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Explicit semi-direct methods based on approximate inverse matrix techniques for solving boundary-value problems on parallel processors |
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| Affiliation: | 1. LMIB-School of Mathematical Sciences, Beihang University, Beijing 100191, PR China;2. Courant Institute of Mathematical Sciences, NYU, New York, NY 10012, USA;1. Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA;2. Department of Mechanical and Industrial Engineering, University of Massachusetts, Amherst, MA 01003, USA;1. State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin 300072, China;2. School of Civil, Environmental and Mining Engineering, The University of Western Australia, Crawley, WA 6009, Australia |
| Abstract: | Generalized approximate inverse matrix techniques and sparse Gauss-Jordan elimination procedures based on the concept of sparse product form of the inverse are introduced for calculating explicitly approximate inverses of large sparse unsymmetric (n × n) matrices. Explicit first and second order semi-direct methods in conjunction with the derived approximate inverse matrix techniques are presented for solving Parabolic and Elliptic difference equations on parallel processors. Application of the new methods on a 2D-model problem is discussed and numerical results are given. |
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