New Stability Criterion for Unstructured Mesh Upwinding FVTD Schemes for Maxwell's Equations

摘要

A new stability criterion applicable to explicit upwind FVTD schemes for solving Maxwell's equations on unstructured meshes is derived. This criterion is based on L_2-norm estimates of specially constructed matrices G_i for each finite volume i. Each such matrix is constructed using the scalar product of the eigenvectors corresponding to the unity eigenvalues of the fluxsplitting operators associated with the facets of volume i. The new stability criterion is obtained numerically once the grid is constructed using these matrices over the mesh and is therefore mesh dependent. The new criterion gives a time-step that is larger than the time-step calculated using previously published stability criteria. On structured meshes the new criterion gives the same time-step limit as the von Neumann analysis. The method incurs a small computational expense at the beginning of each run of the algorithm. The method is generalizable but the extent to which it can be generalized to other time-evolving physical phenomenon is not considered in this paper.