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AN ELLIPTIC LOCAL P...
AN ELLIPTIC LOCAL PROBLEM WITH EXPONENTIAL DECAY OF THE RESONANCE ERROR FOR NUMERICAL HOMOGENIZATION
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- Abdulle, Assyr (författare)
- Ecole Polytech Fed Lausanne, Inst Math, ANMC, Stn 8, Lausanne, Switzerland.
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- Arjmand, Doghonay, 1987- (författare)
- Uppsala universitet,Avdelningen för beräkningsvetenskap,Numerisk analys,Ecole Polytech Fed Lausanne, Inst Math, ANMC, Stn 8, Lausanne, Switzerland.
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- Paganoni, Edoardo (författare)
- Ecole Polytech Fed Lausanne, Inst Math, ANMC, Stn 8, Lausanne, Switzerland.
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Ecole Polytech Fed Lausanne, Inst Math, ANMC, Stn 8, Lausanne, Switzerland Avdelningen för beräkningsvetenskap (creator_code:org_t)
- Society for Industrial & Applied Mathematics (SIAM), 2023
- 2023
- Engelska.
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Ingår i: Multiscale Modeling & simulation. - : Society for Industrial & Applied Mathematics (SIAM). - 1540-3459 .- 1540-3467. ; 21:2, s. 513-541
- Relaterad länk:
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https://urn.kb.se/re...
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https://doi.org/10.1...
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Abstract
Ämnesord
Stäng
- Numerical multiscale methods usually rely on some coupling between a macroscopic and a microscopic model. The macroscopic model is incomplete as effective quantities, such as the homogenized material coefficients or fluxes, are missing in the model. These effective data need to be computed by running local microscale simulations followed by a local averaging of the microscopic information. Motivated by the classical homogenization theory, it is a common practice to use local elliptic cell problems for computing the missing homogenized coefficients in the macro model. Such a consideration results in a first order error O(E/8), where E represents the wavelength of the microscale variations and 8 is the size of the microscopic simulation boxes. This error, called ``resonance error,"" originates from the boundary conditions used in the microproblem and typically dominates all other errors in a multiscale numerical method. Optimal decay of the resonance error remains an open problem, although several interesting approaches reducing the effect of the boundary have been proposed over the last two decades. In this paper, as an attempt to resolve this problem, we propose a computationally efficient, fully elliptic approach with exponential decay of the resonance error.
Ämnesord
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
Nyckelord
- multiscale methods
- homogenization
- resonance error
- Beräkningsvetenskap med inriktning mot numerisk analys
- Scientific Computing with specialization in Numerical Analysis
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