Schwarz Analysis of Iterative Substructuring Algorithms for Elliptic Problems in Three Dimensions

• Published in: SIAM journal on numerical analysis Vol. 31; no. 6; pp. 1662 - 1694
• Main Authors: Dryja, Maksymilian, Smith, Barry F., Widlund, Olof B.
• Format: Journal Article
• Language: English
• Published: Philadelphia, PA Society for Industrial and Applied Mathematics 01.12.1994
• Subjects: Algebra; ALGORITHMS; Applied mathematics; CALCULATION METHODS; Coefficients; Constant coefficients; CONVERGENCE; Decomposition; Decomposition methods; Design; DIFFERENTIAL EQUATIONS; EQUATIONS; Exact sciences and technology; GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; Interpolation; ITERATIVE METHODS; Laboratories; Linear and multilinear algebra, matrix theory; Mathematical constants; MATHEMATICAL LOGIC 990200 > Mathematics & Computers; Mathematics; Methods; Numerical analysis; Numerical analysis. Scientific computation; PARTIAL DIFFERENTIAL EQUATIONS; Partial differential equations, boundary value problems; Sciences and techniques of general use; THREE-DIMENSIONAL CALCULATIONS; Vertices; Numerical approximation; Finite element method; Elliptic equation; Algebraic equation; Convergence rate; Iterative method; Algorithm; Domain decomposition; Partial differential equation; Finite difference method; Equation system

Domain decomposition methods provide powerful preconditioners for the iterative solution of the large systems of algebraic equations that arise in finite element or finite difference approximations of partial differential equations. The preconditioners are constructed from exact or approximate solve...