Absorbing boundaries for wave propagation problems
Journal of Computational Physics
Time-dependent boundary conditions for hyperbolic systems, II
Journal of Computational Physics
Non-reflecting boundary conditions
Journal of Computational Physics
Ten lectures on wavelets
The pseudospectral method for limited-area elastic wave calculations
Computational methods in geosciences
On the representation of operators in bases of compactly supported wavelets
SIAM Journal on Numerical Analysis
Wavelets and the numerical solution of partial differential equations
Journal of Computational Physics
On the spline-based wavelet differentiation matrix
Applied Numerical Mathematics
Adaptive multiresolution collocation methods for initial boundary value problems of nonlinear PDEs
SIAM Journal on Numerical Analysis
An adaptive wavelet-vaguelette algorithm for the solution of PDEs
Journal of Computational Physics
On the adaptive numerical solution of nonlinear partial differential equations in wavelet bases
Journal of Computational Physics
Multiscale computation with interpolating wavelets
Journal of Computational Physics
A new class of time discretization schemes for the solution of nonlinear PDEs
Journal of Computational Physics
Solving Hyperbolic PDEs Using Interpolating Wavelets
SIAM Journal on Scientific Computing
On a wavelet-based method for the numerical simulation of wave propagation
Journal of Computational Physics
On a wavelet-based method for the numerical simulation of wave propagation
Journal of Computational Physics
A modified wavelet approximation of deflections for solving PDEs of beams and square thin plates
Finite Elements in Analysis and Design
Hi-index | 31.45 |
A wavelet-based method for the numerical simulation of acoustic and elastic wave propagation is developed. Using a displacement-velocity formulation and treating spatial derivatives with linear operators, the wave equations are rewritten as a system of equations whose evolution in time is controlled by first-order derivatives. The linear operators for spatial derivatives are implemented in wavelet bases using an operator projection technique with nonstandard forms of wavelet transform. Using a semigroup approach, the discretized solution in time can be represented in an explicit recursive form, based on Taylor expansion of exponential functions of operator matrices. The boundary conditions are implemented by augmenting the system of equations with equivalent force terms at the boundaries. The wavelet-based method is applied to the acoustic wave equation with rigid boundary conditions at both ends in 1-D domain and to the elastic wave equation with a traction-free boundary conditions at a free surface in 2-D spatial media. The method can be applied directly to media with plane surfaces, and surface topography can be included with the aid of distortion of the grid describing the properties of the medium. The numerical results are compared with analytic solutions based on the Cagniard technique and show high accuracy. The wavelet-based approach is also demonstrated for complex media including highly varying topography or stochastic heterogeneity with rapid variations in physical parameters. These examples indicate the value of the approach as an accurate and stable tool for the simulation of wave propagation in general complex media.