Lee, P.; Pasciak, J. E.; Pissanetzky, S. Parallel computation of magnetic fields. (English) Zbl 0733.65082 COMPEL 10, No. 1, 45-55 (1991). The authors consider the problem of obtaining the magnetostatic field in a system wherein all magnetic material is in a simply connected domain which is surrounded by another domain containing conductors. A finite element approximation is used and an algorithm is indicated whereby the preconditioner for the entire problem is obtained with a set of overlapping subdomains whose union covers the complete domain. The method proposed is valid for nonlinear magnetism and the results of two experiments on a particular system are reported. These show that the method proposed can result in a considerate speed up. Reviewer: Ll.G.Chambers (Bangor) MSC: 65Z05 Applications to the sciences 65Y05 Parallel numerical computation 65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs 65N38 Boundary element methods for boundary value problems involving PDEs 78A25 Electromagnetic theory (general) 86A25 Geo-electricity and geomagnetism Keywords:parallel computation; parallel preconditioning; domain decomposition; magnetostatic field; rate of convergence; numerical experiments; finite element; nonlinear magnetism PDFBibTeX XMLCite \textit{P. Lee} et al., COMPEL 10, No. 1, 45--55 (1991; Zbl 0733.65082) Full Text: DOI References: [1] Armstrong A.G.A.M., Version 3.1 (1982) [2] DOI: 10.1109/20.34314 · doi:10.1109/20.34314 [3] DOI: 10.1137/0905040 · Zbl 0548.65017 · doi:10.1137/0905040 [4] Chari M.V.K., Finite Elements in Electrical and Magnetic Field Problems (1980) [5] M. Dryja, An additive Schwarz algorithm for two- and three-dimensional finite element elliptic problems, In T. Chan, R. Glowinski, G.A. Meurant, J. Periaux, and O. Widlund (eds.),Domain Decomposition Methods (SIAM, Philadelphia, 1989) pp.168-172. · Zbl 0681.65075 [6] Chan T., Domain Decomposition Methods (1989) [7] M. Dryja and O. Widlund, An additive variant of the Schwarz alternating method for the case of many subregions, Technical Report 339, Department of Computer Science, Courant Institute, New York, 1987. [8] Golub G., Matrix Computation (1982) [9] DOI: 10.1109/20.43914 · doi:10.1109/20.43914 [10] Lions P.L., First International Symposium on Domain Decomposition Methods for Partial Differential Equations (SIAM pp 1– (1988) [11] Lichnewsky A., Proc. NATO Workshop on High Speed Computations, J. Kowalik (ed.) NATO ASI Scries 7 (1984) [12] DOI: 10.1109/20.34317 · doi:10.1109/20.34317 [13] DOI: 10.1137/1013094 · Zbl 0226.68004 · doi:10.1137/1013094 [14] DOI: 10.1137/1.9781611971774 · doi:10.1137/1.9781611971774 [15] DOI: 10.1109/TMAG.1982.1061884 · doi:10.1109/TMAG.1982.1061884 [16] Schnendel U., Trans. (1984) [17] DOI: 10.1049/ip-f-1.1980.0053 · doi:10.1049/ip-f-1.1980.0053 [18] DOI: 10.1109/20.43845 · doi:10.1109/20.43845 [19] DOI: 10.1109/20.43913 · doi:10.1109/20.43913 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.