Substructuring preconditioners for saddle-point problems arising from Maxwell's equations in three dimensions |
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Authors: | Qiya Hu Jun Zou |
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Institution: | Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China ; Department of Mathematics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong |
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Abstract: | This paper is concerned with the saddle-point problems arising from edge element discretizations of Maxwell's equations in a general three dimensional nonconvex polyhedral domain. A new augmented technique is first introduced to transform the problems into equivalent augmented saddle-point systems so that they can be solved by some existing preconditioned iterative methods. Then some substructuring preconditioners are proposed, with very simple coarse solvers, for the augmented saddle-point systems. With the preconditioners, the condition numbers of the preconditioned systems are nearly optimal; namely, they grow only as the logarithm of the ratio between the subdomain diameter and the finite element mesh size. |
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Keywords: | Maxwell's equations N\'ed\'elec finite elements nonoverlapping domain decomposition condition numbers |
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