Approximation of skewed interfaces with tensor-based model reduction procedures: Application to the reduced basis hierarchical model reduction approach

JOURNAL OF COMPUTATIONAL PHYSICS

卷:321

Article

Ohlberger, Mario¹  Smetana, Kathrin¹ 

[1] Univ Munster, Inst Computat & Appl Math, Einsteinstr 62, D-48149 Munster, Germany

关键词: Dimensional reduction;    Tensor-based model reduction;    Hierarchical model reduction;    Reduced basis methods;    Proper generalized decomposition;    Adaptive modeling;   

DOI  :  10.1016/j.jcp.2016.06.021

来源: Elsevier

【 摘 要 】

In this article we introduce a procedure, which allows to recover the potentially very good approximation properties of tensor-based model reduction procedures for the solution of partial differential equations in the presence of interfaces or strong gradients in the solution which are skewed with respect to the coordinate axes. The two key ideas are the location of the interface either by solving a lower-dimensional partial differential equation or by using data functions and the subsequent removal of the interface of the solution by choosing the determined interface as the lifting function of the Dirichlet boundary conditions. We demonstrate in numerical experiments for linear elliptic equations and the reduced basis-hierarchical model reduction approach that the proposed procedure locates the interface well and yields a significantly improved convergence behavior even in the case when we only consider an approximation of the interface. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free