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We develop a rapid and accurate contour method for the solution of time-fractional PDEs. The method inverts the Laplace transform via an optimised stable quadrature rule, suitable for infinite-dimensional operators, whose error decreases…

Numerical Analysis · Mathematics 2022-02-09 Matthew J. Colbrook , Lorna J. Ayton

We develop a space-time spectral element method for topology optimization of transient heat conduction. The forward problem is discretized with summation-by-parts (SBP) operators, and interface/boundary and initial/terminal conditions are…

Numerical Analysis · Mathematics 2026-01-15 Sarah Nataj , Magnus Appel , Joe Alexandersen

In this paper we introduce a method for solving linear and nonlinear scattering problems for wave equations using a new hybrid approach. This new approach consists of a reformulation of the governing equations into a form that can be solved…

Numerical Analysis · Mathematics 2018-07-04 Aihua Lin , Anastasiia Kuzmina , Per Kristen Jakobsen

The advection-diffusion and wave equations are the fundamental equations governing any physical law and therefore arise in many areas of physics and astrophysics. For complex problems and geometries, only numerical simulations can give…

Computational Physics · Physics 2014-01-08 J. Pétri

We begin by addressing the time-domain full-waveform inversion using the adjoint method. Next, we derive the scaled boundary semi-weak form of the scalar wave equation in heterogeneous media through the Galerkin method. Unlike conventional…

Numerical Analysis · Mathematics 2025-01-14 Alireza Daneshyar , Stefan Kollmannsberger

The high-precision solution of the radial Dirac equation is fundamental to relativistic quantum chemistry, essential for reliable pseudopotential generation and all-electron electronic structure methods. However, standard basis-set…

Numerical Analysis · Mathematics 2026-04-14 Sheng Chen , Sihong Shao , Shuai Wu

A symplectic pseudospectral time-domain (SPSTD) scheme is developed to solve Schrodinger equation. Instead of spatial finite differences in conventional finite-difference time-domain (FDTD) method, the fast Fourier transform is used to…

Computational Physics · Physics 2018-05-09 Jing Shen , Wei E. I. Sha , Xiaojing Kuang , Jinhua Hu , Zhixiang Huang , Xianliang Wu

We introduce a numerical method for the solution of the time-dependent Schrodinger equation with a smooth potential, based on its reformulation as a Volterra integral equation. We present versions of the method both for periodic boundary…

Numerical Analysis · Mathematics 2021-08-03 Jason Kaye , Alex Barnett , Leslie Greengard

Efficient and accurate spectral solvers for nonlocal models in any spatial dimension are presented. The approach we pursue is based on the Fourier multipliers of nonlocal Laplace operators introduced in a previous work. It is demonstrated…

Numerical Analysis · Mathematics 2019-07-30 Bacim Alali , Nathan Albin

An unsteady three-dimensional boundary element method is developed to provide fast calculations of biological and bio-inspired self-propelled locomotion. The approach uniquely combines an unsteady three-dimensional boundary element method,…

Fluid Dynamics · Physics 2017-03-27 Keith W. Moored

Consider the scattering of a time-harmonic acoustic incident wave by a bounded, penetrable, and isotropic elastic solid, which is immersed in a homogeneous compressible air or fluid. The paper concerns the numerical solution for such an…

Numerical Analysis · Mathematics 2017-03-10 Xue Jiang , Peijun Li

This paper develops an explicit spectral representation for solutions of a one-dimensional linear wave equation with a constant time delay. The model is considered on a bounded interval with non-homogeneous Dirichlet boundary data and a…

Analysis of PDEs · Mathematics 2026-02-06 Javad A. Asadzade , Jasarat J. Gasimov , Nazim I. Mahmudov , Ismail T. Huseynov

Numerical simulation of wave propagation in an infinite medium is made possible by surrounding a finite region by a perfectly matched layer (PML). Using this approach a generalized three-dimensional (3D) formulation is proposed for…

Numerical Analysis · Mathematics 2016-12-21 Hisham Assi , Richard S. C. Cobbold

Due to the nonlocal feature of fractional differential operators, the numerical solution to fractional partial differential equations usually requires expensive memory and computation costs. This paper develops a fast scheme for fractional…

Numerical Analysis · Mathematics 2025-03-21 Hao Yuan , Xiaoping Xie

The diffraction of a plane wave by a transversely inhomogeneous isotropic nonmagnetic linearly polarized dielectric layer filled with a Kerr-type nonlinear medium is considered. The analytical and numerical solution techniques are…

Analysis of PDEs · Mathematics 2009-10-13 Yury Shestopalov , Vasil Yatsyk

Consider the scattering of a time-harmonic elastic plane wave by a bi-periodic rigid surface. The displacement of elastic wave motion is modeled by the three-dimensional Navier equation in an open domain above the surface. Based on the…

Numerical Analysis · Mathematics 2020-07-28 Gang Bao , Xue Jiang , Peijun Li , Xiaokai Yuan

This article initiates the study of space-time adaptive mesh refinements for time-dependent boundary element formulations of wave equations. Based on error indicators of residual type, we formulate an adaptive boundary element procedure for…

Numerical Analysis · Mathematics 2025-11-07 Alessandra Aimi , Giulia Di Credico , Heiko Gimperlein , Chiara Guardasoni

An FFT-based algorithm is developed to simulate the propagation of elastic waves in heterogeneous $d$-dimensional rectangular shape domains. The method allows one to prescribe the displacement as a function of time in a subregion of the…

Numerical Analysis · Mathematics 2022-12-21 R. Sancho , V. Rey de Pedraza , P. Lafourcade , R. A. Lebensohn , J. Segurado

This paper is concerned with a numerical solution to the scattering of a time-harmonic electromagnetic wave by a bounded and impenetrable obstacle in three dimensions. The electromagnetic wave propagation is modeled by a boundary value…

Numerical Analysis · Mathematics 2022-02-21 Gang Bao , Mingming Zhang , Xue Jiang , Peijun Li , Xiaokai Yuan

In this paper, for solving a class of linear parabolic equations in rectangular domains, we have proposed an efficient Parareal exponential integrator finite element method. The proposed method first uses the finite element approximation…

Numerical Analysis · Mathematics 2024-12-03 Jianguo Huang , Yuejin Xu