Journal
SIAM JOURNAL ON NUMERICAL ANALYSIS
Volume 54, Issue 3, Pages 1385-1400Publisher
SIAM PUBLICATIONS
DOI: 10.1137/15M1011755
Keywords
Helmholtz equation; transparent boundary condition; pole condition; Hardy space infinite elements
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Funding
- Austrian Science Fund (FWF) [W1245-N25]
- Austrian Science Fund (FWF) [W1245] Funding Source: Austrian Science Fund (FWF)
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We perform a convergence analysis for discretizations of Helmholtz scattering and resonance problems obtained by Hardy space infinite elements. Superalgebraic convergence rates with respect to the number of Hardy space degrees of freedom are achieved. We consider spheres and piecewise polytopes as transparent boundaries. The analysis is based on a Garding-type inequality and standard operator theoretical results. While the obtained results are related to those for the radial perfectly matched layer method, different techniques are used in the analysis.
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