Solving parabolic equations with radial basis meshless domain decomposition method

2011 ◽  
Author(s):  
Qin Xinqiang ◽  
Su Pengxiang ◽  
Duan Xianbao ◽  
Miao Baoshan
Keyword(s):  
Domain Decomposition ◽  
Parabolic Equations ◽  
Decomposition Method ◽  
Domain Decomposition Method ◽  
Radial Basis

The Mass-Preserving S-DDM Scheme for Two-Dimensional Parabolic Equations

2016 ◽  
Vol 19 (2) ◽  
pp. 411-441 ◽  
Author(s):  
Zhongguo Zhou ◽  
Dong Liang
Keyword(s):  
Domain Decomposition ◽  
Parabolic Equations ◽  
Numerical Experiments ◽  
Decomposition Method ◽  
Domain Decomposition Method ◽  
Time Step ◽  
Unconditionally Stable ◽  
One Dimensional ◽  
Splitting Technique ◽  
Theoretical Results

AbstractIn the paper, we develop and analyze a new mass-preserving splitting domain decomposition method over multiple sub-domains for solving parabolic equations. The domain is divided into non-overlapping multi-bock sub-domains. On the interfaces of sub-domains, the interface fluxes are computed by the semi-implicit (explicit) flux scheme. The solutions and fluxes in the interiors of sub-domains are computed by the splitting one-dimensional implicit solution-flux coupled scheme. The important feature is that the proposed scheme is mass conservative over multiple non-overlapping sub-domains. Analyzing the mass-preserving S-DDM scheme is difficult over non-overlapping multi-block sub-domains due to the combination of the splitting technique and the domain decomposition at each time step. We prove theoretically that our scheme satisfies conservation of mass over multi-block non-overlapping sub-domains and it is unconditionally stable. We further prove the convergence and obtain the error estimate in L2-norm. Numerical experiments confirm theoretical results.

Node adaptive domain decomposition method by radial basis functions

2009 ◽  
Vol 25 (6) ◽  
pp. 1482-1501 ◽  
Author(s):  
Pedro González-Casanova ◽  
José Antonio Muñoz-Gómez ◽  
Gustavo Rodríguez-Gómez
Keyword(s):  
Domain Decomposition ◽  
Radial Basis Functions ◽  
Decomposition Method ◽  
Domain Decomposition Method ◽  
Basis Functions ◽  
Radial Basis
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