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Article Dans Une Revue SIAM Journal on Scientific Computing Année : 2013

Locally Adaptive Greedy Approximations for Anisotropic Parameter Reduced Basis Spaces

Résumé

Reduced order models, in particular the reduced basis method, rely on empirically built and problem dependent basis functions that are constructed during an off-line stage. In the on- line stage, the precomputed problem dependent solution space can then be used in order to reduce the size of the computational problem. For complex problems, the number of basis functions required to guarantee a certain error tolerance can become too large in order to benefit computationally from the model reduction. To overcome this, the present work introduces a framework where local approximation spaces (in parameter space) are used to define the reduced order approximation in order to have explicit control over the on-line cost. This approach also adapts the local approximation spaces to local anisotropic behavior in the parameter space. We present the algorithm and present numerous numerical tests.
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Dates et versions

hal-00690830 , version 1 (24-04-2012)

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Yvon Maday, Benjamin Stamm. Locally Adaptive Greedy Approximations for Anisotropic Parameter Reduced Basis Spaces. SIAM Journal on Scientific Computing, 2013, 35 (6), pp.A2417-A2441. ⟨10.1137/120873868⟩. ⟨hal-00690830⟩
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