The generalized local maximum principle for a difference operator $L_h$ asserts that if $L_hu(x) > 0$ then $\Gamma u$ cannot attain its positive maximum at the net ...

A Julia library of summation-by-parts (SBP) operators used in finite difference, Fourier pseudospectral, continuous Galerkin, and discontinuous Galerkin methods to get provably stable ...

Abstract: The finite-difference method is an important approach for solving boundary-value problems of nonlinear ordinary and partial differential equations. In this approach, derivatives and partial ...

Abstract: Optimal coefficients of the spatial finite difference (FD) operator for the complex nonstandard finite difference time-domain (CNS-FDTD) method are presented. To derive the optimal ...

ABSTRACT: Finite difference type preconditioners for spectral element discretizations based on Legendre-Gauss-Lobatto points are analyzed. The latter is employed for the approximation of uniformly ...

This repository contains the code for implementing the finite-difference forward, adjoint, and gradient operators for the groundwater flow equation. The operators are implemented via Devito, a ...

Finite difference type preconditioners for spectral element discretizations based on Legendre-Gauss-Lobatto points are analyzed. The latter is employed for the approximation of uniformly elliptic ...