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A FETI Domain Decomposition Method For Maxwell's Equations With Discontinuous Coefficients In Two Dimensions

By Andrea Toselli and Axel Klawonn


. A class of FETI methods for the edge element approximation of vector eld problems in two dimensions is introduced and analyzed. First, an abstract framework is presented for the analysis of a class of FETI methods where a natural coarse problem, associated with the substructures, is lacking. Then, a family of FETI methods for edge element approximations is proposed. It is shown that the condition number of the corresponding method is independent of the number of substructures and grows only polylogarithmically with the number of unknowns associated with individual substructures. The estimate is also independent of the jumps of both of the coecients of the original problem. Numerical results validating the theoretical bounds are given. The method and its analysis can be easily generalized to Raviart{Thomas element approximations in two and three dimensions. Key words. Edge elements, Maxwell's equations, domain decomposition, FETI, preconditioners, heterogeneous coecients AMS subjec..

Year: 1999
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