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Numerical solution of three-dimensional boundary-value problems by generalized approximate inverse matrix techniques. (English) Zbl 0749.65021

Summary: Generalized approximate inverse matrix (GAIM) techniques based on the concept of LU-type sparse factorization procedures are introduced for calculating explicitly approximate inverses of large sparse unsymmetric matrices of regular structure without inverting the factors \(L\) and \(U\). Explicit first and second-order iterative methods in conjunction with modified forms of the GAIM techniques are presented for solving numerically three-dimensional initial/boundary-value problems on multiprocessor systems. Applications of the new methods on a 3D boundary- value problem is discussed and numerical results are given.

MSC:

65F05 Direct numerical methods for linear systems and matrix inversion
65F10 Iterative numerical methods for linear systems
65N22 Numerical solution of discretized equations for boundary value problems involving PDEs
65N06 Finite difference methods for boundary value problems involving PDEs
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