SciCADE 2013
International Conference on Scientific Computation and Differential Equations
September 16-20, 2013, Valladolid (Spain)

Contributed Talk

Show full list of Contributed Talks Show talk context (CS06)


A pre-fetched BiCGSTAB method in the solution of the trapezoidal rule of large ODEs

S. Nakamura, K. Ozawa and T. Mitsui

Abstract
We are concerned with an efficient numerical solution of linear equations at each time-stepping of the trapezoidal rule applied to a system of linear ordinary differential equations (ODEs) with a constant coefficient matrix of large dimension. We do not assume that the matrix is symmetric. Hence numerical solutions in the family of BiCG method are sought. We propose a method to reuse Krylov subspaces in the BiCGSTAB process over a number of computational steps [1]. It can suppress increase of the memory usage as well as reduce the total number of BiCGSTAB iterations. An influence of the non-autonomous term of ODEs is analyzed on the efficiency of our algorithm. Numerical examples depict its efficiency.

Bibliography
[1] S.Nakamura and T.Mitsui, A pre-fetched BiCGSTAB method in the solution of the trapezoidal rule of large ODEs, FJAM, vol. 36, pp 1-24.

Organized by         Universidad de Valladolid     IMUVA