Reconstruction of Quasi-Local Numerical Effective Models from Low-Resolution Measurements
Artikel i vetenskaplig tidskrift, 2020

We consider the inverse problem of reconstructing an effective model for a prototypical diffusion process in strongly heterogeneous media based on coarse measurements. The approach is motivated by quasi-local numerical effective forward models that are provably reliable beyond periodicity assumptions and scale separation. The goal of this work is to show that an identification of the matrix representation related to these effective models is possible. On the one hand, this provides a reasonable surrogate in cases where a direct reconstruction is unfeasible due to a mismatch between the coarse data scale and the microscopic quantities to be reconstructed. On the other hand, the approach allows us to investigate the requirement for a certain non-locality in the context of numerical homogenization. Algorithmic aspects of the inversion procedure and its performance are illustrated in a series of numerical experiments.

Numerical homogenization

Multiscale methods

Computational inverse problems

Författare

A. Caiazzo

Weierstrass Institute for Applied Analysis and Stochastics

Roland Maier

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Daniel Peterseim

Universität Augsburg

Journal of Scientific Computing

0885-7474 (ISSN) 1573-7691 (eISSN)

Vol. 85 1 10

Ämneskategorier

Beräkningsmatematik

Sannolikhetsteori och statistik

DOI

10.1007/s10915-020-01304-y

Mer information

Senast uppdaterat

2020-10-26