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A mixed, scalable domain decomposition method for incompressible flow

100%

Vergnault E. , Allix O. , Maison-le-Poëc S.

tom Vol. 19, no. 2

173-190

This work deals with the construction of a mixed and extensible domain decomposition method for incompressible flows. In the scheme proposed here, the solution is sought at the intersection of two spaces, one containing the solution of the Navier–Stokes equations considered separately in each subdomain, and theother one containing the solutions of the compatibility equations on the interfaces. A solution verifying all the equations of the two spaces is achieved iteratively. One di?culty is that the interface problem is large and dense. In order to reduce its cost while maintaining the extensibility of the method, we defined an interface macroproblem in terms of a few interface macro unknowns. The best option takes advantage of the incompressibility condition to prescribe an interface macroproblem which propagates the information to the whole domain by making use of only two unknowns per interface. Several examples are used to illustrate the main properties of the method.

Parallel Finite Element Method

86%

Kuczmann M.

tom R. 87, nr 12b

100--102

The paper presents the domain decomposition method as a tool to cut the finite element mesh into smaller sub-meshes. Smaller mass matrices can be assembled and solved in a parallel way, i.e. the solution time can be decreased by this method. The finite element method has been chosen as a numerical tool to present the applicability ofthe technique.

Artykuł przedstawia metodę dekompozycji obszaru jako narzędzie do podzielenia siatki elementów skończonych na mniejsze obszary. Mniejsze macierze układu mogą być składane rozwiązywane w sposób równoległy - czas rozwiązywania może być w tym podejściu zmniejszony. Do przedstawienia skuteczności metody została wybrana metoda elementów skończonych.

Parallel computation of conjugated radiative-conductive heat transfer in thermal insulation layer

58%

Łapka P. , Furmański P.

2006

tom Vol. 27, no. 2

55-80

In this paper the parallel computing of conjugated heat transfer both by radiation and conduction in a two-dimensional lightweight thermal insulation layer was analysed. It was assumed that the medium can emit, absorb and isotropically scatter radiation. Its walls were opaque, absorbing, emitting and reflecting diffusively. At first, the problem was numerically solved by carrying out the sequential calculations. The radiative transfer equation was discretised by the Finite Volume Method. For the heat conduction equation the Alternating Direction Implicit Method was applied. Next the Domain Decomposition Method was used to perform the parallel calculations by dividing the whole domain into two and four sub-domains. Influence of different factors on differences between the results obtained from the parallel computing and from the sequential calculations were studied. Finally, the parallel computing speed up and efficiency were analysed together with factors affecting them.