Numerical instabilities of the integral approach to the interior boundary‐value problem for the two‐dimensional Helmholtz equation | Zendy

Mattioli F. | Zendy

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Numerical instabilities of the integral approach to the interior boundary‐value problem for the two‐dimensional Helmholtz equation

Author(s) -

Mattioli F.

Publication year - 1980

Publication title -

international journal for numerical methods in engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.421

H-Index - 168

eISSN - 1097-0207

pISSN - 0029-5981

DOI - 10.1002/nme.1620150903

Subject(s) - helmholtz equation , mathematics , integral equation , domain (mathematical analysis) , mathematical analysis , helmholtz free energy , boundary value problem , function (biology) , green's function , electric field integral equation , boundary (topology) , physics , quantum mechanics , evolutionary biology , biology

The integral equations arising from the Green's formula, applied to the two‐dimensional Helmholtz equation defined in a limited domain, are considered and the presence of instabilities in their numerical solution, when a real Green's function is adopted, is pointed out. A complete study has been carried out for a circular domain and the conditions under which such instabilities can occur in a domain of arbitrary geometry have been investigated. In particular, it has been shown that in every case the use of a complex Green's function is able to avoid their presence.

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