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Journal of Scientific Computing

Erschienen in:

01.09.2014

Coupled Model and Grid Adaptivity in Hierarchical Reduction of Elliptic Problems

verfasst von: Simona Perotto, Alessandro Veneziani

Erschienen in: Journal of Scientific Computing | Ausgabe 3/2014

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Abstract

In this paper we propose a surrogate model for advection–diffusion–reaction problems characterized by a dominant direction in their dynamics. We resort to a hierarchical model reduction where we couple a modal representation of the transverse dynamics with a finite element approximation along the mainstream. This different treatment of the dynamics entails a surrogate model enhancing a purely 1D description related to the leading direction. The coefficients of the finite element expansion along this direction introduce a generally non-constant description of the transversal dynamics. Aim of this paper is to provide an automatic adaptive approach to locally select the dimension of the modal expansion as well as the finite element step in order to satisfy a prescribed tolerance on a goal functional of interest.

Vorheriger Artikel Multiplicative Denoising Based on Linearized Alternating Direction Method Using Discrepancy Function Constraint

Nächster Artikel Shape Optimization by Free-Form Deformation: Existence Results and Numerical Solution for Stokes Flows

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From (13)–(14), the further upper bound \(|J(e_{\mathbf{m}^+})| \le \beta _\mathbf{m}/(1 -\beta _\mathbf{m})\, |J(\delta u_{\mathbf{mm}^+})|\) trivially follows.

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Titel: Coupled Model and Grid Adaptivity in Hierarchical Reduction of Elliptic Problems
verfasst von: Simona Perotto
Alessandro Veneziani
Publikationsdatum: 01.09.2014
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 3/2014
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-013-9804-y

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