On substructuring algorithms and solution techniques for the numerical approximation of partial differential equations
Abstract
Substructuring methods are in common use in structural mechanics problems where typically the associated linear systems of algebraic equations are positive definite. Here these methods are extended to problems which lead to nonpositive definite, nonsymmetric matrices. The extension is based on an algorithm which carries out the block Gauss elimination procedure without the need for interchanges even when a pivot matrix is singular. Examples are provided wherein the method is used in connection with finite element solutions of the stationary Stokes equations and the Helmholtz equation, and dual methods for secondorder elliptic equations.
 Publication:

Advances in Numerical and Applied Mathematics
 Pub Date:
 March 1986
 Bibcode:
 1986anam.nasa..165G
 Keywords:

 Algorithms;
 Approximation;
 Boundary Value Problems;
 Elastic Properties;
 Finite Element Method;
 Partial Differential Equations;
 Problem Solving;
 Structural Engineering;
 Computational Grids;
 Finite Difference Theory;
 Gaussian Elimination;
 Matrices (Mathematics);
 Stokes Law (Fluid Mechanics);
 Fluid Mechanics and Heat Transfer