Accurate and Stable Matrix-Free Time-Domain Method in 3-D Unstructured Meshes for General Electromagnetic Analysis


We develop a brand new time-domain technique that is naturally matrix free, i.e., requiring no matrix answer, irrespective of whether the discretization is a structured grid or an unstructured mesh. Its matrix-free property, manifested by a naturally diagonal mass matrix, is independent of the component shape used for discretization and its implementation is easy. No twin mesh, interpolation, projection, and mass lumping are required. Furthermore, we show that such a capability will be achieved with typical vector basis functions without any need for modifying them. Moreover, a time-marching scheme is developed to ensure the soundness for simulating an unsymmetrical numerical system whose eigenvalues can be advanced-valued and even negative, whereas preserving the matrix-free merit of the proposed method. Intensive numerical experiments are carried out on a variety of unstructured triangular, tetrahedral, triangular prism part, and mixed-part meshes. Correlations with analytical solutions and therefore the results obtained from the time-domain finite-component methodology, in any respect points in the computational domain and across all time instants, have validated the accuracy, matrix-free property, stability, and generality of the proposed methodology.

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