Boundary Elements: An Introductory Course

Brebbia, Carlos Alberto; Domínguez, José Manuel; Tassoulas, John L.

doi:10.1115/1.2897280

Cited by 761 publications

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“…This effect cannot be observed when the numerical solution bases on the macro approach. Now, the problems connected with the boundary element method (Brebbia et al, 1984;Brebbia & Dominguez, 1992;Majchrzak, 2001) application in the scope of solidification process modeling will be discussed. So, the boundary element method constitutes the effective tool for numerical simulation of solidification processes (Majchrzak & Mochnacki, 1995;Majchrzak & Mochnacki, 1996;Majchrzak & Szopa, 2001;Mochnacki & Majchrzak, 2007b).…”

Section: Examples Of Numerical Methods Applicationmentioning

confidence: 99%

“…So, the boundary element method constitutes the effective tool for numerical simulation of solidification processes (Majchrzak & Mochnacki, 1995;Majchrzak & Mochnacki, 1996;Majchrzak & Szopa, 2001;Mochnacki & Majchrzak, 2007b). The method assures the exact approximation of real shapes of the boundaries and also the very good exactness of boundary conditions approximation (Brebbia et al, 1984;Brebbia & Dominguez, 1992). These features of the BEM are very essential in the case of solidification processes modeling because the big gradients of temperature near the boundary require the adequate exact method of temperature field computations.…”

Section: Examples Of Numerical Methods Applicationmentioning

confidence: 99%

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Numerical Modeling of Solidification Process

Mochnacki¹

2011

Computational Simulations and Applications

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Section: Examples Of Numerical Methods Applicationmentioning

confidence: 99%

Section: Examples Of Numerical Methods Applicationmentioning

confidence: 99%

Numerical Modeling of Solidification Process

Mochnacki¹

2011

Computational Simulations and Applications

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“…The integrals are defined, but they have to be suitably evaluated to avoid numerical problems. This topic has been studied intensively and an overview of the available techniques can be found in [78][79][80][81][82][83][84][85][86][87].…”

Section: Numerical Integrationmentioning

confidence: 99%

“…In this study we regularize the second kernel using the rigid body method [78], that provides an indirect way to calculate the jump term as:…”

Section: Numerical Integrationmentioning

confidence: 99%

A 3d Isogeometrical Boundary Element Analysis for Non-Linear Gravity Wave Propagation

Maestre¹,

Pallarès²,

Cuesta³

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. In this paper we describe a three-dimensional Isogeometric BEM in the time domain based on the T-spline and Non Uniform Rational B-Splines (NURBS) basis to study the free surface behavior. Traditionally, the Lagrange polynomials have been used to discretize the geometry and the BEMs variables. The Lagrange basis are discontinues across the elements although the physical variables are continuous. In dynamics problems with high mesh distortions this approach can produce numerical instabilities that can be quickly propagated. This problem could be overcome using T-spline or NURB basis. The main advantages of this approach are: (1) the control of the continuity and smoothness of the T-spline and NURBS basis, which makes the model numerically stable without the need of artificial smooth techniques;(2) the high order geometrical approximation by non-rational splines;(3) the refinement capabilities without affecting the geometry and BEM's variables; and (4) the direct integration with computer aid geometrical design tools. We use the concept of the Bézier extraction operation which provides an element point of view of the T-Spline and NURBS similar to the traditional finite element. The boundary integral Equation is solved at each time step by the GMRES algorithm and the time marching scheme is performed with a fourth-order Runge-Kutta method to update the model. Additionally, the hydrodynamic force is calculated by an auxiliary boundary equation. Some numerical benchmark examples are analysed to show the accuracy and the stability of the method 7967 J. Maestre, J. Pallarés and I. Cuesta

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“…With the development of such methods, it has become possible to create automated techniques to solve various boundary problems. The most popular and widely used methods for solving these problems are undoubtedly finite difference method [1,2], finite element method [3,4] and boundary element method [5][6][7][8][9]. A characteristic feature of all these methods is the need for the discretization of the domain or the boundary into elements.…”

Section: Introductionmentioning

confidence: 99%

Triangular Bézier surface patches in modeling shape of boundary geometry for potential problems in 3D

Zieniuk

Szerszeń

2012

Engineering with Computers

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This paper presents a new boundary shape representation for 3D boundary value problems based on parametric triangular Bézier surface patches. Formed by the surface patches, the graphical representation of the boundary is directly incorporated into the formula of parametric integral equation system (PIES). This allows us to eliminate the need for both boundary and domain discretizations. The possibility of eliminating the discretization of the boundary and the domain in PIES significantly reduces the number of input data necessary to define the boundary. In this case, the boundary is described by a small set of control points of surface patches. Three numerical examples were used to validate the solutions of PIES with analytical and numerical results available in the literature.

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Boundary Elements: An Introductory Course

Cited by 761 publications

References 0 publications

Numerical Modeling of Solidification Process

Numerical Modeling of Solidification Process

A 3d Isogeometrical Boundary Element Analysis for Non-Linear Gravity Wave Propagation

Triangular Bézier surface patches in modeling shape of boundary geometry for potential problems in 3D

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