Domain decomposition-based exponential time differencing methods for semilinear parabolic equations

Li, Xiao; Ju, Lili; Hoang, Thi-Thao-Phuong

doi:10.1007/s10543-020-00817-0

Domain decomposition-based exponential time differencing methods for semilinear parabolic equations

Journal Article · Fri May 01 00:00:00 EDT 2020 · BIT Numerical Mathematics

DOI:https://doi.org/10.1007/s10543-020-00817-0· OSTI ID:1631280

Li, Xiao ^[1]; Ju, Lili ^[2]; Hoang, Thi-Thao-Phuong ^[3]

Hong Kong Polytechnic Univ. (Hong Kong); University of South Carolina
Univ. of South Carolina, Columbia, SC (United States)
Auburn Univ., AL (United States)

The localized exponential time differencing method based on overlapping domain decomposition has been recently introduced and successfully applied to parallel computations for extreme-scale numerical simulations of coarsening dynamics based on phase field models. In this paper, we focus on numerical solutions of a class of semilinear parabolic equations with the well-known Allen-Cahn equation as a special case. We initially study the semi-discrete system under the standard central difference spatial discretization and prove the equivalence between the monodomain problem and the corresponding multidomain problem obtained by the Schwarz waveform relaxation iteration. Then we develop the fully discrete localized exponential time differencing schemes and, by establishing the maximum bound principle, prove the convergence of the fully discrete localized solutions to the exact semi-discrete solution and the convergence of the iterative solutions. Numerical experiments are carried out to confirm the theoretical results in one-dimensional space and test the convergence and accuracy of the proposed algorithms with different numbers of subdomains in two-dimensional space.

View Accepted Manuscript (DOE)

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

Sponsoring Organization:: National Natural Science Foundation of China (NSFC); National Science Foundation (NSF); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE Office of Science (SC), Biological and Environmental Research (BER). Climate and Environmental Sciences Division

Grant/Contract Number:: SC0016540; SC0020270

OSTI ID:: 1631280

Alternate ID(s):: OSTI ID: 1852289

Journal Information:: BIT Numerical Mathematics, Journal Name: BIT Numerical Mathematics Vol. 61; ISSN 0006-3835

Publisher:: Springer NatureCopyright Statement

Country of Publication:: United States

Language:: English

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97 MATHEMATICS AND COMPUTING
localized exponential time differencing
overlapping domain decompositio
parallel Schwarz iteration
semilinear parabolic equation

Domain decomposition-based exponential time differencing methods for semilinear parabolic equations

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