SIAM Journal on Scientific and Statistical Computing
Domain decomposition on parallel computers
IMPACT of Computing in Science and Engineering
A domain partitioning algorithm without subdomain overlap for solving parabolic equations
Computational Mathematics and Mathematical Physics
Multiplicative Schwarz methods for parabolic problems
SIAM Journal on Scientific Computing
SIAM Journal on Numerical Analysis
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Domain Decomposition Operator Splittings for the Solution of Parabolic Equations
SIAM Journal on Scientific Computing
A class of stable, globally noniterative, nonoverlapping domain decomposition algorithms for the simulation of parabolic evolutionary systems
A Highly Parallel Algorithm for the Numerical Simulation of Unsteady Diffusion Processes
IPDPS '05 Proceedings of the 19th IEEE International Parallel and Distributed Processing Symposium (IPDPS'05) - Papers - Volume 01
Journal of Computational and Applied Mathematics
Fault tolerant algorithms for heat transfer problems
Journal of Parallel and Distributed Computing
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In this paper, we report a class of stabilized explicit-implicit domain decomposition (SEIDD) methods for the parallel solution of parabolic problems, based on the explicit-implicit domain decomposition (EIDD) methods. EIDD methods are globally non-iterative, non-overlapping domain decomposition methods which, when compared with Schwarz alternating algorithm based parabolic solvers, are computationally and communicationally efficient for each simulation time step but suffer from time step size restrictions due to conditional stability or conditional consistency. By adding a stabilization step to the EIDD methods, the SEIDD methods are freed from time step size restrictions while retaining EIDD's computational and communicational efficiency for each time step, rendering themselves excellent candidates for large-scale parallel simulations. Three algorithms of the SEIDD type are implemented, which are experimentally tested to show excellent stability, computation and communication efficiencies, and high parallel speedup and scalability.