method, in unstructured meshes. This method is free of matrix solutions regardless of the element shape used for discretization. Meanwhile, it avoids the use of higher-order 3-D vector basis functions, and hence significantly reduces the number of unknowns required to solve the same problem. Moreover, its time-domain stability is guaranteed featuring real-valued eigenvalues despite an unsymmetrical numerical system. Numerical experiments have validated its accuracy, efficiency, and stability.