Solution of nonsymmetric systems of equations on a multiprocessor
Chandrika Kamath · 1986
We consider the iterative solution of large sparse linear systems of equations arising from elliptic and parabolic partial differential equations in two and three space dimensions. Specifically, we focus our attention on non-symmetric systems of equations whose eigenvalues lie on both sides of the imaginary axis, or whose symmetric part is not positive definite. This system of equations is solved using the projection methods with conjugate gradient acceleration. The algorithm has been designed with special emphasis on its suitability for multiprocessors. In the first part of the thesis, we study the numerical properties of the algorithm and compare its performance with other algorithms such as the conjugate gradient method on the normal equations, the Chebyshev method, Orthomin(k), GCR(k) and GMRES(k). We also study the effect of various preconditioners on these methods. In the second part of the thesis, we implement our algorithm on the CRAY X-MP/48 multiprocessor and study its behavior as the number of processors is increased.