Non-iterative domain decomposition for the Helmholtz equation with strong material discontinuities

Evan North, Semyon Tsynkov, Eli Turkel

Research output: Contribution to journalArticlepeer-review


Many wave propagation problems involve discontinuous material properties. We propose to solve such problems by non-overlapping domain decomposition combined with the method of difference potentials (MDP). The MDP reduces the Helmholtz equation on each subdomain to a Calderon's boundary equation with projection on the boundary. The unknowns for the Calderon's equation are the Dirichlet and Neumann data. Coupling between neighboring subdomains is rendered by applying their respective Calderon's equations to the same data at the common interface. Solutions on individual subdomains are computed concurrently using a direct solver. Our method proves to be insensitive to large jumps in the wavenumber for transmission problems, as well as interior cross-points and mixed boundary conditions, which may be a challenge to many other domain decomposition methods.

Original languageEnglish
Pages (from-to)51-78
Number of pages28
JournalApplied Numerical Mathematics
StatePublished - Mar 2022


  • Calderon's operators
  • Compact finite difference schemes
  • Complexity bounds
  • Difference potentials
  • Direct solution
  • Discontinuous coefficients
  • Exact coupling between subdomains
  • High-order accuracy
  • Interior cross-points
  • Non-overlapping domain decomposition
  • Spectral representation at the boundary
  • Time-harmonic waves


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