Generalized Convolution Quadrature with Variable Time Stepping. Part II: Algorithm and Numerical Results∗
نویسندگان
چکیده
In this paper, we will address the implementation of the Generalized Convolution Quadrature (GCQ) presented and analyzed in [M. LópezFernández, S. Sauter: A Generalized Convolution Quadrature with Variable Time Stepping, Preprint 17-2011, University of Zurich (2011)] for solving linear parabolic and hyperbolic evolution equations. Our main goal is to overcome the current restriction to uniform time steps of Lubich’s Convolution Quadrature (CQ). A major challenge for the efficient realization of the new method is the evaluation of high-order divided differences for the transfer function in a fast and stable way. Our algorithm is based on contour integral representation of the numerical solution and quadrature in the complex plane. As the main application we will consider the wave equation in exterior domains which is formulated as a retarded boundary integral equation.
منابع مشابه
A Generalized Convolution Quadrature with Variable Time Stepping
In this paper, we will present a generalized convolution quadrature for solving linear parabolic and hyperbolic evolution equations. The original convolution quadrature method by Lubich works very nicely for equidistant time steps while the generalization of the method and its analysis to non-uniform time stepping is by no means obvious. We will introduce the generalized convolution quadrature ...
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