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Parallel split least‐squares mixed finite element method for parabolic problem
Author(s) -
Zhang Jiansong,
Liu Zhaohui,
Yang Danping,
Zhu Jiang
Publication year - 2018
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22258
Subject(s) - mathematics , finite element method , domain decomposition methods , partition of unity , convergence (economics) , partition (number theory) , rate of convergence , least squares function approximation , degree (music) , mixed finite element method , iterative method , algorithm , mathematical optimization , mathematical analysis , computer science , combinatorics , statistics , physics , estimator , acoustics , economics , thermodynamics , economic growth , computer network , channel (broadcasting)
Based on overlapping domain decomposition, a new class of parallel split least‐squares (PSLS) mixed finite element methods is presented for solving parabolic problem. The algorithm is fully parallel. In the overlapping domains, the partition of unity is applied to distribute the corrections reasonably, which makes that the new method only needs one or two iteration steps to reach given accuracy at each time step while the classical Schwarz alternating methods need many iteration steps. The dependence of the convergence rate on the spacial mesh size, time increment, iteration times, and subdomains overlapping degree is analyzed. Some numerical results are reported to confirm the theoretical analysis.