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Isogeometric Analysis (IgA) is a spline based approach to the numerical solution of partial differential equations. There are two major issues that IgA was designed to address. The first issue is the exact representation of domains stemming…

Numerical Analysis · Mathematics 2024-05-16 Stefan Tyoler , Stefan Takacs

In their article "Coupling at a distance HDG and BEM", Cockburn, Sayas and Solano proposed an iterative coupling of the hybridizable discontinuous Galerkin method (HDG) and the boundary element method (BEM) to solve an exterior Dirichlet…

Numerical Analysis · Mathematics 2022-05-19 Nestor Sánchez , Tonatiuh Sánchez-Vizuet , Manuel E. Solano

This work presents a numerical model for the simulation of potential flow past three dimensional lifting surfaces. The solver is based on the collocation Boundary Element Method, combined with Galerkin variational formulation of the…

Numerical Analysis · Mathematics 2024-10-15 Luca Cattarossi , Filippo Sacco , Nicola Giuliani , Nicola Parolini , Andrea Mola

The Immersed Boundary (IB) method of Peskin (J. Comput. Phys., 1977) is useful for problems involving fluid-structure interactions or complex geometries. By making use of a regular grid that is independent of the geometry, the IB framework…

Numerical Analysis · Mathematics 2022-10-17 Brittany J. Leathers

The reduction of computational costs in the numerical solution of nonstationary problems is achieved through splitting schemes. In this case, solving a set of less computationally complex problems provides the transition to a new level in…

Numerical Analysis · Mathematics 2022-10-26 Petr N. Vabishchevich

This work presents an unfitted boundary algebraic equation (BAE) method for solving three-dimensional elliptic partial differential equations on complex geometries using finite difference on structured meshes. We demonstrate that replacing…

Numerical Analysis · Mathematics 2025-02-11 Qing Xia

In this paper, we consider $C^1$ cubic Powell-Sabin splines for the numerical solution of boundary value problems on planar and spatial surface domains. We first review the construction and basic properties of polynomial and rational $C^1$…

Numerical Analysis · Mathematics 2026-03-24 Jan Grošelj , Ada Šadl Praprotnik , Hendrik Speleers

We introduce a new class of computationally tractable scattering problems in unbounded domains, which we call decomposable problems. In these decomposable problems, the computational domain can be split into a finite collection of…

Numerical Analysis · Mathematics 2024-11-19 Tristan Goodwill , Charles L. Epstein

The presented paper concentrates on the boundary element method (BEM) for the heat equation in three spatial dimensions. In particular, we deal with tensor product space-time meshes allowing for quadrature schemes analytic in time and…

Numerical Analysis · Mathematics 2021-11-23 Jan Zapletal , Raphael Watschinger , Günther Of , Michal Merta

Isogeometric analysis (IGA) represents a recently developed technology in computational mechanics that offers the possibility of integrating methods for analysis and Computer Aided Design (CAD) into a single, unified process. The…

Numerical Analysis · Computer Science 2016-02-01 Vinh Phu Nguyen , Stéphane P. A. Bordas , Timon Rabczuk

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

Our objective is to stabilise and accelerate the time-domain boundary element method (TDBEM) for the three-dimensional wave equation. To overcome the potential time instability, we considered using the Burton--Miller-type boundary integral…

Numerical Analysis · Mathematics 2022-01-05 Toru Takahashi , Masaki Tanigawa , Naoya Miyazawa

A novel multi-scale finite element formulation for contact mechanics between nominally smooth but microscopically rough surfaces is herein proposed. The approach integrates the interface finite element method (FEM) for modelling interface…

Computational Engineering, Finance, and Science · Computer Science 2025-04-03 Jacopo Bonari , Maria R. Marulli , Nora Hagmeyer , Matthias Mayr , Alexander Popp , Marco Paggi

The Immersed Boundary (IB) method is a widely-used numerical methodology for the simulation of fluid-structure interaction problems. The IB method utilizes an Eulerian discretization for the fluid equations of motion while maintaining a…

Numerical Analysis · Mathematics 2012-10-09 Varun Shankar , Grady B. Wright , Aaron L. Fogelson , R. M. Kirby

This paper presents an immersed, isogeometric finite element framework to predict the response of multi-material, multi-physics problems with complex geometries using locally refined discretizations. To circumvent the need to generate…

Numerical Analysis · Mathematics 2022-12-05 Mathias Schmidt , Lise Noel , Keenan Doble , John A. Evans , Kurt Maute

When modeling scientific and industrial problems, geometries are typically modeled by explicit boundary representations obtained from computer-aided design software. Unfitted (also known as embedded or immersed) finite element methods offer…

Computational Engineering, Finance, and Science · Computer Science 2024-05-24 Pere A. Martorell , Santiago Badia

A method for analytical computation of the double surface integrals for all layer potential kernels associated with the Laplace Green's function, in the Galerkin boundary element method (BEM) in $\mathbb{R}^3$ using piecewise constant flat…

Numerical Analysis · Mathematics 2023-02-08 Nail A. Gumerov , Shoken Kaneko , Ramani Duraiswami

A methodology for determining the scattered Electromagnetic (EM) fields present for interconnected regions with common metasurface boundaries is presented. The method uses a Boundary Element Method (BEM) formulation of the frequency domain…

Computational Physics · Physics 2020-01-08 Scott A. Stewart , Sanam Moslemi-Tabrizi , Tom. J. Smy , Shulabh Gupta

Since their advent nearly a decade ago, physics-informed neural networks (PINNs) have been studied extensively as a novel technique for solving forward and inverse problems in physics and engineering. The neural network discretization of…

Numerical Analysis · Mathematics 2025-12-18 Conor Rowan , Kai Hampleman , Kurt Maute , Alireza Doostan

A system of Boundary-Domain Integral Equations is derived from the mixed (Dirichlet-Neumann) boundary value problem for the diffusion equation in inhomogeneous media defined on an unbounded domain. Boundary-domain integral equations are…

Analysis of PDEs · Mathematics 2020-11-23 C. Fresneda-Portillo