Third degree polynomial transformation for boundary element integrals: Further improvements

Telles, J. C. F.; Tardin, Rodrigo H.

doi:10.1016/0955-7997(94)90016-7

Cited by 67 publications

(62 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The integrals within (16) can be evaluated with appropriate quadrature; the BEM literature has a rich variety of discussion on this subject including [23,24]. In the conventional BEM, collocation points are placed on nodal points.…”

Section: Igabemmentioning

confidence: 99%

Extended isogeometric boundary element method (XIBEM) for two-dimensional Helmholtz problems

Peake

Trevelyan

Coates

2013

Computer Methods in Applied Mechanics and Engineering

122

View full text Add to dashboard Cite

Publisher's copyright statement: NOTICE: this is the author's version of a work that was accepted for publication in Computer methods in applied mechanics and engineering. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be re ected in this document. Changes may have been made to this work since it was submitted for publication. A de nitive version was subsequently published in Computer methods in applied mechanics and engineering, 259, 2013, 10.1016/j.cma.2013.03.016 Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details.

show abstract

Section: Igabemmentioning

confidence: 99%

Extended isogeometric boundary element method (XIBEM) for two-dimensional Helmholtz problems

Peake

Trevelyan

Coates

2013

Computer Methods in Applied Mechanics and Engineering

122

View full text Add to dashboard Cite

show abstract

“…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%

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)

View full text Add to dashboard Cite

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

show abstract

“…As expected, the regular Gaussian quadrature is unable to compute the integral accurately, even using 20 Gauss-points. The application of the 3rd-order Telles transformation [45,47] for the same number of Gauss-points reduces the integration error by several orders of magnitude. If the integral is partitioned at the singularity and Sato Fig.…”

Section: Computation Of Weakly Singular Integralsmentioning

confidence: 99%

“…The most widely used non-linear coordinate transformation for nearly weakly singular integrals was proposed by Telles [45,47]. This utilises an optimisation parameter r that is dependent on both the order of the singularity and the closest distance D from the element to the near singular point [45,47].…”

Section: Computation Of Nearly Singular Integralsmentioning

confidence: 99%

“…These include analytical evaluation [41,42], division of the interval about the singularity [43], subtraction of the singularity [42], special quadrature routines [44], and the use of non-linear coordinate transformations [45][46][47][48][49]. Each method has its own particular advantages and disadvantages depending on the type and order of the boundary elements used, and the form of the singular integral.…”

Section: Computation Of Weakly Singular Integralsmentioning

confidence: 99%

See 1 more Smart Citation

A practical examination of the errors arising in the direct collocation boundary element method for acoustic scattering

Treeby

2009

Engineering Analysis with Boundary Elements

View full text Add to dashboard Cite

a b s t r a c tFor many engineers and acousticians, the boundary element method (BEM) provides an invaluable tool in the analysis of complex problems. It is particularly well suited for the examination of acoustical problems within large domains. Unsurprisingly, the widespread application of the BEM continues to produce an academic interest in the methodology. New algorithms and techniques are still being proposed, to extend the functionality of the BEM, and to compute the required numerical tasks with greater accuracy and efficiency. However, for a given global error constraint, the actual computational accuracy that is required from the various numerical procedures is not often discussed. Within this context, this paper presents an investigation into the discretisation and computational errors that arise in the BEM for acoustic scattering. First, accurate routines to compute regular, weakly singular, and nearly weakly singular integral kernels are examined. These are then used to illustrate the effect of the requisite boundary discretisation on the global error. The effects of geometric and impedance singularities are also considered. Subsequently, the actual integration accuracy required to maintain a given global error constraint is established. Several regular and irregular scattering examples are investigated, and empirical parameter guidelines are provided.

show abstract

Third degree polynomial transformation for boundary element integrals: Further improvements

Cited by 67 publications

References 7 publications

Extended isogeometric boundary element method (XIBEM) for two-dimensional Helmholtz problems

Extended isogeometric boundary element method (XIBEM) for two-dimensional Helmholtz problems

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

A practical examination of the errors arising in the direct collocation boundary element method for acoustic scattering

Contact Info

Product

Resources

About