English
Related papers

Related papers: BEM3D: a free adaptive fast multipole boundary ele…

200 papers

The Boundary Element Method (BEM) is a powerful numerical approach for solving 3D elastostatic problems, particularly useful for crack propagation in fracture mechanics and half-space problems. A key challenge in BEM lies in handling…

Numerical Analysis · Mathematics 2025-10-30 Vibudha Lakshmi Keshava , Martin Schanz

This paper proposes a fast time-domain boundary element method (TDBEM) to solve three-dimensional transient electromagnetic scattering problems regarding perfectly electric conductors in the classical marching-on-in-time manner. The…

Computational Physics · Physics 2023-03-10 Toru Takahashi

We analyze an adaptive boundary element method for the weakly-singular and hypersingular integral equations for the 2D and 3D Helmholtz problem. The proposed adaptive algorithm is steered by a residual error estimator and does not rely on…

Numerical Analysis · Mathematics 2019-03-21 Alex Bespalov , Timo Betcke , Alexander Haberl , Dirk Praetorius

This work is a user guide to the FEMPAR scientific software library. FEMPAR is an open-source object-oriented framework for the simulation of partial differential equations (PDEs) using finite element methods on distributed-memory…

Mathematical Software · Computer Science 2019-11-26 Santiago Badia , Alberto F. Martín

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

This paper presents a matrix-free approach for implementing the shifted boundary method (SBM) in finite element analysis. The SBM is a versatile technique for solving partial differential equations on complex geometries by shifting boundary…

Numerical Analysis · Mathematics 2025-07-24 Michał Wichrowski

The Boundary Element Method (BEM) is implemented using piecewise linear elements to solve the two-dimensional Dirichlet problem for Laplace's equation posed on a disk. A benefit of the BEM as opposed to many other numerical solution…

Numerical Analysis · Mathematics 2024-01-23 Misael M. Morales , Shirley Pomeranz

In this paper, we propose a review of the free boundary formulation for BVPs defined on semi-infinite intervals. The main idea and theorem are illustrated, for the reader convenience, by using a class of second-order BVPs. Moreover, we are…

Numerical Analysis · Mathematics 2020-11-17 Riccardo Fazio

We present a design through analysis workflow that enables virtual prototyping of electric devices. A CAD plugin establishes the interaction between design and analysis, allowing the preparation of analysis models and the visualization of…

Computational Engineering, Finance, and Science · Computer Science 2025-07-01 Benjamin Marussig , Jürgen Zechner , Thomas Rüberg , Lars Kielhorn , Domagoj Bošnjak , Thomas-Peter Fries

The paper presents a two-dimensional geometrically nonlinear formulation of a beam element that can accommodate arbitrarily large rotations of cross sections. The formulation is based on the integrated form of equilibrium equations, which…

Numerical Analysis · Mathematics 2021-04-20 Milan Jirásek , Emma La Malfa Ribolla , Martin Horák

The boundary element method (BEM) enables solving three-dimensional electromagnetic problems using a two-dimensional surface mesh, making it appealing for applications ranging from electrical interconnect analysis to the design of…

Numerical Analysis · Mathematics 2021-12-14 Shashwat Sharma , Piero Triverio

In theory, diffusion curves promise complex color gradations for infinite-resolution vector graphics. In practice, existing realizations suffer from poor scaling, discretization artifacts, or insufficient support for rich boundary…

Numerical Analysis · Mathematics 2023-11-27 Seungbae Bang , Kirill Serkh , Oded Stein , Alec Jacobson

The peridynamic theory brings advantages in dealing with discontinuities, dynamic loading, and non-locality. The integro-differential formulation of peridynamics poses challenges to numerical solutions of complicated and practical problems.…

Numerical Analysis · Mathematics 2021-06-01 Xue Liang , Linjuan Wang , Jifeng Xu , Jianxiang Wang

We describe here a library aimed at automating the solution of partial differential equations using the finite element method. By employing novel techniques for automated code generation, the library combines a high level of expressiveness…

Mathematical Software · Computer Science 2012-05-15 Anders Logg , Garth N. Wells

This paper presents a technique for stress and fracture analysis by using the scaled boundary finite element method (SBFEM) with quadtree mesh of high-order elements. The cells of the quadtree mesh are modelled as scaled boundary polygons…

Numerical Analysis · Mathematics 2026-03-19 Hou Man , Chongmin Song , Sundararajan Natarajan , Ean Tat Ooi , Carolin Birk

In this paper, we are concerned with the numerical treatment of boundary integral equations by means of the adaptive wavelet boundary element method (BEM). In particular, we consider the second kind Fredholm integral equation for the double…

Numerical Analysis · Mathematics 2016-10-10 Stephan Dahlke , Helmut Harbrecht , Manuela Utzinger , Markus Weimar

Dynamical energy analysis was recently introduced as a new method for determining the distribution of mechanical and acoustic wave energy in complex built up structures. The technique interpolates between standard statistical energy…

Computational Physics · Physics 2012-08-21 David J. Chappell , Gregor Tanner , Stefano Giani

Chaotic free surface flows are challenging problems to simulate numerically, mainly due to the significant changes in geometry and frequent topological changes. Methods that track the evolution of the fluid in a Lagrangian formulation are a…

Fluid Dynamics · Physics 2025-12-24 Thomas Leyssens , Jonathan Lambrechts , Jean-François Remacle

This work presents a polyhedral scaled boundary finite element method (PSBFEM) for three dimensional seepage analysis. We first derive the scaled boundary formulation for 3D seepage problems, and subsequently incorporate Wachspress shape…

Numerical Analysis · Mathematics 2025-06-11 Mingjiao Yan , Yang Yang , Zongliang Zhang , Dengmiao Hao , Chao Su , Qingsong Duan

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