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Analysis of the Boundary Knot Method for 3D Helmholtz-Type Equation

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  • F. Z. Wang
  • K. H. Zheng

Abstract

Numerical solutions of the boundary knot method (BKM) always perform oscillatory convergence when using a large number of boundary points in solving the Helmholtz-type problems. The main reason for this phenomenon may contribute to the severely ill-conditioned full coefficient matrix. In order to obtain admissible stable convergence results, regularization techniques and the effective condition number are employed in the process of simulating 3D Helmholtz-type problems. Numerical results are tested for the 3D Helmholtz-type equation with noisy and non-noisy boundary conditions. It is shown that the BKM in combination with the regularization techniques is able to produce stable numerical solutions.

Suggested Citation

  • F. Z. Wang & K. H. Zheng, 2014. "Analysis of the Boundary Knot Method for 3D Helmholtz-Type Equation," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-9, March.
    • Handle: RePEc:hin:jnlmpe:853252
    DOI: 10.1155/2014/853252
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