zbMATH — the first resource for mathematics

A matrix decomposition method for orthotropic elasticity problems. (English) Zbl 0669.73010
The SAS (symmetrical and antisymmetrical) matrix decomposition method proposed by the authors is a highly parallelizable method for solving linear systems \(Ax=b\) of algebraic equations, eigenvalue problems \(Ax=\lambda x\), and generalized eigenvalue problems \(Ax=\lambda Bx\), provided that the matrices involved possess the SAS-property \(A=PAP\), or \(B=PBP\), with respect to some symmetrical signed permutation matrix P.
Such problems are decomposable into independent subproblems which can be solved in parallel. The solution of the original problem can be easily recovered from the solution of the subproblems. The recursive approach is possible as long as the matrices of the subproblems have the SAS- property. Matrices possessing the SAS-property arise, e.g., from symmetrical discretization of boundary value problems for the differential operator, the boundary conditions and the geometry of which are characterized by certain symmetry properties.
The authors apply their SAS-method to some special orthotropic, three- dimensional, linear elasticity problems, and present numerical results impressively substantiating the applicability and usefulness of the SAS- technique for sequential, vector, and multiprocessor computers.
Reviewer: U.Langer

74S30 Other numerical methods in solid mechanics (MSC2010)
65F05 Direct numerical methods for linear systems and matrix inversion
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
15A04 Linear transformations, semilinear transformations
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65Y05 Parallel numerical computation
Full Text: DOI