Weiying Zheng

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We develop an adaptive edge finite element method based on reliable and efficient residual-based a posteriori error estimates for low-frequency time-harmonic Maxwell's equations with singularities. The resulting discrete problem is solved by the multigrid preconditioned minimum residual iteration algorithm. We demonstrate the efficiency and robustness of(More)
This paper is concerned with the analysis of the electromagnetic wave scattering in inhomogeneous medium with infinite rough surfaces. Consider a time-harmonic electromagnetic field generated by either a magnetic dipole or an electric dipole incident on an infinite rough surface. Throughout the dielectric permittivity is assumed to have a positive imaginary(More)
In this paper, we propose a uniaxial perfectly matched layer (PML) method for solving the time-harmonic scattering problems in two-layered media. The exterior region of the scatterer is divided into two half spaces by an infinite plane, on two sides of which the wave number takes different values. We surround the computational domain where the scattering(More)
In this paper, we develop an adaptive finite element method based on reliable and efficient a posteriori error estimates for the H − ψ formulation of eddy current problems with multiply connected conductors. Multiply connected domains are considered by making " cuts ". The competitive performance of the method is demonstrated by an engineering benchmark(More)
In this paper, we propose a new eddy current model for the nonlinear Maxwell equations with laminated conductors. Direct simulation of three-dimensional (3D) eddy currents in grain-oriented (GO) silicon steel laminations is very challenging since the coating film over each lamination is only several microns thick and the magnetic reluctivity is nonlinear(More)
This paper studies the homogenization of quasi-static and nonlinear Maxwell's equations in grain-oriented (GO) silicon steel laminations. GO silicon steel laminations have multiple scales and the ratio of the largest scale to the smallest scale can be up to 10 6. Direct solution of three-dimensional nonlinear Maxwell's equations is very challenging and(More)
To deal with the divergence-free constraint in a double curl problem: curl µ −1 curl u = f and div εu = 0 in Ω, where µ and ε represent the physical properties of the materials occupying Ω, we develop a δ-regularization method: curl µ −1 curl u δ + δεu δ = f to completely ignore the divergence-free constraint div εu = 0. It is shown that u δ converges to u(More)