Numerical upscaling for heterogeneous materials in fractured domains
| Autor: | Axel Målqvist, Fredrik Hellman, Siyang Wang |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Numerical Analysis
Forcing (recursion theory) Darcy's law Scale (ratio) Applied Mathematics 010103 numerical & computational mathematics Sparse approximation Numerical Analysis (math.NA) 01 natural sciences 010101 applied mathematics Computational Mathematics Modeling and Simulation FOS: Mathematics A priori and a posteriori Applied mathematics 35J15 65N12 65N15 65N30 Mathematics - Numerical Analysis 0101 mathematics Exponential decay Representation (mathematics) Porous medium Analysis Mathematics |
| Popis: | We consider numerical solution of elliptic problems with heterogeneous diffusion coefficients containing thin highly conductive structures. Such problems arise e.g. in fractured porous media, reinforced materials, and electric circuits. The main computational challenge is the high resolution needed to resolve the data variation. We propose a multiscale method that models the thin structures as interfaces and incorporate heterogeneities in corrected shape functions. The construction results in an accurate upscaled representation of the system that can be used to solve for several forcing functions or to simulate evolution problems in an efficient way. By introducing a novel interpolation operator, defining the fine scale of the problem, we prove exponential decay of the shape functions which allows for a sparse approximation of the upscaled representation. An a priori error bound is also derived for the proposed method together with numerical examples that verify the theoretical findings. Finally we present a numerical example to show how the technique can be applied to evolution problems. |
| Databáze: | OpenAIRE |
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