A simple and effective preconditioner for integrated-RBF-based Cartesian-grid schemes
N. Mai-Duy; and T. Tran-Cong

doi:10.3970/icces.2010.014.051
Source International Conference on Computational & Experimental Engineering and Sciences, Vol. 14, No. 2, pp. 51-56, 2010
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Keywords preconditioner, integrated radial basis functions, Cartesian grids.
Abstract This paper presents a preconditioning scheme to improve the condition number of integrated radial-basis-function (RBF) matrices in solving large-scale 2D elliptic problems. The problem domain is discretised using a Cartesian grid, over which integrated RBF networks are employed to represent the field variable. The present preconditioner is constructed from 1D integrated RBF networks along grid lines. Test problems defined on rectangular and non-rectangular domains are employed to study the performance of the scheme.
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