Abstract
We study the boundary element method for weakly singular and hypersingular integral equations of the first kind on screens resulting from the Dirichlet and Neumann problems for the Helmholtz equation. It is shown that the hp-version with geometrical refined meshes converges exponentially fast in both cases. We underline our theoretical results by numerical experiments for the pure h-, p-versions, the graded mesh and the hp-version with geometrically refined mesh.
Zusammenfassung
Wir betrachten die Randelementmethode für schwachsinguläre und hypersinguläre Integralgleichungen erster Art auf Schirmen. Die Integralgleichungen sind äquivalent zum Dirichlet- beziehungsweise Neumann-Problem für die Helmholtz-Gleichung im Außengebiet. Es wird gezeigt, daß die hp-Version mit geometrischem Gitter in beiden Fällen exponentiell in Abhängigkeit von den Freiheitsgraden konvergiert. Wir bestätigen unsere theoretischen Ergebnisse durch numerische Experimente für die reine h- und p-Version, für das graduierte Gitter und für die hp-Version mit geometrischem Gitter.
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Holm, H., Maischak, M. & Stephan, E.P. The hp-version of the boundary element method for Helmholtz screen problems. Computing 57, 105–134 (1996). https://doi.org/10.1007/BF02276875
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DOI: https://doi.org/10.1007/BF02276875