New Stability Criterion for Unstructured Mesh Upwinding FVTD Schemes for Maxwell’s Equations
Keywords:
Finite-volume time-domain, unstructured mesh, Maxwell’s equations, and stability criterion.Abstract
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 L2-norm estimates of specially constructed
matrices Gi 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.
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References
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