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Preconditioners based on splitting for time domain photonic crystal modeling

Cloet, Jeroen de and Marissen, Jasper and Westendorp, Ties (2015) Preconditioners based on splitting for time domain photonic crystal modeling.

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Abstract:Today the Maxwell equations of electrodynamics are still solved using the finite-difference time-domain method, because of the relative simplicity of the method. In order to solve these equations on an infinite domain, absorbing boundary conditions need to be imposed. We consider Maxwell's equations discretized in space only (using the Yee scheme) with a PML on the boundary to absorb outgoing waves. To solve the resulting system of ODEs we use exponential time integration. Because we solve the Maxwell equations in 3D, direct sparse linear solvers are not efficient for these systems. Therefore we have to use preconditioned iterative solvers based on the Krylov subspace methods. These methods require a solution of a linear system with shifted Maxwell operator. In this work we compare the accuracy and speed (in terms of computation time) of different splitting-based predontitioners of the discretized Maxwell operator for several interesting test cases.
Item Type:Essay (Bachelor)
Faculty:EEMCS: Electrical Engineering, Mathematics and Computer Science
Subject:31 mathematics, 33 physics, 53 electrotechnology
Programme:Applied Mathematics BSc (56965)
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