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The aim of this work is to introduce and analyze a finite element discontinuous Galerkin method on polygonal meshes for the numerical discretization of acoustic waves propagation through poroelastic materials. Wave propagation is modeled by…

Numerical Analysis · Mathematics 2021-04-14 Paola F. Antonietti , Michele Botti , Ilario Mazzieri , Simone Nati Poltri

We propose a time stepping scheme for the space-time systems obtained from Galerkin time-domain boundary element methods for the wave equation. Based on extrapolation, the method proves stable, becomes exact for increasing degrees of…

Numerical Analysis · Mathematics 2020-03-06 Heiko Gimperlein , David Stark

In this paper, numerical solutions of singularly perturbed boundary value problems are given by using variants of finite element method. Both Galerkin and subdomain Galerkin method based on quadratic B-spline functions are applied over the…

Numerical Analysis · Mathematics 2017-02-09 Ozlem Ersoy Hepson , Idris Dag

We address the spatial discretization of an evolution problem arising from the coupling of viscoelastic and acoustic wave propagation phenomena by employing a discontinuous Galerkin scheme on polygonal and polyhedral meshes. The coupled…

Numerical Analysis · Mathematics 2018-12-11 Paola F. Antonietti , Francesco Bonaldi , Ilario Mazzieri

We consider the initial/boundary value problem for the fractional diffusion and diffusion-wave equations involving a Caputo fractional derivative in time. We develop two "simple" fully discrete schemes based on the Galerkin finite element…

Numerical Analysis · Mathematics 2015-10-13 Bangti Jin , Raytcho Lazarov , Zhi Zhou

This paper aims to address two issues of integral equations for the scattering of time-harmonic electromagnetic waves by a perfect electric conductor with Lipschitz continuous boundary: ill-conditioned {boundary element Galerkin matrices}…

Numerical Analysis · Mathematics 2024-10-29 Van Chien Le , Kristof Cools

In this article a simplified weak Galerkin finite element method is developed for the Dirichlet boundary value problem of convection-diffusion-reaction equations. The simplified weak Galerkin method utilizes only the degrees of freedom on…

Numerical Analysis · Mathematics 2018-08-29 Yujie Liu , Junping Wang

In this work, we investigate time-dependent wave scattering by multiple small particles of arbitrary shape. To approximate the solution of the associated boundary-value problem, we derive an asymptotic model that is valid in the limit as…

Numerical Analysis · Mathematics 2025-11-17 Maryna Kachanovska , Adrian Savchuk

A Petrov-Galerkin finite element method is constructed for a singularly perturbed elliptic problem in two space dimensions. The solution contains a regular boundary layer and two characteristic boundary layers. Exponential splines are used…

Numerical Analysis · Mathematics 2023-11-02 Alan F. Hegarty , Eugene O'Riordan

We present a novel computational scheme to solve acoustic wave transmission problems over composite scatterers, i.e. penetrable obstacles possessing junctions or triple points. Our continuous problem is cast as a multiple traces time-domain…

Numerical Analysis · Mathematics 2022-04-01 Carlos Jerez-Hanckes , Ignacio Labarca

We present a boundary integral formulation of electromagnetic scattering by homogeneous bodies that are characterized by linear constitutive equations in the frequency domain. By working with the Cartesian components of the electric, E and…

Computational Physics · Physics 2018-12-18 Qiang Sun , Evert Klaseboer , Derek Y. C. Chan

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

The paper focuses on numerical solution of parametrized diffusion equations with scalar parameter-dependent coefficient function by the stochastic (spectral) Galerkin method. We study preconditioning of the related discretized problems…

Numerical Analysis · Mathematics 2020-01-20 Marie Kubínová , Ivana Pultarová

We analyse the dispersion properties of two types of explicit finite element methods for modelling acoustic and elastic wave propagation on tetrahedral meshes, namely mass-lumped finite element methods and symmetric interior penalty…

Numerical Analysis · Mathematics 2019-01-29 S. Geevers , W. A. Mulder , J. J. W. van der Vegt

In this paper, we develop an efficient spectral-Galerkin-type search extension method (SGSEM) for finding multiple solutions to semilinear elliptic boundary value problems. This method constructs effective initial data for multiple…

Numerical Analysis · Mathematics 2023-08-15 Wei Liu , Ziqing Xie , Yongjun Yuan

We consider the Shallow Water equations in the supercritical and subcritical cases in one space variable,posed in a finite spatial interval with characteristic boundary conditions at the endpoints, which, as is well known, are…

Numerical Analysis · Mathematics 2016-03-01 D. C. Antonopoulos , V. A. Dougalis

We apply boundary integral equations for the first time to the two-dimensional scattering of time-harmonic waves from a smooth obstacle embedded in a continuously-graded unbounded medium. In the case we solve the square of the wavenumber…

Numerical Analysis · Mathematics 2016-05-04 Alex. H. Barnett , Bradley J. Nelson , J. Matthew Mahoney

The discontinuous Galerkin (DG) method is an established method for computing approximate solutions of partial differential equations in many applications. Unlike continuous finite elements, in DG methods, numerical fluxes are used to…

Numerical Analysis · Mathematics 2019-12-02 Kenneth Duru , Leonhard Rannabauer , Alice-Agnes Gabriel , Heiner Igel

In this paper, we focus on designing a well-conditioned Glarkin spectral methods for solving a two-sided fractional diffusion equations with drift, in which the fractional operators are defined neither in Riemann-Liouville nor Caputo sense,…

Numerical Analysis · Mathematics 2019-09-13 Lijing Zhao , Xudong Wang

We consider solving the exterior Dirichlet problem for the Helmholtz equation with the $h$-version of the boundary element method (BEM) using the standard second-kind combined-field integral equations. We prove a new, sharp bound on how the…

Numerical Analysis · Mathematics 2019-02-25 Jeffrey Galkowski , Eike H. Müller , Euan A. Spence