Schwarz methods for discrete elliptic and parabolic problems with an application to nuclear waste repository modelling

Blaheta, Radim; Kohut, Roman; Neytcheva, Maya; Starý, J.

doi:10.1016/j.matcom.2007.01.028

Cited by 9 publications

(6 citation statements)

References 12 publications

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“…For presentations of Schwarz‐type domain decomposition methods, see the works of Chan and Mathew, Smith et al, and Toselli and Widlund . For a nice shorter overview, see the work of Blaheta; for a more recent presentation, see the work of Axelsson and Blaheta; and for a particular application, see the work of Blaheta et al In this section, the presentation is devoted to the use of striped domain decomposition methods and odd–even‐numbered sets of subdomains.…”

Section: A Schwarz Alternating Iteration Methods and Its Stabilizationmentioning

confidence: 99%

A coarse–fine‐mesh stabilization for an alternating Schwarz domain decomposition method

Axelsson

Gustafsson

2019

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Summary Domain decomposition methods can be solved in various ways. In this paper, domain decomposition in strips is used. It is demonstrated that a special version of the Schwarz alternating iteration method coupled with coarse–fine‐mesh stabilization leads to a very efficient solver, which is easy to implement and has a behavior nearly independent of mesh and problem parameters. The novelty of the method is the use of alternating iterations between odd‐ and even‐numbered subdomains and the replacement of the commonly used coarse‐mesh stabilization method with coarse–fine‐mesh stabilization.

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Section: A Schwarz Alternating Iteration Methods and Its Stabilizationmentioning

confidence: 99%

A coarse–fine‐mesh stabilization for an alternating Schwarz domain decomposition method

Axelsson

Gustafsson

2019

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“…V can be also constructed from h V by aggregation, which means that the basis functions of h V are divided into disjoint groups (aggregates) and sums of the basis functions in the individual groups create the basis of 0 V . For more details see (Blaheta et al 2006(Blaheta et al , 2007 and the references therein.…”

Section: Au=b (11)mentioning

confidence: 99%

“…An illustrative example is the performance and safety assessment of projects for deep underground deposition of the spent nuclear fuel, for which the analysis of T-H-M processes in the host rocks is crucial, cf. (Blaheta et al 2005(Blaheta et al , 2007, (Hudson et al 2005).…”

Section: Introductionmentioning

confidence: 99%

Modeling THM Processes in Rocks with the Aid of Parallel Computing

Blaheta¹,

Byczanski²,

Kohut³

et al. 2013

Thermo‐Hydromechanical and Chemical Coupling in Geomaterials and Applications

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“…(1)- (10). Setting T B (r, z, t) = T B (r, z, t) − T 0 and T R (r, z, t) = T R (r, z, t) − T 0 and taking the Laplace transforms to Eqs.…”

Section: Laplace-domain Solutionsmentioning

confidence: 99%

“…Their result showed that decreasing the spacing between the canisters had a larger effect on temperature distribution than decreasing the spacing between the tunnels. Blaheta et al [10] investigated the efficiency of the overlapping Schwarz methods for both elliptic and parabolic problems with an application to a nuclear waste repository model. They mentioned that the twolevel Schwarz method was necessary for the efficient solution of discrete elliptic problems and the one-level Schwarz method was sufficiently efficient for elliptic problems.…”

Section: Introductionmentioning

confidence: 99%