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Nonoverlapping Localized Exponential Time Differencing Methods for Diffusion Problems

Journal Article · · Journal of Scientific Computing
 [1];  [2];  [3];  [2]
  1. Auburn Univ., AL (United States); University of South Carolina
  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
+ Show Author Affiliations
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.
Research Organization:
Univ. of South Carolina, Columbia, SC (United States)
Sponsoring Organization:
NSF; USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21); USDOE Office of Science (SC), Biological and Environmental Research (BER) (SC-23). Climate and Environmental Sciences Division
Grant/Contract Number:
SC0016540; SC0020270
OSTI ID:
1594011
Journal Information:
Journal of Scientific Computing, Journal Name: Journal of Scientific Computing Journal Issue: 2 Vol. 82; ISSN 0885-7474
Publisher:
SpringerCopyright Statement
Country of Publication:
United States
Language:
English

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Related Subjects

Mass conservation
58 GEOSCIENCES
97 MATHEMATICS AND COMPUTING
Cross points
Exponential time differencing
Finite differences
Nonoverlapping domain decomposition