High-order numerical solution of the Helmholtz equation for domains with reentrant corners

S. Magura, S. Petropavlovsky, S. Tsynkov, E. Turkel

Research output: Contribution to journalArticlepeer-review


Standard numerical methods often fail to solve the Helmholtz equation accurately near reentrant corners, since the solution may become singular. The singularity has an inhomogeneous contribution from the boundary data near the corner and a homogeneous contribution that is determined by boundary conditions far from the corner. We present a regularization algorithm that uses a combination of analytical and numerical tools to distinguish between these two contributions and ultimately subtract the singularity. We then employ the method of difference potentials to numerically solve the regularized problem with high-order accuracy over a domain with a curvilinear boundary. Our numerical experiments show that the regularization successfully restores the design rate of convergence.

Original languageEnglish
Pages (from-to)87-116
Number of pages30
JournalApplied Numerical Mathematics
StatePublished - 1 Aug 2017


  • Asymptotic expansion near singularity
  • Compact differencing
  • Curvilinear boundaries
  • Difference potentials
  • Regularization
  • Singularity subtraction


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