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Botchev, M.A. (2012) A short guide to exponential Krylov subspace time integration for Maxwell's equations. Memorandum 1992, Department of Applied Mathematics, University of Twente, Enschede. ISSN 1874-4850
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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.
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