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Runge-Kutta convolution coercivity and its use for time-dependent boundary integral equations

Banjai, Lehel; Lubich, Christian

Abstract:
A coercivity property of temporal convolution operators is an essential tool in the analysis of time-dependent boundary integral equations and their space and time discretisations. It is known that this coercivity property is inherited by convolution quadrature time discretisation based on A-stable multistep methods, which are of order at most two. Here we study the ques- tion as to which Runge–Kutta-based convolution quadrature methods inherit the convolution coercivity property. It is shown that this holds without any restriction for the third-order Radau IIA method, and on permitting a shift in the Laplace domain variable, this holds for all algebraically stable Runge– Kutta methods and hence for methods of arbitrary order. As an illustration, the discrete convolution coercivity is used to analyse the stability and convergence properties of the time discretisation of a non-linear boundary integral equation that originates from a non-linear scattering problem for the linear wave equation. Numerical experiments illustrate the error behaviour of the Runge–Kutta convolution quadrature time discretisation.


Zugehörige Institution(en) am KIT Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht
Jahr 2017
Sprache Englisch
Identifikator DOI(KIT): 10.5445/IR/1000067263
ISSN: 2365-662X
URN: urn:nbn:de:swb:90-672630
KITopen ID: 1000067263
Verlag KIT, Karlsruhe
Umfang 24 S.
Serie CRC 1173 ; 2017/3
Schlagworte Runge–Kutta convolution quadrature, coercivity, stability, boundary integral equation, wave equation
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