TY - JOUR
T1 - Approximation of skewed interfaces with tensor-based model reduction procedures
T2 - Application to the reduced basis hierarchical model reduction approach
AU - Ohlberger, Mario
AU - Smetana, Kathrin
N1 - No PDF entered as this publication does not belong to UT.
PY - 2016
Y1 - 2016
N2 - 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.
AB - 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.
KW - Adaptive modeling
KW - Dimensional reduction
KW - Hierarchical model reduction
KW - Proper generalized decomposition
KW - Reduced basis methods
KW - Tensor-based model reduction
UR - http://www.scopus.com/inward/record.url?scp=84978859409&partnerID=8YFLogxK
U2 - 10.1016/j.jcp.2016.06.021
DO - 10.1016/j.jcp.2016.06.021
M3 - Article
AN - SCOPUS:84978859409
VL - 321
SP - 1185
EP - 1205
JO - Journal of computational physics
JF - Journal of computational physics
SN - 0021-9991
ER -