Journal Article10.1137/S1064827501384755
Stabilized Explicit-Implicit Domain Decomposition Methods for the Numerical Solution of Parabolic Equations
Yu Zhuang,Xian-He Sun +1 more
TL;DR: Three SEIDD algorithms are presented in this paper, which are experimentally tested to show excellent stability, computation and communication efficiencies, and high parallel speedup and scalability.
read more
Abstract: We report a class of stabilized explicit-implicit domain decomposition (SEIDD) methods for the numerical solution of parabolic equations. Explicit-implicit domain decomposition (EIDD) methods are globally noniterative, nonoverlapping domain decomposition methods, which, when compared with Schwarz-algorithm-based parabolic solvers, are computationally and communicationally efficient for each simulation time step but suffer from small time step size restrictions. By adding a stabilization step to EIDD, the SEIDD methods retain the time-stepwise efficiency in computation and communication of the EIDD methods but exhibit much better numerical stability. Three SEIDD algorithms are presented in this paper, which are experimentally tested to show excellent stability, computation and communication efficiencies, and high parallel speedup and scalability.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
Parallel, non-iterative, multi-physics domain decomposition methods for time-dependent Stokes-Darcy systems
TL;DR: Two parallel, non-iterative, multi-physics, domain decomposition methods are proposed to solve a coupled time-dependent Stokes-Darcy system with the Beavers-Joseph-Saffman-Jones interface condition; the unconditional stability and convergence of the first method is proved and illustrated through numerical experiments.
Non-iterative domain decomposition methods for a non-stationary Stokes–Darcy model with Beavers–Joseph interface condition☆
TL;DR: A three-step backward differentiation is used in the second method to achieve an accuracy order O ( h 3 + Δ t 3 ) , which is illustrated by a numerical example.
65
Unconditional Stability of Corrected Explicit-Implicit Domain Decomposition Algorithms for Parallel Approximation of Heat Equations
Han-Sheng Shi,Hong-lin Liao +1 more
TL;DR: By adding an interface correction step to Kuznetsov's EIDs, the one-dimensional CEIDD procedure achieves unconditional stability without discarding the time-stepwise efficiency of the EIDD method.
59
A domain decomposition discretization of parabolic problems
Maksymilian Dryja,Xuemin Tu +1 more
TL;DR: In this paper, a direct domain decomposition method is introduced to discretize the parabolic problems and the stability and convergence of this algorithm are analyzed.
37
Conservative domain decomposition schemes for solving two-dimensional heat equations
Zhongguo Zhou,Lin Li +1 more
TL;DR: In this paper, a new mass-conserved domain decomposition method for two-dimensional heat equations is proposed by combining the operator splitting technique and the C-N implicit scheme.
30
References
A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type
J. Crank,P. Nicolson,D. R. Hartree +2 more
- 01 Jan 1947
TL;DR: In this paper, the authors present methods of evaluating numerical solutions of the non-linear partial differential equation to the boundary conditions A, k, q are known constants, where q is the rate of heat generation.
3.4K
•Book
Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations
Barry Smith,Petter E. Bjorstad,William Gropp +2 more
- 13 Jun 1996
TL;DR: 1. One level algorithms 2. Two level algorithms 3. Multilevel algorithms 4. Substructuring methods 5. A convergence theory
2.2K
Gesammelte mathematische Abhandlungen
Hermann Amandus Schwarz
- 01 Jan 1890
TL;DR: Weierstrass et al. as discussed by the authors presented an algebraic model of the Minimalflache, which was used for the analysis of the Variationsrechnung.