A non-overlapping domain decomposition for low-frequency time-harmonic Maxwell’s equations in unbounded domains |
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Authors: | Yang Liu Qiya Hu Dehao Yu |
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Institution: | (1) LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100080, People’s Republic of China;(2) Graduate University of Chinese Academy of Sciences, Beijing, 100049, People’s Republic of China |
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Abstract: | In this paper, we are concerned with a non-overlapping domain decomposition method for solving the low-frequency time-harmonic
Maxwell’s equations in unbounded domains. This method can be viewed as a coupling of finite elements and boundary elements
in unbounded domains, which are decomposed into two subdomains with a spherical artificial boundary. We first introduce a
discretization for the coupled variational problem by combining Nédélec edge elements of the lowest order and curvilinear
elements. Then we design a D-N alternating method for solving the discrete problem. In the method, one needs only to solve
the finite element problem (in a bounded domain) and calculate some boundary integrations, instead of solving a boundary integral
equation. It will be shown that such iterative algorithm converges with a rate independent of the mesh size.
The work of Qiya Hu was supported by Natural Science Foundation of China G10371129. |
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Keywords: | Maxwell’ s equations Unbounded domains Domain decomposition Boundary integral Nédélec finite elements D-N alternation |
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