Domain Decomposition Algorithm for Coupling of Finite Element and Boundary Element Methods

Haghighat, Abbas Eslami; Binesh, S.M.

doi:10.1007/s13369-014-0995-9

Cited by 9 publications

(9 citation statements)

References 16 publications

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“…Given the complexity of direct FSI coupling techniques, iterative domain decomposition method became a popular approach [19]. Therefore, we describe a simple means to combine hp-adaptivity with domain decomposition (DD) parallelization.…”

Section: Introductionmentioning

confidence: 99%

Adaptive FEM with Domain Decomposition Method for Partitioned-Based Fluid–Structure Interaction

Abas

Abdul-Rahman

2015

Arab J Sci Eng

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A numerical assessment on the solution performance of adaptive finite element methods for fluid-structure interaction (FSI) is presented in this paper. The partitionedbased approach involving separate fluid and structure solvers is considered for adaptive finite element computation with triangular mesh. The performance of the hp-adaptivity, in which error in energy norm is reduced by way of mesh refinement (h) and polynomial order extension ( p), is of particular interest. In addition, parallel solution process based on the domain decomposition method is also assessed due to the complexity of two way coupling scheme. Based on its numerical convergence, the hp-adaptive procedure for the FSI problem is shown to yield the fastest convergence as generally expected. Moreover, our domain decomposition parallelization scheme shows reduction in the computation time by up to order 2. Subsequently, the convergence performance is highly dependent on the aspect ratios of the triangular elements. The solution performance strongly suggests the viability of the parallel hp-adaptive method in partitioned-based FSI formulation.Keywords Fluid-structure interaction · Adaptive finite element method · Arbitrary Lagrangian-Eulerian · Error estimator · Domain decomposition B Aizat Abas

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Section: Introductionmentioning

confidence: 99%

Adaptive FEM with Domain Decomposition Method for Partitioned-Based Fluid–Structure Interaction

Abas

Abdul-Rahman

2015

Arab J Sci Eng

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“…To verify the basic idea of HAM for a nonlinear system of ordinary differential equations (Bataineh, Noorani, & Hashim, 2009;Gabriel, 2016;Liao, 2004;Wazwaz, 2009), let us consider this problem:…”

Section: Solution By Homotopy Analysis Methodsmentioning

confidence: 99%

“…Flockerzi and Sundmacher (2011) assumed that in the qualitative analysis for the solutions. In the following, we produce an approximate solution for the above nonlinear problem using the HAM (Bataineh et al, 2009;Gabriel, 2016;Liao, 2004;Wazwaz, 2009). In order to implement this method to the current system, we will solve the system introduced by Rach et al (2014) which is used in the modified ADM.…”

Section: The Ham For Solving the Lane-emden Boundary Value Problemmentioning

confidence: 99%

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Boundary-domain integral method and homotopy analysis method for systems of nonlinear boundary value problems in environmental engineering

AL-Jawary

Rahdi

Ravnik

2020

Arab Journal of Basic and Applied Sciences

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In this paper we present the development of numerical methods for two problems in chemical engineering: adsorption of carbon dioxide into phenyl glycidyl ether and diffusion and reaction processes in a porous catalyst. Both problems are modelled by systems of two coupled nonlinear ordinary differential equations. Dirichlet and Neumann type boundary conditions are considered. We develop the standard homotopy analysis method and the boundary-domain element method to solve for the unknown steady-state concentrations of reactants. The validity of the proposed methods is checked and demonstrated by numerical examples. Convergence rates are compared and the advantages and drawbacks of the proposed methods are discussed and compared to the Mathematica NDSOLVE solver. We show, that the proposed homotopy analysis method features exponential convergence rate and is highly accurate and efficient. As low as 6 terms are needed to reach error norms of 10 À5 : Furthermore, the boundary-domain integral approach is also capable of solving the same problem very efficiently, using a very coarse computational mesh (21 nodes).

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“…Coupling of the finite element method (FEM) and the boundary element method (BEM) has a rich tradition, see e.g. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] and the references cited therein. This is justified as researchers were motivated to develop coupled methods in order to utilize "appropriate" discretization techniques in different sub-domains of the original problem, a need that arises from the different physics of sub-domains and/or for a better computational efficiency and accuracy.…”

Section: Introductionmentioning

confidence: 99%

Some Recent Developments in Coupling of Finite Element and Boundary Element Methods - Part I: An Overview

Elleithy

Leong

2014

AMM

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Conventional and a class of domain decomposition finite element–boundary element coupling (FEM–BEM) methods are reviewed. This is Part I of two papers. In Part II, a review of the mixed Dirichlet-Neumann domain decomposition FEM-BEM coupling method is presented and optimal dynamic values of the relaxation parameters for the mixed Dirichlet-Neumann FEM-BEM coupling method are, furthermore, derived.

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Domain Decomposition Algorithm for Coupling of Finite Element and Boundary Element Methods

Cited by 9 publications

References 16 publications

Adaptive FEM with Domain Decomposition Method for Partitioned-Based Fluid–Structure Interaction

Adaptive FEM with Domain Decomposition Method for Partitioned-Based Fluid–Structure Interaction

Boundary-domain integral method and homotopy analysis method for systems of nonlinear boundary value problems in environmental engineering

Some Recent Developments in Coupling of Finite Element and Boundary Element Methods - Part I: An Overview

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