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A matrix decomposition MFS algorithm for certain linear elasticity problems

Abstract

We propose an efficient matrix decomposition Method of Fundamental Solutions algorithm for the solution of certain two-dimensional linear elasticity problems. In particular, we consider the solution of the Cauchy–Navier equations in circular domains subject to Dirichlet boundary conditions, that is when the displacements are prescribed on the boundary. The proposed algorithm is extended to the case of annular domains. Numerical experiments for both types of problems are presented.

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Correspondence to A. Karageorghis.

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Parts of this work were undertaken whilst the corresponding author was a Visiting Professor in the Department of Mathematical and Computer Sciences, Colorado School of Mines, Golden, Colorado 80401, USA

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Karageorghis, A., Smyrlis, Y.S. & Tsangaris, T. A matrix decomposition MFS algorithm for certain linear elasticity problems. Numer Algor 43, 123–149 (2006). https://doi.org/10.1007/s11075-006-9045-3

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  • DOI: https://doi.org/10.1007/s11075-006-9045-3

Keywords

  • method of fundamental solutions
  • Cauchy–Navier system
  • matrix decomposition algorithm
  • fast Fourier transform
  • circulant matrices

Mathematics Subject Classifications (2000)

  • Primary 35J55
  • 35E05
  • 65N35
  • Secondary 65N38
  • 65F30
  • 65T50