Related papers: A high order finite difference method for the elas…
We develop a fourth order accurate finite difference method for the three dimensional elastic wave equation in isotropic media with the piecewise smooth material property. In our model, the material property can be discontinuous at curved…
We use high order finite difference methods to solve the wave equation in the second order form. The spatial discretization is performed by finite difference operators satisfying a summation-by-parts property. The focus of this work is on…
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…
We analyze two types of summation-by-parts finite difference operators for approximating the second derivative with variable coefficient. The first type uses ghost points, while the second type does not use any ghost points. A previously…
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…
A high order cut finite element method is formulated for solving the elastic wave equation. Both a single domain problem and an interface problem are treated. The boundary or interface are allowed to cut through the background mesh. To…
In this paper, we propose a novel high order unfitted finite element method on Cartesian meshes for solving the acoustic wave equation with discontinuous coefficients having complex interface geometry. The unfitted finite element method…
The diffusive viscous wave equation describes wave propagation in diffusive and viscous media. Examples include seismic waves traveling through the Earth's crust, taking into account of both the elastic properties of rocks and the…
We develop a hybrid spatial discretization for the wave equation in second order form, based on high-order accurate finite difference methods and discontinuous Galerkin methods. The hybridization combines computational efficiency of finite…
We present a finite-difference scheme which solves the Stokes problem in the presence of curvilinear non-conforming interfaces and provides second-order accuracy on physical field (velocity, vorticity) and especially on pressure. The gist…
We propose a finite difference method to solve Maxwell's equations in time domain in the presence of a perfect electric conductor that impedes the propagations of electromagnetic waves. Our method is a modification of the existing approach…
In this paper, we consider finite difference approximations of the second order wave equation. We use finite difference operators satisfying the summation-by-parts property to discretize the equation in space. Boundary conditions and grid…
In this paper we present a one dimensional second order accurate method to solve Elliptic equations with discontinuous coefficients on an arbitrary interface. Second order accuracy for the first derivative is obtained as well. The method is…
We develop a high order accurate numerical method for solving the elastic wave equation in second-order form. We hybridize the computationally efficient Cartesian grid formulation of finite differences with geometrically flexible…
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…
We define a new finite element method for a steady state elliptic problem with discontinuous diffusion coefficients where the meshes are not aligned with the interface. We prove optimal error estimates in the $L^2$ norm and $H^1$ weighted…
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…
Second order accurate Cartesian grid methods have been well developed for interface problems in the literature. However, it is challenging to develop third or higher order accurate methods for problems with curved interfaces and internal…
We consider a stabilized finite element method based on a spacetime formulation, where the equations are solved on a global (unstructured) spacetime mesh. A unique continuation problem for the wave equation is considered, where data is…
In this work, we propose a novel formulation for the solution of partial differential equations using finite element methods on unfitted meshes. The proposed formulation relies on the discrete extension operator proposed in the aggregated…