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arXiv · 1304.4513

The method of freezing as a new tool for nonlinear reduced basis approximation of parameterized evolution equations

Mario Ohlberger·Stephan Rave
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Abstract

We present a new method for the nonlinear approximation of the solution manifolds of parameterized nonlinear evolution problems, in particular in hyperbolic regimes with moving discontinuities. Given the action of a Lie group on the solution space, the original problem is reformulated as a partial differential algebraic equation system by decomposing the solution into a group component and a spatial shape component, imposing appropriate algebraic constraints on the decomposition. The system is then projected onto a reduced basis space. We show that efficient online evaluation of the scheme is possible and study a numerical example showing its strongly improved performance in comparison to a scheme without freezing.

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Mario Ohlberger, Stephan Rave. 2013-04-16. The method of freezing as a new tool for nonlinear reduced basis approximation of parameterized evolution equations. https://doi.org/10.1016/j.crma.2013.10.028

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