Staggered-grid Finite-difference Scheme Research Articles

Yee‐like schemes on a tetrahedral mesh, with diagonal lumping

A Galerkin edge-element solution technique for Maxwell's equations in time domain is discussed. With proper diagonal lumping of one of the mass matrices, it can be seen as a generalization to a tetrahedral mesh and its barycentric dual of the staggered-grid finite difference scheme known nowadays as FDTD, or Yee's scheme. A new approach to the lumping, backed by a specific convergence-proof technique, is proposed. Copyright © 1999 John Wiley & Sons, Ltd.

Quadrangle-grid velocity-stress finite-difference method for elastic-wave-propagation simulation

SUMMARY I present a 2-D numerical-modelling algorithm based on a first-order velocity-stress hyperbolic system and a non-rectangular-grid finite-difference operator. In this method the velocity and stress are defined at different nodes for a staggered grid. The scheme uses non-orthogonal grids, thereby surface topography and curved interfaces can be easily modelled in the seismic-wave-propagation stimulation. The free-surface conditions of complex geometry are achieved by using integral equilibrium equations on the surface, and the stability of the free-surface conditions is improved by introducing local filter modification. The method incorporates desirable qualities of the finite-element method and the staggered-grid finite-difference scheme, which is of high accuracy and low computational cost.

A mixed finite element formulation for Maxwell's equations in the time domain

A Galerkin finite element solution technique for the Maxwell's equations is discussed. This new formulation can be viewed as a generalization of certain staggered-grid finite difference schemes to arbitrary meshes. It is shown that this technique is simple to implement and is more accurate as well as more cost effective than the standard equal-order finite element approach. Numerical are presented to evaluate the performance of this new element relative to the standard element.