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1.
3D multidomain BEM for a Poisson equation
Matjaž Ramšak, Leopold Škerget, 2009, original scientific article

Abstract: This paper deals with the efficient 3D multidomain boundary element method (BEM) for solving a Poisson equation. The integral boundary equation is discretized using linear mixed boundary elements. Sparse system matrices similar to the finite element method are obtained, using a multidomain approach, also known as the ćsubdomain techniqueć. Interface boundary conditions between subdomains lead to an overdetermined system matrix, which is solved using a fast iterative linear least square solver. The accuracy, efficiency and robustness of the developed numerical algorithm are presented using cube and sphere geometry, where the comparison with the competitive BEM is performed. The efficiency is demonstrated using a mesh with over 200,000 hexahedral volume elements on a personal computer with 1 GB memory.
Keywords: fluid mechanics, Poisson equation, multidomain boundary element method, boundary element method, mixed boundary elements, multidomain method
Published: 31.05.2012; Views: 1555; Downloads: 64
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2.
3D multidomain BEM for solving the Laplace equation
Matjaž Ramšak, Leopold Škerget, 2007, original scientific article

Abstract: An efficient 3D multidomain BEM for solving problems governed by the Laplace equation is presented. Integral boundary equations are discretized using mixed boundary elements. The field function is interpolated using a continuous linear function while its derivative in a normal direction is interpolated using a discontiuous constant function over surface boundaey elements. Using amultidomain approach, also known as the subdomain technique, sparse system matrices similar to FEM are obtained. Interface boundary conditions between subdomains leads to an over-determined system matrix which is solved using a fast iterative linear least square solver. The accuracy and the robustness of the developed algorithm is presented on a scalar diffusion problem using simple cube geometry and various types of meshes. The efficiency is demonstrated with potential flow around a complex geometry of a fighter airplane using a tetrahedral mesh with over 100.000 subdomains on a personal computer.
Keywords: fluid mechanics, aerodynamics, multidomain boundary element method, Laplace equation, mixed boundary elements, potential flow
Published: 31.05.2012; Views: 1393; Downloads: 64
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3.
Mixed boundary elements for laminar flows
Matjaž Ramšak, Leopold Škerget, 1999, original scientific article

Abstract: This paper presents a mixed boundary element formulation of the boundary domain integral method (BDIM) for solving diffusion-convective transport problems. The basic idea of mixed elements is the use of a continuos interpolation polynomial for conservative field function approximation and a discontinuous interpolation polynomial for its normal derivative along the boundary element. In this way, the advantages of continuous field function approximation are retained and its conservation is preserved while the normal flux values are approximated by interpolation nodal points with a uniquely defined normal direction. Due to the use of mixed boundary elements, the final discretized matrix system is overdetermined and a special solver based on the least squares method is applied. Driven cavity, natural and forced convection in a closed cavity are studied. Driven caviaty results at Re=100, 400 and 1000 agree better with the benchmark solution than Finite Element Method of Finite Volume Method results for the same grid density with 21 x 21 degrees of freedom. The average Nusselt number values for natural convection ▫$10^3$▫▫$le$▫Ra▫$le$▫▫$10^6$▫ agree better than 0.1% with benchmark solutions for maximal calculated grid desities 61 x 61 degrees for freedom.
Keywords: fluid mechanics, incompressible fluid, laminar flow, velocity vorticity formulation, boundary element method, mixed boundary elements
Published: 01.06.2012; Views: 1197; Downloads: 55
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