Schwarz domain decomposition method for multidimensional and nonlinear parabolic equations: multidimensional subdomains with overlaps

1997 ◽  
Vol 63 (1-2) ◽  
pp. 101-119
Author(s):  
Qiming He ◽  
David J. Evans ◽  
Lishan Kang
Keyword(s):  
Domain Decomposition ◽  
Parabolic Equations ◽  
Decomposition Method ◽  
Domain Decomposition Method ◽  
Nonlinear Parabolic Equations ◽  
Nonlinear Parabolic

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.

Kinetics of oxidation of ammonia on cobalt catalyst I model of the reactor with catalytically active wall

1982 ◽  
Vol 47 (8) ◽  
pp. 2087-2096 ◽  
Author(s):  
Bohumil Bernauer ◽  
Antonín Šimeček ◽  
Jan Vosolsobě
Keyword(s):  
Parabolic Equations ◽  
Cobalt Catalyst ◽  
Nonlinear Parabolic Equations ◽  
Catalytic Reactions ◽  
Temperature Profiles ◽  
Dimensional Model ◽  
Kinetics Of Oxidation ◽  
Nonlinear Parabolic ◽  
Catalytically Active ◽  
Kinetics Of

A two dimensional model of a tabular reactor with the catalytically active wall has been proposed in which several exothermic catalytic reactions take place. The derived dimensionless equations enable evaluation of concentration and temperature profiles on the surface of the active component. The resulting nonlinear parabolic equations have been solved by the method of orthogonal collocations.

scholarly journals A non-overlapping Schwarz domain decomposition method with high-order finite elements for flow acoustics

2020 ◽  
Vol 369 ◽  
pp. 113223
Author(s):  
Alice Lieu ◽  
Philippe Marchner ◽  
Gwénaël Gabard ◽  
Hadrien Bériot ◽  
Xavier Antoine ◽  
...  
Keyword(s):  
Finite Elements ◽  
Domain Decomposition ◽  
Decomposition Method ◽  
Domain Decomposition Method ◽  
High Order ◽  
Overlapping Schwarz
Sign in / Sign up

Export Citation Format

Share Document