Consistent Infinitesimal Finite Element Cell Method: Three-Dimensional Scalar Wave Equation

1996 ◽  
Vol 63 (3) ◽  
pp. 650-654 ◽  
Author(s):  
J. P. Wolf ◽  
Chongmin Song
Keyword(s):  
Finite Element ◽  
Wave Equation ◽  
Three Dimensional ◽  
Time Domain Analysis ◽  
Spatial Dimension ◽  
Element Formulation ◽  
Scalar Wave ◽  
Scalar Wave Equation ◽  
Cell Method ◽  
Unbounded Medium

To calculate the unit-impulse response matrix of an unbounded medium governed by the scalar wave equation for use in a time-domain analysis of unbounded medium-structure interaction, the consistent infinitesimal finite element cell method is developed for the three-dimensional case. Its derivation is based on the finite element formulation and on similarity. The discretization is only performed on the structure-medium interface, yielding a reduction of the spatial dimension by 1. The procedure is exact in the radial direction and converges to the exact solution in the finite element sense in the circumferential directions.

Finite Element Solution and Dispersion Analysis for the Transient Structural Acoustics Problem

1990 ◽  
Vol 43 (5S) ◽  
pp. S381-S388 ◽  
Author(s):  
N. N. Abboud ◽  
P. M. Pinsky
Keyword(s):  
Finite Element ◽  
Wave Equation ◽  
Three Dimensional ◽  
Finite Element Approximation ◽  
Dispersion Analysis ◽  
Time Dependent ◽  
Element Approximation ◽  
Element Formulation ◽  
Structural Acoustics ◽  
Boundary Operators

In this paper a finite element formulation is proposed for solution of the time-dependent coupled wave equation over an infinite fluid domain. The formulation is based on a finite computational fluid domain surrounding the structure and incorporates a sequence of boundary operators on the fluid truncation boundary. These operators are designed to minimize reflection of outgoing waves and are based on an asymptotic expansion of the exact solution for the time-dependent problem. The variational statement of the governing equations is developed from a Hamiltonian approach that is modified for nonconservative systems. The dispersive properties of finite element semidiscretizations of the three dimensional wave equation are examined. This analysis throws light on the performance of the finite element approximation over the entire range of wavenumbers and the effects of the order of interpolation, mass lumping, and direction of wave propagation are considered.

Wave‐equation migration in the presence of lateral velocity variations

Geophysics ◽  
1982 ◽  
Vol 47 (7) ◽  
pp. 1001-1011 ◽  
Author(s):  
Richard Jay Castle
Keyword(s):  
Wave Equation ◽  
Three Dimensional ◽  
Scalar Wave ◽  
Lateral Velocity ◽  
Scalar Wave Equation ◽  
Common Depth Point ◽  
Velocity Gradients ◽  
Velocity Variations ◽  
Integral Solutions ◽  
Dimensional Wave

An algorithm for three‐dimensional wave equation migration in the presence of lateral velocity gradients is developed. The algorithm is based geophysically on the exploding reflector model and mathematically on integral solutions to the scalar wave equation. In addition, the velocity is assumed to vary slowly over a seismic wavelength. The primary application of the algorithm is to stacked sections. However, if the velocity is a function of depth only, the algorithm may be used to migrate and/or image common‐depth‐point gathers.

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