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Title: Nonoverlapping Localized Exponential Time Differencing Methods for Diffusion Problems

Abstract

In this paper, we propose nonoverlapping localized exponential time differencing (ETD) methods for diffusion problems. The model time-dependent diffusion equation is first reformulated on subdomains based on the nonoverlapping domain decomposition, in which Neumann boundary conditions are imposed on the interfaces for the subdomain problems and Dirichlet type conditions are enforced to form a space-time interface problem. After spatial discretization by standard central finite differences and temporal integration with the first or second order ETD methods, the fully discrete interface problem is obtained. Such an interface problem is then solved iteratively either at each time step or over the whole time interval: the former involves the solution of stationary problems in each subdomain at each iteration while the latter involves the solution of time-dependent subdomain problems at each iteration. For both approaches, we prove that localized ETD solutions conserve mass exactly and converge in time to the exact space semidiscrete solution. Numerical experiments in two dimensions are also presented to illustrate the performance of the proposed methods.

Authors:
 [1];  [2];  [3];  [2]
+ Show Author Affiliations
  1. Auburn Univ., AL (United States)
  2. Univ. of South Carolina, Columbia, SC (United States)
  3. Chinese Academy of Sciences (CAS), Beijing (China). State Key Laboratory of Scientific and Engineering Computing
Publication Date:
Research Org.:
Univ. of South Carolina, Columbia, SC (United States)
Sponsoring Org.:
Office of Science (SC), Biological and Environmental Research (BER). Earth and Environmental Systems Science Division; USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); National Science Foundation (NSF)
OSTI Identifier:
1594011
Grant/Contract Number:  
SC0016540; SC0020270; DMS-1818438; DMS-1913073
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Scientific Computing
Additional Journal Information:
Journal Volume: 82; Journal Issue: 2; Journal ID: ISSN 0885-7474
Publisher:
Springer
Country of Publication:
United States
Language:
English
Subject:
58 GEOSCIENCES; 97 MATHEMATICS AND COMPUTING; Exponential time differencing; Nonoverlapping domain decomposition; Mass conservation; Finite differences; Cross points

Citation Formats

Hoang, Thi-Thao-Phuong, Ju, Lili, Leng, Wei, and Wang, Zhu. Nonoverlapping Localized Exponential Time Differencing Methods for Diffusion Problems. United States: N. p., 2020. Web. doi:10.1007/s10915-020-01136-w.
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Hoang, Thi-Thao-Phuong, Ju, Lili, Leng, Wei, & Wang, Zhu. Nonoverlapping Localized Exponential Time Differencing Methods for Diffusion Problems. United States. https://doi.org/10.1007/s10915-020-01136-w
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Hoang, Thi-Thao-Phuong, Ju, Lili, Leng, Wei, and Wang, Zhu. Wed . "Nonoverlapping Localized Exponential Time Differencing Methods for Diffusion Problems". United States. https://doi.org/10.1007/s10915-020-01136-w. https://www.osti.gov/servlets/purl/1594011.
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@article{osti_1594011,
title = {Nonoverlapping Localized Exponential Time Differencing Methods for Diffusion Problems},
author = {Hoang, Thi-Thao-Phuong and Ju, Lili and Leng, Wei and Wang, Zhu},
abstractNote = {In this paper, we propose nonoverlapping localized exponential time differencing (ETD) methods for diffusion problems. The model time-dependent diffusion equation is first reformulated on subdomains based on the nonoverlapping domain decomposition, in which Neumann boundary conditions are imposed on the interfaces for the subdomain problems and Dirichlet type conditions are enforced to form a space-time interface problem. After spatial discretization by standard central finite differences and temporal integration with the first or second order ETD methods, the fully discrete interface problem is obtained. Such an interface problem is then solved iteratively either at each time step or over the whole time interval: the former involves the solution of stationary problems in each subdomain at each iteration while the latter involves the solution of time-dependent subdomain problems at each iteration. For both approaches, we prove that localized ETD solutions conserve mass exactly and converge in time to the exact space semidiscrete solution. Numerical experiments in two dimensions are also presented to illustrate the performance of the proposed methods.},
doi = {10.1007/s10915-020-01136-w},
journal = {Journal of Scientific Computing},
number = 2,
volume = 82,
place = {United States},
year = {Wed Jan 29 00:00:00 EST 2020},
month = {Wed Jan 29 00:00:00 EST 2020}
}
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https://doi.org/10.1007/s10915-020-01136-w
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