Adaptive Ritz Block Lanczos for Algebraic Systems arising from Fluid Flow Problems

Pedro Torres¹; Christian Schaerer¹; Amit Bhaya²

¹ Polytechnic School - National University of Asuncion; ² Federal University of Rio de Janeiro

doi:10.20906/CPS/CILAMCE2015-0423

Resumo

Block Methods based on conjugate directions are promising for efficient implementation on new computational architectures, improving the arithmetic intensity and the rate of convergence with respect to classical ones. In this article the Block Lanczos method - BLM, previously introduced for computing eigenvalues, is used for the resolution of algebraic linear systems $Ax=b$ with $A$ symmetric positive definite. A drawback of the method lies in the adequate choice of block size. This article, propose a rule that adaptively updates the size of the block in the BCG algorithm and uses a threshold to determine when the rule acts. The rule is based on indirect measure of the distribution of the eigenvalues by approximating them and their relative clusterization using Ritz values. The resulting method shows an acceleration of the convergence of the algorithm decreasing the computational cost, if an adequate threshold is set. Results for on matrices arising from computational fluid problems are presented.

Palavras-chave: Block Conjugate Gradient; Ritz Values; Symmetric Positive Definite Problems; Fluid Flow Problems