Abstract
In this paper we summarize recent progresses on the parallel method for solving time-dependent problems using the Fourier-Laplace transformation. These problems arise in the study of elastic wave equations with absorbing boundary conditions, for example. Instead of solving the time-dependent problems in the space-time domain, we solve them as follows. First, take the Fourier-Laplace transformation of given problems originally set in the space-time domain, and consider the corresponding problems in the space-frequency domain which form a set of indefinite, complex-valued elliptic problems. Such problems are solved in a natural parallel manner since each problem is independent of others. The Fourier-Laplace inversion formula will then recover the solution in the space-time domain.
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Sheen, D. (2000). Parallel Methods for Solving Time-Dependent Problems Using the Fourier-Laplace Transformation. In: Chen, Z., Ewing, R.E., Shi, ZC. (eds) Numerical Treatment of Multiphase Flows in Porous Media. Lecture Notes in Physics, vol 552. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45467-5_23
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DOI: https://doi.org/10.1007/3-540-45467-5_23
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