The IDR(s) method for solving nonsymmetric systems: a performance study for CFD problems
نویسندگان
چکیده
The recently proposed method IDR(s) [6] for solving large and sparse nonsymmetric systems of linear equations has proven to be highly efficient for important classes of applications. This paper presents an performance comparison of IDR(s) with GMRES [3], Bi-CGSTAB [7] and BiCGstab(l) [4] for representative fluid dynamics test problems. The computations are done with the MATLAB finite element program IFISS [1]. In our computations we only consider a default value of s = 4 for the parameter in IDR(s). Our experimental results show that IDR(4) is a promising method for solving the type of incompressible flow problems that we consider in this paper. The method is based on short recurrences and therefore more efficient than GMRES in memory consumption and computing time if many GMRES-iterations have to be performed. Furthermore, IDR(4) is competitive or faster than Bi-CGSTAB and BiCGstab(l) for all physically relevant examples.
منابع مشابه
DELFT UNIVERSITY OF TECHNOLOGY REPORT 07-07 IDR(s): a family of simple and fast algorithms for solving large nonsymmetric linear systems
We present IDR(s), a new family of efficient, short-recurrence methods for large nonsymmetric systems of linear equations. The new methods are based on the Induced Dimension Reduction (IDR) method proposed by Sonneveld in 1980. While state-ofthe-art methods such as Bi-CGSTAB require at most 2N matrix-vector products to compute an exact solution in exact arithmetic, IDR(s) requires at most N + N...
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The Induced Dimension Reduction method [12] was proposed in 1980 as an iterative method for solving large nonsymmetric linear systems of equations. IDR can be considered as the predecessor of methods like CGS (Conjugate Gradient Squared) [9]) and Bi-CGSTAB (Bi-Conjugate Gradients STABilized, [11]). All three methods are based on efficient short recurrences. An important similarity between the m...
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