Reduced Collocation Methods: Reduced Basis Methods in the Collocation Framework

Details Reduced Collocation Methods: Reduced Basis Methods in the Collocation Framework Reduced Collocation Methods: Reduced Basis Methods in the Collocation Framework

2012-01-19

arxiv.org/abs/1201.4188v1

Mathematics

Numerical Analysis

Scientific paper

In this paper, we present {\em the first} reduced basis method well-suited for the collocation framework. Two fundamentally different algorithms are presented: the so-called Least Squares Reduced Collocation Method (LSRCM) and Empirical Reduced Collocation Method (ERCM). This work provides a reduced basis strategy to practitioners who require a collocation, rather than Galerkin, approach. Furthermore, the empirical reduced collocation method {\em eliminates} a potentially costly online procedure that is needed for non-affine problems with Galerkin approach. Numerical results demonstrate the high efficiency and accuracy of the reduced collocation methods, which match or exceed that of the traditional reduced basis method in the Galerkin framework.

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