Solving time-harmonic scattering problems based on the pole condition. II: Convergence of the PML method
In this paper we study the PML method for Helmholtz-type scattering problems with radially symmetric potential. The PML method consists of surrounding the computational domain with a perfectly matched sponge layer. We prove that the approximate solution obtained by the PML method converges exponenti...
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| Veröffentlicht in: | SIAM journal on mathematical analysis 2003-01, Vol.35 (3), p.547-560 |
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| creator | HOHAGE, Thorsten SCHMIDT, Frank ZSCHIEDRICH, Lin |
| description | In this paper we study the PML method for Helmholtz-type scattering problems with radially symmetric potential. The PML method consists of surrounding the computational domain with a perfectly matched sponge layer. We prove that the approximate solution obtained by the PML method converges exponentially fast to the true solution in the computational domain as the thickness of the sponge layer tends to infinity. This is a generalization of results by Lassas and Somersalo based on boundary integral equation techniques. Here we use techniques based on the pole condition instead. This makes it possible to treat problems without an explicitly known fundamental solution. |
| doi_str_mv | 10.1137/S0036141002406485 |
| format | Article |
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| source | LOCUS - SIAM's Online Journal Archive |
| subjects | Boundary value problems Exact sciences and technology Integral equations Mathematical analysis Mathematics Methods Sciences and techniques of general use |
| title | Solving time-harmonic scattering problems based on the pole condition. II: Convergence of the PML method |
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