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

Abstract

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.2 An ansatz for approximating skewed interfaces with tensor-based model reduction approachesLet Ω ⊂ R 2 denote the computational domain with Lipschitz boundary ∂Ω, Σ D ⊂ ∂Ω the Dirichlet boundary, and Σ N ⊂ ∂Ω the Neumann boundary. We require that Σ D has

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