Related papers: Bembel: The Fast Isogeometric Boundary Element C++…
We present an indirect higher order boundary element method utilising NURBS mappings for exact geometry representation and an interpolation-based fast multipole method for compression and reduction of computational complexity, to counteract…
We present a coupling of the Finite Element and the Boundary Element Method in an isogeometric framework to approximate either two-dimensional Laplace interface problems or boundary value problems consisting in two disjoint domains. We…
Isogeometric approach applied to Boundary Element Methods is an emerging research area. In this context, the aim of the present contribution is that of investigating, from a numerical point of view, the Symmetric Galerkin Boundary Element…
The design, implementation and analysis of a free library for boundary element calculations is presented. The library is free in the sense of the GNU General Public Licence and is intended to allow users to solve a wide range of problems…
This paper presents a shape optimisation system to design the shape of an acoustically-hard object in the three-dimensional open space. Boundary element method (BEM) is suitable to analyse such an exterior field. However, the conventional…
Boundary integral equations are an efficient and accurate tool for the numerical solution of elliptic boundary value problems. The solution is expressed as a layer potential; however, the error in its evaluation grows large near the…
We consider the efficient numerical solution of the three-dimensional wave equation with Neumann boundary conditions via time-domain boundary integral equations. A space-time Galerkin method with $C^\infty$-smooth, compactly supported basis…
In this work we address the complexity problem of the isogeometric Boundary Element Method by proposing a collocation scheme for practical problems in linear elasticity and the application of hierarchical matrices. For mixed boundary value…
The isogeometric formulation of Boundary Element Method (BEM) is investigated within the adaptivity framework. Suitable weighted quadrature rules to evaluate integrals appearing in the Galerkin BEM formulation of 2D Laplace model problems…
Many boundary element integral equation kernels are based on the Green's functions of the Laplace and Helmholtz equations in three dimensions. These include, for example, the Laplace, Helmholtz, elasticity, Stokes, and Maxwell's equations.…
MNPBEM is a Matlab toolbox for the simulation of metallic nanoparticles (MNP), using a boundary element method (BEM) approach. The main purpose of the toolbox is to solve Maxwell's equations for a dielectric environment where bodies with…
We present a new approach to three-dimensional electromagnetic scattering problems via fast isogeometric boundary element methods. Starting with an investigation of the theoretical setting around the electric field integral equation within…
In recent years there have been tremendous advances in the theoretical understanding of boundary integral equations for Maxwell problems. In particular, stable dual pairing of discretisation spaces have been developed that allow robust…
The boundary element method (BEM) is an efficient numerical method for simulating harmonic wave propagation. It uses boundary integral formulations of the Helmholtz equation at the interfaces of piecewise homogeneous domains. The…
This work focuses on model preparation for electrostatic simulations of CAD designs to realize a rapid virtual prototyping concept. We present a boundary element method (BEM) allowing discontinuous fields between surfaces. The corresponding…
MFEM is an open-source, lightweight, flexible and scalable C++ library for modular finite element methods that features arbitrary high-order finite element meshes and spaces, support for a wide variety of discretization approaches and…
The displacement field for three dimensional dynamic elasticity problems in the frequency domain can be decomposed into a sum of a longitudinal and a transversal part known as a Helmholtz decomposition. The Cartesian components of both the…
We solve first-kind Fredholm boundary integral equations arising from Helmholtz and Laplace problems on bounded, smooth screens in three-dimensions with either Dirichlet or Neumann conditions. The proposed Galerkin-Bubnov method takes as…
Two recently introduced quadrature schemes for weakly singular integrals [Calabr\`o et al. J. Comput. Appl. Math. 2018] are investigated in the context of boundary integral equations arising in the isogeometric formulation of Galerkin…
The use of integral equation methods for the efficient numerical solution of PDE boundary value problems requires two main tools: quadrature rules for the evaluation of layer potential integral operators with singular kernels, and fast…