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Improved successive constraint method based a posteriori error estimate for reduced basis approximation of 2D Maxwell’s problem. (English) Zbl 1181.78019

The authors study, improve and test the successive constraint method on non-coercive problems illustrated by an electromagnetic cavity problem. The new successive constraint method is superior to the standard one in the following two ways: (i) it is more stable in the sense that it applies a monotonic process (in contrast to being oscillatory before); (ii) the method developed in the present paper needs to solve less eigenvalue problems.
In the first part of this paper the authors describe the original and the improved successive constraint method and they prove the above-mentioned properties. Next, several numerical results are given in order to verify the main claims. Some concluding remarks are provided in the last section of the paper.

MSC:

78M25 Numerical methods in optics (MSC2010)
65N15 Error bounds for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
78A25 Electromagnetic theory (general)
35Q61 Maxwell equations
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References:

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