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Variational methods for time-dependent wave propagation problems. (English) Zbl 1049.78028
Ainsworth, Mark (ed.) et al., Topics in computational wave propagation. Direct and inverse problems. Berlin: Springer (ISBN 3-540-00744-X/pbk). Lect. Notes Comput. Sci. Eng. 31, 201-264 (2003).
The author develops two alternative variational methods for the study of some classes of time-dependent wave propagation problems. The main objective is related to the treatment of complex geometries with finite difference time domain schemes. The author takes into account the following three directions: (i) the data of the problem remains structured; (ii) the time discretisation remains explicit, and (iii) the stability condition is not affected by the geometry of the computational domain.
The first method developed in the paper involves the introduction of a Lagrange multiplier on the coarse-fine gride interface, while the second method does not. However, both approaches require the solution of a small, sparse, positive definite linear system on the interface. Numerical phenomena due to a change of grid are also described.
For the entire collection see [Zbl 1018.00017].

78M30 Variational methods applied to problems in optics and electromagnetic theory
78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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