Introduction to Boundary Elements

Hartmann, Friedel

doi:10.1007/978-3-642-48873-3

Cited by 100 publications

(37 citation statements)

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“…The numerical analysis of boundary value problems for partial differential equations using element methods is usually based on dividing a domain of interest into a mesh of finite elements within the finite element method (FEM) [1][2][3][4] or into boundary elements within the boundary element method (BEM) [5][6][7][8][9][10]. All of these methods allow one to consider the various computational domains due to the fact that even the most complex geometrical (including multiconnected) domains can be divided into finite elements, or only the boundary (external and internal) into boundary elements.…”

Section: Introductionmentioning

confidence: 99%

Nonelement boundary representation with Bézier surface patches for 3D linear elasticity problems in parametric integral equation system (PIES) and its solving using Lagrange polynomials

Zieniuk

Szerszeń

2017

Numerical Methods Partial

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In this article, we present a strategy of using rectangular and triangular Bézier surface patches for nonelement representation of 3D boundary geometries for problems of linear elasticity. The boundary generated in this way is directly incorporated in the parametric integral equation system (PIES), which has been developed by the authors. The boundary values on each surface patch are approximated by Lagrange polynomials. Three illustrative examples are presented to confirm the effectiveness of the proposed boundary representation in connection with PIES and to show good accuracy of numerical results.

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Section: Introductionmentioning

confidence: 99%

Nonelement boundary representation with Bézier surface patches for 3D linear elasticity problems in parametric integral equation system (PIES) and its solving using Lagrange polynomials

Zieniuk

Szerszeń

2017

Numerical Methods Partial

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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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“…As it is well known, boundary element methods, or panel methods [5], are a natural choice for obtaining numerical solutions of boundary integral equations [6] through collocation or Galerkin techniques [7], as well as they are closely related to the Green function theory [8].…”

Section: Introductionmentioning

confidence: 99%

A semi-analytical computation of the Kelvin kernel for potential flows with a free surface

D’Elı́a¹,

Battaglia²,

Storti³

2011

Comput. Appl. Math.

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Abstract.A semi-analytical computation of the three dimensional Green function for seakeeping flow problems is proposed. A potential flow model is assumed with an harmonic dependence on time and a linearized free surface boundary condition. The multiplicative Green function is expressed as the product of a time part and a spatial one. The spatial part is known as the Kelvin kernel, which is the sum of two Rankine sources and a wave-like kernel, being the last one written using the Haskind-Havelock representation. Numerical efficiency is improved by an analytical integration of the two Rankine kernels and the use of a singularity subtractive technique for the Haskind-Havelock integral, where a globally adaptive quadrature is performed for the regular part and an analytic integration is used for the singular one. The proposed computation is employed in a low order panel method with flat triangular elements. As a numerical example, an oscillating floating unit hemisphere in heave and surge modes is considered, where analytical and semi-analytical solutions are taken as a reference.Mathematical subject classification: Primary: 33F05; Secondary: 65N38.

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Introduction to Boundary Elements

Cited by 100 publications

References 0 publications

Nonelement boundary representation with Bézier surface patches for 3D linear elasticity problems in parametric integral equation system (PIES) and its solving using Lagrange polynomials

Nonelement boundary representation with Bézier surface patches for 3D linear elasticity problems in parametric integral equation system (PIES) and its solving using Lagrange polynomials

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

A semi-analytical computation of the Kelvin kernel for potential flows with a free surface

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