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2014.18: Block Preconditioners for Linear Systems Arising from Multiscale Collocation with Compactly Supported RBFs

2014.18: Patricio Farrell and Jennifer Pestana (2014) Block Preconditioners for Linear Systems Arising from Multiscale Collocation with Compactly Supported RBFs.

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Abstract

Symmetric multiscale collocation methods with radial basis functions allow approximation of the solution of a partial differential equation, even if the right-hand side is only known at scattered data points, without needing to generate a grid. However, the benefit of a guaranteed symmetric positive definite block system comes at a high computational cost. In particular, the condition number and sparsity deteriorate with the number of data points. Therefore, we study certain block diagonal and triangular preconditioners. We investigate ideal preconditioners and determine the spectra of the preconditioned matrices before proposing more practical preconditioners based on a restricted additive Schwarz method with coarse grid correction (ARASM). Numerical results verify the effectiveness of the preconditioners.

Item Type:MIMS Preprint
Subjects:MSC 2000 > 65 Numerical analysis
MIMS number:2014.18
Deposited By:Dr Jennifer Pestana
Deposited On:09 March 2015

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