Finite difference method

About: Finite difference method is a research topic. Over the lifetime, 21603 publications have been published within this topic receiving 468852 citations. The topic is also known as: Finite-difference methods & FDM.

A hybrid scheme for absorbing edge reflections in numerical modeling of wave propagation

Abstract: We propose an efficient scheme to absorb reflections from the model boundaries in numerical solutions of wave equations. This scheme divides the computational domain into boundary, transition, and inner areas. The wavefields within the inner and boundary areas are computed by the wave equation and the one-way wave equation, respectively. The wavefields within the transition area are determined by a weighted combination of the wavefields computed by the wave equation and the one-way wave equation to obtain a smooth variation from the inner area to the boundary via the transition zone. The results from our finite-difference numerical modeling tests of the 2D acoustic wave equation show that the absorption enforced by this scheme gradually increases with increasing width of the transition area. We obtain equally good performance using pseudospectral and finite-element modeling with the same scheme. Our numerical experiments demonstrate that use of 10 grid points for absorbing edge reflections attains nearly perfect absorption.

Axisymmetric dynamic snap-through of elastic clamped shallow spherical shells.

Abstract: The behavior of axisymmetric dynamic snap-through of elastic, clamped shallow spherical shells under a uniform pressure has been investigated by.several authors. In most of the previous work, approximate methods were used, and as yet no positive conclusion has been made on the critical load for snap-through. In this paper, a numerical method is developed for solving the governing nonlinear differential equations of this problem. Two types of loading conditions are included-—an impulsive load and an instantaneous ly applied step load with infinite duration. In the case of impulsive loading, it is found from the quasi-static problem under zero load that the only equilibrium, position of the shell is its undeformed configuration. Hence, if we define the dynamic snap-through based on the finite jump behavior of deflection then there is no possibility for dynamic snap-through under impulsive loading. In the case of step loading, the snap-through loads are evaluated for a wide range of the geometrical parameter of the shell. Comparison of the present calculated critical loads with the previous results from approximate methods is made. It is found that the present critical load checks closely with an experimental value of the critical load for one value of the geometrical parameter of the shell.

Ocean Acoustic Propagation by Finite Difference Methods

Abstract: Foreword. Preface. Introduction. Ocean acoustic wave propagation problems. Finite difference schemes. Initial and boundary conditions. Range step size analysis. Wide-angle capability. Applicable solution methods other than the implicit finite difference scheme. Representative test examples. Listing of computer codes. Reference citation index. Subject index.