Offline-Enhanced Reduced Basis Method through adaptive construction of the Surrogate Parameter

2017 SIAM Conference on Computational Science and Engineering

Abstract. Classical Reduced Basis Method (RBM) is a popular certified model reduction approach for solving parametrized partial differential equations. However, the large size or high dimension of the parameter domain leads to prohibitively high computational costs in the offline stage. In this work we propose and test effective strategies to mitigate this difficulty by performing greedy algorithms on surrogate parameter domains that are adaptively constructed. These domains are much smaller in size yet accurate enough to induce the solution manifold of interest at the current step. In fact, we propose two ways to construct the surrogate parameter domain, one through an Inverse Cumulative Distribution Function (ICDF) and the other based on the Cholesky Decomposition of an error correlation matrix. The algorithm is capable of speeding up RBM by effectively alleviating the computational burden in offline stage without degrading accuracy, assuming that the solution manifold has low Kolmogorov width. We demonstrate the algorithm’s effectiveness through numerical experiments.