Computational strategies for impedance boundary condition integral equations in frequency and time domainsTools Dély, Alexandre (2019) Computational strategies for impedance boundary condition integral equations in frequency and time domains. PhD thesis, University of Nottingham.
AbstractThe Electric Field Integral Equation (EFIE) is widely used to solve wave scattering problems in electromagnetics using the Boundary Element Method (BEM). In the frequency domain, the linear systems stemming from the BEM suffer, amongst others, from two illconditioning problems: the low frequency breakdown and the dense mesh breakdown. Consequently, the iterative solvers require more iterations to converge to the solution, or they do not converge at all in the worst cases. These breakdowns are also present in the time domain, in addition to the DC instability which causes the solution to be completely wrong in the late time steps of the simulations. The time discretization is achieved using a convolution quadrature based on Implicit RungeKutta (IRK) methods, which yields a system that is solved by MarchingOninTime (MOT).
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