Preconditioning for radial basis function partition of unity methods

Alfa Heryudono, Elisabeth Larsson, Alison Ramage, Lina von Sydow

Research output: Contribution to journalArticle

17 Citations (Scopus)
113 Downloads (Pure)

Abstract

Meshfree radial basis function (RBF) methods are of interest for solving partial differential equations due to attractive convergence properties, flexibility with respect to geometry, and ease of implementation. For global RBF methods, the computational cost grows rapidly with dimension and problem size, so localised approaches, such as partition of unity or stencil based RBF methods, are currently being developed. An RBF partition of unity method (RBF--PUM) approximates functions through a combination of local RBF approximations. The linear systems that arise are locally unstructured, but with a global structure due to the partitioning of the domain. Due to the sparsity of the matrices, for large scale problems, iterative solution methods are needed both for computational reasons and to reduce memory requirements. In this paper we implement and test different algebraic preconditioning strategies based on the structure of the matrix in combination with incomplete factorisations. We compare their performance for different orderings and problem settings and find that a no-fill incomplete factorisation of the central band of the original discretisation matrix provides a robust and efficient preconditioner.
Original languageEnglish
Pages (from-to)1089-1109
Number of pages21
JournalJournal of Scientific Computing
Volume67
Issue number3
DOIs
Publication statusPublished - 19 Oct 2015

Fingerprint

Partition of Unity Method
Preconditioning
Radial Functions
Basis Functions
Incomplete Factorization
Factorization
Meshfree
Partition of Unity
Function Approximation
Iterative Solution
Large-scale Problems
Sparsity
Preconditioner
Convergence Properties
Computational Cost
Partitioning
Partial differential equation
Partial differential equations
Discretization
Flexibility

Keywords

  • radial basis function
  • partition of unity
  • iterative method
  • preconditioning
  • algebraic preconditioner

Cite this

Heryudono, Alfa ; Larsson, Elisabeth ; Ramage, Alison ; von Sydow, Lina. / Preconditioning for radial basis function partition of unity methods. In: Journal of Scientific Computing. 2015 ; Vol. 67, No. 3. pp. 1089-1109.
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Preconditioning for radial basis function partition of unity methods. / Heryudono, Alfa; Larsson, Elisabeth; Ramage, Alison; von Sydow, Lina.

In: Journal of Scientific Computing, Vol. 67, No. 3, 19.10.2015, p. 1089-1109.

Research output: Contribution to journalArticle

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