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Numerical integration of partial differential equations using principles of multidimensional wave digital filters

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Abstract

Physical systems described by partial differential equations (PDEs) are usually passive (due to conservation of energy) and furthermore massively parallel and only locally interconnected (due to the principle of action at proximity, as opposed to action at a distance). An approach is developed for numerically integrating such PDEs by means of algorithms that offer massive parallelism and require only local interconnections. These algorithms are based on the principles of multidimensional wave digital filtering and amount to directly simulating the actual physical system by means of a discrete passive dynamical system. They inherit all the good properties known to hold for wave digital filters, in particular the full range of robustness properties typical for these filters.

In this paper, only the linear case is considered, with particular emphasis on systems of PDEs of hyperbolic type. The main features are explained by means of an example.

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Authors and Affiliations

  1. Lehrstuhl fuer Nachrichtentechnik, Ruhr-Universitaet Bochum, Postfach 10 21 48, D-4630, Bochum 1, Germany

    Alfred Fettweis & Gunnar Nitsche

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  1. Alfred Fettweis
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  2. Gunnar Nitsche
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Fettweis, A., Nitsche, G. Numerical integration of partial differential equations using principles of multidimensional wave digital filters. J VLSI Sign Process Syst Sign Image Video Technol 3, 7–24 (1991). https://doi.org/10.1007/BF00927832

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  • DOI: https://doi.org/10.1007/BF00927832

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