Reduced Basis Methods Based upon Adaptive Snapshot Computations
نویسنده
چکیده
We use asymptotically optimal adaptive numerical methods (here specifically a wavelet scheme) within the offline phase of the Reduced Basis Method (RBM). The resulting parameter-dependent discretizations do not permit the standard RB “truth space”, but allow for error estimation of the RB approximation with respect to the exact solution of the considered parameterized partial differential equation. The evaluation of the estimators is also performed adaptively. This RBM with adaptive offline computations is analyzed. We show that multiple selection of snapshots may occur and devise strategies to avoid this. Numerical experiments for stationary and instationary problems show potential and challenges of this approach.
منابع مشابه
Reduced basis methods with adaptive snapshot computations
We use asymptotically optimal adaptive numerical methods (here specifically a wavelet scheme) for snapshot computations within the offline phase of the Reduced Basis Method (RBM). The resulting discretizations for each snapshot (i.e., parameter-dependent) do not permit the standard RB ‘truth space’, but allow for error estimation of the RB approximation with respect to the exact solution of the...
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