Related papers: A new efficient staggered grid finite difference s…
This work focuses on developing high-order energy-stable schemes for wave-dominated problems in closed domains using staggered finite-difference summation-by-parts (SBP FD) operators. We extend the previously presented uniform staggered…
This work combines the consistency in lower-order differential operators with external approximations of functional spaces to obtain error estimates for finite difference finite volume schemes on unstructured non-uniform meshes. This…
We develop a stable finite difference method for the elastic wave equation in bounded media, where the material properties can be discontinuous at curved interfaces. The governing equation is discretized in second order form by a fourth or…
In this work, we present a new high order Discontinuous Galerkin time integration scheme for second-order (in time) differential systems that typically arise from the space discretization of the elastodynamics equation. By rewriting the…
This paper presents a spatial two-grid (STG) compact difference scheme for a two-dimensional (2D) nonlinear diffusion-wave equation with variable exponent, which describes, e.g., the propagation of mechanical diffusive waves in viscoelastic…
We present a first order scheme based on a staggered grid for the shallow water equations with topography in two space dimensions, which enjoys several properties: positivity of the water height, preservation of constant states, and weak…
We introduce a novel class of finite difference approximations, termed zigzag schemes, that employ a hybrid stencil that is neither symmetrical, nor fully one-sided. These zigzag schemes often enjoy more permissive stability constraints and…
In this paper, we consider the development and analysis of a new explicit compact high-order finite difference scheme for acoustic wave equation formulated in divergence form, which is widely used to describe seismic wave propagation…
We propose two stable and one conditionally stable finite difference schemes of second-order in both time and space for the time-fractional diffusion-wave equation. In the first scheme, we apply the fractional trapezoidal rule in time and…
New implicit and implicit-explicit time-stepping methods for the wave equation in second-order form are described with application to two and three-dimensional problems discretized on overset grids. The implicit schemes are single step,…
This paper introduces an adaptive time splitting technique for the solution of stiff evolutionary PDEs that guarantees an effective error control of the simulation, independent of the fastest physical time scale for highly unsteady…
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 presents an extension of a recently developed high order finite difference method for the wave equation on a grid with non-conforming interfaces. The stability proof of the existing methods relies on the interpolation operators…
A quasi-second order scheme is developed to obtain approximate solutions of the shallow water equationswith bathymetry. The scheme is based on a staggered finite volume scheme for the space discretization:the scalar unknowns are located in…
Many multiscale wave systems exhibit macroscale emergent behaviour, for example, the fluid dynamics of floods and tsunamis. Resolving a large range of spatial scales typically requires a prohibitively high computational cost. The small…
This paper is part of a program to combine a staggered time and staggered spatial discretization of continuum wave equations so that important properties of the continuum that are proved using vector calculus can be proven in an analogous…
Phase field models are promising to tackle various fracture problems where a diffusive crack is introduced and modelled using the phase variable. Owing to the non-convexity of the energy functional, the derived partial differential…
We present a simple method to solve spherical harmonics moment systems, such as the the time-dependent $P_N$ and $SP_N$ equations, of radiative transfer. The method, which works for arbitrary moment order $N$, makes use of the specific…
We propose highly accurate finite-difference schemes for simulating wave propagation problems described by linear second-order hyperbolic equations. The schemes are based on the summation by parts (SBP) approach modified for applications…
In this paper, we present a novel local and parallel two-grid finite element scheme for solving the Stokes equations, and rigorously establish its a priori error estimates. The scheme admits simultaneously small scales of subproblems and…