English
Related papers

Related papers: Simultaneous approximation terms for elastic wave …

200 papers

We compare two high order finite-difference methods that solve the elastic wave equation in two dimensional domains with curved boundaries and material discontinuities. Two numerical experiments are designed with focus on wave boundary…

Numerical Analysis · Mathematics 2015-11-25 Kristoffer Virta , Christopher Juhlin , Gunilla Kreiss

Curvilinear, multiblock summation-by-parts finite difference operators with the simultaneous approximation term method provide a stable and accurate framework for solving the wave equation in second order form. That said, the standard…

Numerical Analysis · Mathematics 2022-09-07 Brittany A Erickson , Jeremy E Kozdon , Tobias W Harvey

This paper extends previous work on finitedifference schemes over staggered grids for infinite-dimensional port-Hamiltonian systems. In the one-dimensional setting, it generalizes the discretization approach originally developed for the…

Numerical Analysis · Mathematics 2025-12-09 Ignacio Diaz Alastuey , Yann Le Gorrec , Yongxin Wu

We develop a numerical method for solving the acoustic wave equation in covariant form on staggered curvilinear grids in an energy conserving manner. The use of a covariant basis decomposition leads to a rotationally invariant scheme that…

Numerical Analysis · Mathematics 2020-04-22 Ossian O'Reilly , N. Anders Petersson

We show that the semi-implicit time discretization approaches previously introduced for multilayer shallow water models for the barotropic case can be also applied to the variable density case with Boussinesq approximation. Furthermore,…

Numerical Analysis · Mathematics 2021-04-27 Luca Bonaventura , José Garres-Díaz

Approximated numerical techniques, for the solution of the elastic wave scattering problem over semi-infinite domains are reviewed. The approximations involve the representation of the half-space by a boundary condition described in terms…

Computational Engineering, Finance, and Science · Computer Science 2014-10-14 Nicolás Guarín-Zapata , Juan Gómez , Juan Jaramillo

Numerical modeling of elastic wave propagation in the subsurface requires applicability to heterogeneous, anisotropic and discontinuous media, as well as support of free surface boundary conditions. Here we study the cell-centered finite…

Numerical Analysis · Mathematics 2025-03-24 Ingrid Kristine Jacobsen , Inga Berre , Jan Martin Nordbotten , Ivar Stefansson

Large-scale simulations of the wave equation in electromagnetism, seismology, and acoustics, can be solved efficiently by finite difference methods. The accuracy of these numerical solutions usually depends on the minimization of…

Medical Physics · Physics 2021-06-23 Gianmarco Pinton

We study space--time isogeometric discretizations of the linear acoustic wave equation that use splines of arbitrary degree p, both in space and time. We propose a space--time variational formulation that is obtained by adding a…

Numerical Analysis · Mathematics 2024-08-02 Sara Fraschini , Gabriele Loli , Andrea Moiola , Giancarlo Sangalli

Finite difference schemes for the simulation of elastic waves in materi- als with jump discontinuities are presented. The key feature is the highly accurate treatment of interfaces where media discontinuities arise. The schemes are…

Geophysics · Physics 2013-09-24 Kristoffer Virta , Kenneth Duru

This paper is part of a program to combine a staggered time and staggered spatial discretization of continuum mechanics problems so that any property of the continuum that is proved using vector calculus can be proven in an analogous way…

Numerical Analysis · Mathematics 2019-01-15 Stanly L. Steinberg

We develop a new spatial semidiscrete multiscale method based upon the edge multiscale methods to solve semilinear parabolic problems with heterogeneous coefficients and smooth initial data. This method allows for a cheap spatial…

Numerical Analysis · Mathematics 2025-12-16 Leonardo A. Poveda , Shubin Fu , Guanglian Li , Eric Chung

Finite difference based micromagnetic simulations are a powerful tool for the computational investigation of magnetic structures. In this paper, we demonstrate how the discretization of continuous micromagnetic equations introduces a…

Materials Science · Physics 2024-12-17 Samuel J. R. Holt , Andrea Petrocchi , Martin Lang , Swapneel A. Pathak , Hans Fangohr

We establish a decoupling result for the $P$ and $S$ waves of linear, isotropic elasticity, in the setting of twice-differentiable Lam\'e parameters. Precisely, we show that the $P\leftrightarrow S$ components of the wave propagation…

Analysis of PDEs · Mathematics 2010-09-07 Valeriy Brytik , Maarten de Hoop , Hart Smith , Gunther Uhlmann

We consider the discretization and subsequent model reduction of a system of partial differential-algebraic equations describing the propagation of pressure waves in a pipeline network. Important properties like conservation of mass,…

Numerical Analysis · Mathematics 2017-04-12 Herbert Egger , Thomas Kugler , Björn Liljegren-Sailer , Nicole Marheineke , Volker Mehrmann

The aim of this paper is to develop stable and accurate numerical schemes for boundary integral formulations of the heat equation with Dirichlet boundary conditions. The accuracy of Galerkin discretisations for the resulting boundary…

Numerical Analysis · Mathematics 2018-05-01 Alexey Chernov , Anne Reinarz

We propose a computationally efficient technique for extrapolating seismic waves in an arbitrary isotropic elastic medium. The method is based on factorizing the full elastic wave equation into a product of pseudo-differential operators.…

Geophysics · Physics 2012-06-05 Musa Maharramov

The Laplacian appears in several partial differential equations used to model wave propagation. Summation-by-parts--simultaneous approximation term (SBP-SAT) finite difference methods are often used for such equations, as they combine…

Numerical Analysis · Mathematics 2020-02-11 Martin Almquist , Eric M. Dunham

We study the propagation properties of the solutions of the finite-difference space semi-discrete wave equation on an uniform grid of the whole Euclidean space. We provide a construction of high frequency wave packets that propagate along…

Analysis of PDEs · Mathematics 2010-08-03 Aurora-Mihaela Marica , Enrique Zuazua

This paper is devoted to the multigrid convergence analysis for the linear systems arising from the conforming linear finite element discretization of the second order elliptic equations with anisotropic diffusion. The multigrid convergence…

Numerical Analysis · Mathematics 2011-05-09 Guozhu Yu , Jinchao Xu , Ludmil Zikatanov