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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…

Computational Physics · Physics 2019-10-02 Evert Klaseboer , Qiang Sun , Derek Y. C. Chan

A simple, yet efficient procedure to solve quasistatic problems of special linear visco-elastic solids at small strains with equal rheological response in all tensorial components, utilizing boundary element method (BEM), is introduced.…

Numerical Analysis · Mathematics 2014-02-27 C. G. Panagiotopoulos , V. Mantic , T. Roubicek

Conventionally, piecewise polynomials have been used in the boundary elements method (BEM) to approximate unknown boundary values. Since infinitely smooth radial basis functions (RBFs) are more stable and accurate than the polynomials for…

Numerical Analysis · Mathematics 2023-09-13 Hossein Hosseinzadeh , Zeinab Sedaghatjoo

A boundary element method (BEM) simulation is used to compare the efficiency of numerical inverse Laplace transform strategies, considering general requirements of Laplace-space numerical approaches. The two-dimensional BEM solution is used…

Numerical Analysis · Mathematics 2016-07-20 Kristopher L. Kuhlman

A handy technique for the Finite Element Method (FEM) is presented that uses the null space for the implementation of Dirichlet and constraint boundary conditions. The focus of this method is to present an illustrative approach to modeling…

Numerical Analysis · Mathematics 2024-03-12 Stefan Schoder

The scaled boundary finite element method (SBFEM) is a relatively recent boundary element method that allows the approximation of solutions to PDEs without the need of a fundamental solution. A theoretical framework for the convergence…

Numerical Analysis · Mathematics 2021-03-23 Fleurianne Bertrand , Daniele Boffi , Gonzalo G. de Diego

The boundary element method (BEM) provides an efficient numerical framework for solving multiple scattering problems in unbounded homogeneous domains, since it reduces the discretization to the domain boundaries, thereby condensing the…

Machine Learning · Computer Science 2025-12-03 Rémi Marsal , Stéphanie Chaillat

Time-domain Boundary Element Methods (BEM) have been successfully used in acoustics, optics and elastodynamics to solve transient problems numerically. However, the storage requirements are immense, since the fully populated system matrices…

Numerical Analysis · Mathematics 2020-06-11 Daniel Seibel

An isogeometric boundary element method (BEM) is presented to solve scattering problems in an isotropic homogeneous medium. We consider wave problems governed by the scalar wave equation as in acoustics and the Lam\'e-Navier equations for…

Computational Engineering, Finance, and Science · Computer Science 2025-10-09 Thomas Kramer , Benjamin Marussig , Martin Schanz

We present a new discretization method for homogeneous convection-diffusion-reaction boundary value problems in 3D that is a non-standard finite element method with PDE-harmonic shape functions on polyhedral elements. The element stiffness…

Numerical Analysis · Mathematics 2017-08-29 Clemens Hofreither , Ulrich Langer , Steffen Weißer

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…

Computational Engineering, Finance, and Science · Computer Science 2024-12-13 Benjamin Marussig , Thomas Rüberg , Jürgen Zechner , Lars Kielhorn , Thomas-Peter Fries

A Neural Network (NN) based numerical method is formulated and implemented for solving Boundary Value Problems (BVPs) and numerical results are presented to validate this method by solving Laplace equation with Dirichlet boundary condition…

Machine Learning · Computer Science 2019-09-25 Sethu Hareesh Kolluru

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…

Numerical Analysis · Mathematics 2018-02-14 Jürgen Dölz , Helmut Harbrecht , Stefan Kurz , Sebastian Schöps , Felix Wolf

An efficient and easy-to-implement method is proposed to regularize integral equations in the 3D boundary element method (BEM). The method takes advantage of an assumed three-noded triangle discretization of the boundary surfaces. The…

Classical Physics · Physics 2009-01-26 Patrick Dangla , Jean-François Semblat , H. Xiao , Nicolas Delépine

The finite element method(FEM) is applied to bound leading eigenvalues of Laplace operator over polygonal domain. Compared with classical numerical methods, most of which can only give concrete eigenvalue bounds over special domain of…

Numerical Analysis · Mathematics 2012-04-23 Xuefeng Liu , Shin'ichi Oishi

Motivated by problems where the response is needed at select localized regions in a large computational domain, we devise a novel finite element discretization that results in exponential convergence at pre-selected points. The two key…

Numerical Analysis · Mathematics 2016-08-03 Murthy N. Guddati , Vladimir Druskin , Ali Vaziri Astaneh

For the solution of 2D exterior Dirichlet Poisson problems we propose the coupling of a Curved Virtual Element Method (CVEM) with a Boundary Element Method (BEM), by using decoupled approximation orders. We provide optimal convergence error…

Numerical Analysis · Mathematics 2022-03-28 Luca Desiderio , Silvia Falletta , Matteo Ferrari , Letizia Scuderi

In this paper, we propose an efficient parallelization strategy for boundary element method (BEM) solvers that perform the electromagnetic analysis of structures with lossy conductors. The proposed solver is accelerated with the adaptive…

Distributed, Parallel, and Cluster Computing · Computer Science 2022-11-30 Damian Marek , Shashwat Sharma , Piero Triverio

In this paper, we deal with an elliptic problem with the Dirichlet boundary condition. We operate in Sobolev spaces and the main analytic tool we use is the Lax-Milgram lemma. First, we present the variational approach of the problem which…

Analysis of PDEs · Mathematics 2025-02-12 Eriselda Goga , Besiana Hamzallari

We propose a new fictitious domain finite element method, well suited for elliptic problems posed in a domain given by a level-set function without requiring a mesh fitting the boundary. To impose the Dirichlet boundary conditions, we…

Numerical Analysis · Mathematics 2019-07-09 Michel Duprez , Alexei Lozinski