Related papers: Simultaneous approximation terms for elastic wave …
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…
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…
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…
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…
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,…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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,…
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…
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.…
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…
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…
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…