Abstract
Applications of the multidomain Local Fourier Basis method [1], for the solution of PDEs on parallel computers are described. The present approach utilizes, in an explicit way, the rapid (exponential) decay of the fundamental solutions of elliptic operators resulting from semi-implicit discretizations of parabolic time-dependent problems. As a result, the global matching relations for the elemental solutions are decoupled into local interactions between pairs of solutions in neighboring domains. Such interactions require only local communications between processors with short communication links. Thus the present algorithm overcomes the global coupling, inherent both in the use of the spectral Fourier method and implicit time discretization scheme.
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Israeli, M., Vozovoi, L., and Averbuch, A. (1993). Spectral multidomain technique with Local Fourier BasisJ. of Sci. Comp. 8, 135–149.
Macaraeg, M. G. and Street, C. L. (1986). Improvements in spectral collocation discretization through a multidomain technique,Appl. Numeric. Mathem. 2, 95–108.
Vozovoi, L., Israeli, M., and Averbuch, A. Spectral Multidomain Technique with Local Fourier Basis II: Decomposition into Cells (to be published).
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This research is supported partly by a grant from the French-Israeli Binational Foundation for 1991–1992.
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Israeli, M., Vozovoi, L. & Averbuch, A. Parallelizing implicit algorithms for time-dependent problems by parabolic domain decomposition. J Sci Comput 8, 151–166 (1993). https://doi.org/10.1007/BF01060870
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DOI: https://doi.org/10.1007/BF01060870