A short guide to exponential Krylov subspace time integration for Maxwell’s equationsI
نویسنده
چکیده
The exponential time integration, i.e., time integration which involves the matrix exponential, is an attractive tool for solving Maxwell’s equations in time. However, its application in practice often requires a substantial knowledge of numerical linear algebra algorithms, in particular, of the Krylov subspace methods. This note provides a brief guide on how to apply exponential Krylov subspace time integration in practice. Although we consider Maxwell’s equations, the guide can readily be used for other similar time-dependent problems. In particular, we discuss in detail the Arnoldi shift-and-invert method combined with recently introduced residual-based stopping criterion. Two of the algorithms described here are available as MATLAB codes and can be downloaded from the website http://eprints.eemcs.utwente. nl/ together with this note.
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