Domain decomposition methods for solving parabolic PDEs on multiprocessors
This paper concentrates mainly on local approaches for solving parabolic partial differential equations. After an introduction to various approaches of domain decomposition and a discussion of time-dependent problems, the authors present a novel parabolic domain decomposition method with local matching procedures on the interface. One novel feature is that the solutions to the homogeneous algebraic equations in each subdomain found by (spatial) discretization (at each time-step) are written analytically, hence this enables and simplifies the explicit derivation of the interface matching relations. Another basic feature is the use of the local Fourier basis, constructed by \textit{R. R. Coifman} and \textit{Y. Meyer} [C. R. Acad. Sci. Paris, Sér. I 312, No. 3, 259-261 (1991; Zbl 0748.42012)]. Further, another approach to solve parabolic equations is discussed, which has been introduced by \textit{Yu. A. Kuznetsov} [see e.g. in: Computing Methods in Applied Sciences and Engineering, ed. R. Glowinski, A. Lichnewsky, SIAM (1990; Zbl 0744.65063)]. For a smooth modification of the overlapping domain decomposition method of Kuznetsov a simple one- dimensional equation is given to show the numerical efforts.
scientific article; zbMATH DE number 205165
scientific article