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Efficient finite element method for grating profile reconstruction. (English) Zbl 1349.65594

Summary: This paper concerns the reconstruction of grating profiles from scattering data. The inverse problem is formulated as an optimization problem with a regularization term. We devise an efficient finite element method (FEM) and employ a quasi-Newton method to solve it. For the direct problems, the FEM stiff and mass matrices are assembled once at the beginning of the numerical procedure. Then only minor changes are made to the mass matrix at each iteration, which significantly saves the computation cost. Numerical examples show that the method is effective and robust.

MSC:

65N21 Numerical methods for inverse problems for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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