Nonoverlapping Localized Exponential Time Differencing Methods for Diffusion Problems

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...

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Bibliographic Details
Published in:Journal of scientific computing 2020-02, Vol.82 (2), p.37, Article 37
Main Authors: Hoang, Thi-Thao-Phuong, Ju, Lili, Wang, Zhu
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Boundary conditions
Computational Mathematics and Numerical Analysis
Cross points
Decomposition
Dirichlet problem
Domain decomposition methods
Exponential time differencing
Finite differences
GEOSCIENCES
Iterative methods
Mass conservation
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
MATHEMATICS AND COMPUTING
Mathematics and Statistics
Nonoverlapping domain decomposition
Partial differential equations
Spacetime
Theoretical
Time dependence
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Summary: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.
ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-020-01136-w