Identifier: 2009-14
Author(s): Y. Chen, J.S. Hesthaven, Y. Maday, and J. Rodriguez
Title: Certified reduced basis methods and output bounds for the harmonic Maxwell's equations
Page count: 31 pp.
Date: 2009-03-12
Abstract:
We propose certi ed reduced basis methods for the ecient and reliable evaluation of a general output that is implicitly connected to a given parameterized input through the harmonic Maxwell's equations. The truth approximation and the development of the reduced basis through a greedy approach is based on a discontinuous Galerkin approximation of the linear partial di erential equation. The formulation allows the use of di erent approximation spaces for solving the primal and the dual truth approximation problems to respect the characteristics of both problem types, leading to an overall reduction in the o -line computational e ort. The main features of the method are: i) rapid convergence on the entire set of parameters, ii) rigorous a posteriori error estimators for the output and iii) a parameter independent o -line phase and a computationally very ecient on-line phase to enable the rapid solution of manyquery problems arising in control, optimization, and design. The versatility and performance of this approach is shown through a numerical experiment, illustrating the modeling of material variations and problems with resonant behavior.
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