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Title: Localized harmonic characteristic basis functions for multiscale finite element methods

Abstract

We solve elliptic systems of equations posed on highly heterogeneous materials. Examples of this class of problems are composite structures and geological processes. We focus on a model problem which is a second-order elliptic equation with discontinuous coefficients. These coefficients represent the conductivity of a composite material. We assume a background with a low conductivity that contains inclusions with different thermal properties. Under this scenario, we design a multiscale finite element method to efficiently approximate solutions. The method is based on an asymptotic expansion of the solution in terms of the ratio between the conductivities. The resulting method constructs (locally) finite element basis functions (one for each inclusion). These bases generate the multiscale finite element space where the approximation of the solution is computed. Numerical experiments show the good performance of the proposed methodology.

Authors:
 [1];  [2];  [3]
  1. Universidade de São Paulo, Departamento de Matemática Aplicada, Instituto de Matemática e Estatística (Brazil)
  2. Universidad Nacional de Colombia, Departamento de Matemáticas (Colombia)
  3. Curtin University, Applied Geology Department, Western Australian School of Mines (Australia)
Publication Date:
OSTI Identifier:
22769325
Resource Type:
Journal Article
Journal Name:
Computational and Applied Mathematics
Additional Journal Information:
Journal Volume: 37; Journal Issue: 2; Other Information: Copyright (c) 2018 SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0101-8205
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; ASYMPTOTIC SOLUTIONS; DESIGN; EQUATIONS; FINITE ELEMENT METHOD; HARMONICS; THERMODYNAMIC PROPERTIES

Citation Formats

Poveda, Leonardo A., E-mail: lpovedac@ime.usp.br, Galvis, Juan, and Calo, Victor M., E-mail: victor.calo@curtin.edu.au. Localized harmonic characteristic basis functions for multiscale finite element methods. United States: N. p., 2018. Web. doi:10.1007/S40314-017-0431-3.
Poveda, Leonardo A., E-mail: lpovedac@ime.usp.br, Galvis, Juan, & Calo, Victor M., E-mail: victor.calo@curtin.edu.au. Localized harmonic characteristic basis functions for multiscale finite element methods. United States. doi:10.1007/S40314-017-0431-3.
Poveda, Leonardo A., E-mail: lpovedac@ime.usp.br, Galvis, Juan, and Calo, Victor M., E-mail: victor.calo@curtin.edu.au. Tue . "Localized harmonic characteristic basis functions for multiscale finite element methods". United States. doi:10.1007/S40314-017-0431-3.
@article{osti_22769325,
title = {Localized harmonic characteristic basis functions for multiscale finite element methods},
author = {Poveda, Leonardo A., E-mail: lpovedac@ime.usp.br and Galvis, Juan and Calo, Victor M., E-mail: victor.calo@curtin.edu.au},
abstractNote = {We solve elliptic systems of equations posed on highly heterogeneous materials. Examples of this class of problems are composite structures and geological processes. We focus on a model problem which is a second-order elliptic equation with discontinuous coefficients. These coefficients represent the conductivity of a composite material. We assume a background with a low conductivity that contains inclusions with different thermal properties. Under this scenario, we design a multiscale finite element method to efficiently approximate solutions. The method is based on an asymptotic expansion of the solution in terms of the ratio between the conductivities. The resulting method constructs (locally) finite element basis functions (one for each inclusion). These bases generate the multiscale finite element space where the approximation of the solution is computed. Numerical experiments show the good performance of the proposed methodology.},
doi = {10.1007/S40314-017-0431-3},
journal = {Computational and Applied Mathematics},
issn = {0101-8205},
number = 2,
volume = 37,
place = {United States},
year = {2018},
month = {5}
}