Fast convolution quadrature based impedance boundary conditions

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• 作者：Ralf Hiptmair ; Mar铆a L贸pez-Fern谩ndez ; Alberto Paganini
• 关键词：65M15 ; 65M60 ; 65M20 ; 65R20
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：June, 2014
• 年：2014
• 卷：263
• 期：Complete
• 页码：500-517
• 全文大小：582 K

文摘

We consider an eddy current problem in time-domain relying on impedance boundary conditions on the surface of the conductor(s). We pursue its full discretization comprising (i) a finite element Galerkin discretization by means of lowest order edge elements in space, and (ii) temporal discretization based on Runge-Kutta Convolution Quadrature (CQ) for the resulting Volterra integral equation in time. The final algorithm also involves the fast and oblivious approximation of CQ.

For this method we give a comprehensive convergence analysis and establish that the errors of spatial discretization, CQ and of its approximate realization add up to the final error bound.