Isogeometric boundary element method for acoustic scattering by a submarine

Venås, Jon Vegard; Kvamsdal, Trond

doi:10.1016/j.cma.2019.112670

Cited by 35 publications

(15 citation statements)

References 43 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The potential benefits of using IGA for the solution of boundary integral equations were already mentioned in the conclusions of [123], but it has only been considered first in [172]. The research on IGABEM has steadily grown since then, although not as fast as for IGAFEM, with applications in acoustics [189,76,61,198], elasticity [13,162], electromagnetics [197,188,77], lifting flow [63], potential flow [112,134,135], and solid mechanics [183,150], see also the recent book [17] for a comprehensive survey of the topic and a complete review of the existing literature. An implementation of (non-adaptive) IGABEM is available in the open-source library Bembel [75].…”

Section: Isogeometric Analysis For Bem (Igabem)mentioning

confidence: 99%

Mathematical Foundations of Isogeometric Analysis

et al. 2020

View full text Add to dashboard Cite

isogeometric analysis, with special focus on the mathematical theory. This includes an overview of available spline technologies for the local resolution of possible singularities as well as the state-of-the-art formulation of convergence and quasi-optimality of adaptive algorithms for both the finite element method (FEM) and the boundary element method (BEM) in the frame of isogeometric analysis (IGA).

show abstract

Section: Isogeometric Analysis For Bem (Igabem)mentioning

confidence: 99%

Mathematical Foundations of Isogeometric Analysis

et al. 2020

View full text Add to dashboard Cite

show abstract

“…Isogeometric Analysis (IGA) [32,12] has in recent years brought a renewed interest in developing highly accurate simulation models in Boundary Element Method (BEM); e.g., see advances in local and adaptive mesh refinements [27,23,24], trimming [5], fast matrix formation [14], fluid-structure interaction [31], fracture [43], shape optimization [37], acoustics and linear elasticity problems [49,53,50], and references therein. A predominant setting in IGA combines exact representation of the geometry using CAD standards such as polynomial and rational splines, and the same type of basis functions to represent the approximate solutions of PDEs.…”

Section: Introductionmentioning

confidence: 99%

Isoparametric singularity extraction technique for 3D potential problems in BEM

Kanduc

2022

Preprint

View full text Add to dashboard Cite

To solve boundary integral equations for potential problems using collocation Boundary Element Method (BEM) on smooth curved 3D geometries, an analytical singularity extraction technique is employed. By adopting the isoparametric approach, curved geometries that are represented by mapped rectangles or triangles from the parametric domain are considered. The singularity extraction on the governing singular integrals can be performed either as an operation of subtraction or division, each having some advantages.A particular series expansion of a singular kernel about a source point is investigated. The series in the intrinsic coordinates consists of functions of a type R p x q y r , where R is a square root of a quadratic bivariate homogeneous polynomial, corresponding to the first fundamental form of a smooth surface, and p, q, r are integers, satisfying p ≤ −1 and q, r ≥ 0. By extracting more terms from the series expansion of the singular kernel, the smoothness of the regularized kernel at the source point can be increased. Analytical formulae for integrals of such terms are obtained from antiderivatives of R p x q y r , using recurrence formulae, and by evaluating them at the edges of rectangular or triangular parametric domains.Numerical tests demonstrate that the singularity extraction technique can be a useful prerequisite for a numerical quadrature scheme to obtain accurate evaluations of the governing singular integrals in 3D collocation BEM.

show abstract

“…Peng et al [11] used a geometric algorithm to propagate fractures, based on the fatigue Paris law, and IGA-BEM to analyze them. Venas and Kvamsdal [12] used IGA-BEM to solve the acoustic scattering problem of a submarine.…”

Section: Introductionmentioning

confidence: 99%

An Application of Isogeometric Analysis and Boundary Integral Element Method for Solving Nonlinear Contact Problems

et al. 2020

View full text Add to dashboard Cite

A novel method to solve nonlinear contact between two bodies with plane strain behavior is presented in this paper. This method is based on the Boundary Integral Equation (BIE) and the Isogeometric Analysis (IGA). Unlike works that divide the boundary into elements, this method evaluates it as a single element, reducing the degrees of freedom in the solution. Moreover, the Particle Swarm Optimization Algorithm (PSO) was used in order to estimate the deformation when two bodies are in contact and there is penetration between them. The obtained results were compared with the Finite Element Method (FEM) and the Hertz contact equation.

show abstract

Isogeometric boundary element method for acoustic scattering by a submarine

Cited by 35 publications

References 43 publications

Mathematical Foundations of Isogeometric Analysis

Mathematical Foundations of Isogeometric Analysis

Isoparametric singularity extraction technique for 3D potential problems in BEM

An Application of Isogeometric Analysis and Boundary Integral Element Method for Solving Nonlinear Contact Problems

Contact Info

Product

Resources

About