Nonoverlapping Localized Exponential Time Differencing Methods for Diffusion Problems

Hoang, Thi-Thao-Phuong; Ju, Lili; Leng, Wei; Wang, Zhu

doi:10.1007/s10915-020-01136-w

Title: Nonoverlapping Localized Exponential Time Differencing Methods for Diffusion Problems

Journal Article · Wed Jan 29 00:00:00 EST 2020 · Journal of Scientific Computing

DOI:https://doi.org/10.1007/s10915-020-01136-w· OSTI ID:1594011

Hoang, Thi-Thao-Phuong ^[1]; Ju, Lili ^[2]; Leng, Wei ^[3]; Wang, Zhu ^[2]

Auburn Univ., AL (United States)
Univ. of South Carolina, Columbia, SC (United States)
Chinese Academy of Sciences (CAS), Beijing (China). State Key Laboratory of Scientific and Engineering Computing

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.

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Research Organization:: Univ. of South Carolina, Columbia, SC (United States)

Sponsoring Organization:: 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)

Grant/Contract Number:: SC0016540; SC0020270; DMS-1818438; DMS-1913073

OSTI ID:: 1594011

Journal Information:: Journal of Scientific Computing, Vol. 82, Issue 2; ISSN 0885-7474

Publisher:: SpringerCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 2 works

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