Hesthaven, Jan S.
Stamm, Benjamin
Zhang, Shun
Efficient greedy algorithms for high-dimensional parameter spaces with applications to empirical interpolation and reduced basis methods
Mathematical Modelling and Numerical Analysis
0764-583X
10.1051/m2an/2013100
48
01
259-283
We propose two new and enhanced algorithms for greedy sampling of high- dimensional functions. While the techniques have a substantial degree of generality, we frame the discussion in the context of methods for empirical interpolation and the devel- opment of reduced basis techniques for high-dimensional parametrized functions. The first algorithm, based on a assumption of saturation of error in the greedy algorithm, is shown to result in a significant reduction of the workload over the standard greedy algorithm. In an improved approach, this is combined with an algorithm in which the train set for the greedy approach is adaptively sparsefied and enriched. A safety check step is added at the end of the algorithm to certify the quality of the basis set. Both these techniques are applicable to high-dimensional problems and we shall demonstrate their performance on a number of numerical examples.
EDP Sciences
2014
http://infoscience.epfl.ch/record/190659/files/M2AN482014.pdf;