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This paper is concerned with the problem of an acoustic wave scattering in a locally perturbed periodic structure. As the total wavefield is non-quasi-periodic, effective truncation techniques are pursued for high-accuracy numerical…

Numerical Analysis · Mathematics 2025-12-16 Wangtao Lu , Kuanrong Shen , Ruming Zhang

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

For many biological systems that involve elastic structures immersed in fluid, small length scales mean that inertial effects are also small, and the fluid obeys the Stokes equations. One way to solve the model equations representing such…

Numerical Analysis · Mathematics 2019-07-24 Ondrej Maxian , Wanda Strychalski

The aim of this note is to present a numerical method to solve the Stokes problem in a bounded domain with a Dirac source term, which preserves optimality for any approximation order by the finite-element method. It is based on the…

Numerical Analysis · Mathematics 2015-05-20 Loïc Lacouture

We derive two systems of boundary-domain integral equations (BDIEs) equivalent to the Dirichlet problem for the compressible Stokes system using the potential method with an explicit parametrix (Levi function). The BDIEs are given in terms…

Analysis of PDEs · Mathematics 2021-07-08 M. A. Dagnaw , C. Fresneda-Portillo

We present a 3D hybrid method which combines the Finite Element Method (FEM) and the Spectral Boundary Integral method (SBIM) to model nonlinear problems in unbounded domains. The flexibility of FEM is used to model the complex,…

Numerical Analysis · Mathematics 2021-02-18 Gabriele Albertini , Ahmed Elbanna , David S. Kammer

We introduce an integral equation formulation of the surface Stokes equations, constructed using two-dimensional Stokeslets. The resulting integral equations are Fredholm integral equations of the second kind and can be discretized to high…

Numerical Analysis · Mathematics 2026-02-25 Tristan Goodwill , Jeremy Hoskins , Zydrunas Gimbutas , Bowei Wu

A data-driven surrogate framework to accelerate particle-resolved modelling of quasi-dilute suspensions of rigid, non-spherical particles in Stokes flow is introduced. A regularized-Stokeslet boundary element method (BEM) is implemented to…

Fluid Dynamics · Physics 2025-12-17 Marco Laudato

This paper constructs and analyzes a boundary correction finite element method for the Stokes problem based on the Scott-Vogelius pair on Clough-Tocher splits. The velocity space consists of continuous piecewise quadratic polynomials, and…

Numerical Analysis · Mathematics 2021-05-24 Haoran Liu , Michael Neilan , Baris Otus

This paper presents a new finite element (FE) formulation for liquid shells that is based on an explicit, 3D surface discretization using $C^1$-continuous finite elements constructed from NURBS interpolation. Both displacement-based and…

Computational Engineering, Finance, and Science · Computer Science 2017-01-04 Roger A. Sauer , Thang X. Duong , Kranthi K. Mandadapu , David J. Steigmann

The manuscript describes a quadrature rule that is designed for the high order discretization of boundary integral equations (BIEs) using the Nystr\"{o}m method. The technique is designed for surfaces that can naturally be parameterized…

Numerical Analysis · Mathematics 2020-07-07 Bowei Wu , Per-Gunnar Martinsson

We consider the stationary Stokes problem in a three-dimensional fluid domain $\mathcal F$ with non-homogeneous Dirichlet boundary conditions. We assume that this fluid domain is the complement of a bounded obstacle $\mathcal B$ in a…

Analysis of PDEs · Mathematics 2015-06-16 M Hillairet , Takfarinas Kelai

We present a finite element method for the Stokes equations involving two immiscible incompressible fluids with different viscosities and with surface tension. The interface separating the two fluids does not need to align with the mesh. We…

Numerical Analysis · Mathematics 2015-03-20 Peter Hansbo , Mats G. Larson , Sara Zahedi

In this paper, we propose a new virtual interpolation point method to formulate the discrete Stokes equations. We form virtual staggered structure for the velocity and pressure from the actual computation node set. The virtual interpolation…

Numerical Analysis · Mathematics 2014-01-28 Seong-Kwan Park , Gahyung Jo , Hi Jun Choe

We present new integral representations in two dimensions for the elastance problem in electrostatics and the mobility problem in Stokes flow. These representations lead to resonance-free Fredholm integral equations of the second kind and…

Numerical Analysis · Mathematics 2017-12-25 Manas Rachh , Leslie Greengard

In this work, we provide a fast, spectrally accurate method for the evaluation of boundary integral operators (BIOs) on a suspension of prolate and oblate spheroids. We first derive formulas for the standard layer potential operators for…

Numerical Analysis · Mathematics 2025-06-27 Leo Crowder , Tianyue Li , Eduardo Corona , Shravan Veerapaneni

We present a high-order boundary integral equation (BIE) method for the frequency-domain acoustic scattering of a point source by a singly-periodic, infinite, corrugated boundary. We apply it to the accurate numerical study of acoustic…

Numerical Analysis · Mathematics 2024-03-19 Fruzsina J. Agocs , Alex H. Barnett

For scattering problems of time-harmonic waves, the boundary integral equation (BIE) methods are highly competitive, since they are formulated on lower-dimension boundaries or interfaces, and can automatically satisfy outgoing radiation…

Numerical Analysis · Mathematics 2018-04-24 Wangtao Lu , Ya Yan Lu , Jianliang Qian

In this paper we advance the analysis of discretizations for a fluid-structure interaction model of the monolithic coupling between the free flow of a viscous Newtonian fluid and a deformable porous medium separated by an interface. A…

Numerical Analysis · Mathematics 2023-06-27 Wietse M. Boon , Martin Hornkjøl , Miroslav Kuchta , Kent-Andre Mardal , Ricardo Ruiz-Baier

A Skeleton-stabilized ImmersoGeometric Analysis technique is proposed for incompressible viscous flow problems with moderate Reynolds number. The proposed formulation fits within the framework of the finite cell method, where essential…