Adaptive multiresolution collocation methods for initial boundary value problems of nonlinear PDEs
SIAM Journal on Numerical Analysis
Journal of Computational Physics
A fast adaptive wavelet collocation algorithm for multidimensional PDEs
Journal of Computational Physics
Adaptive Wavelet Methods for Hyperbolic PDEs
Journal of Scientific Computing
A Wavelet-Optimized, Very High Order Adaptive Grid and Order Numerical Method
SIAM Journal on Scientific Computing
Solving Hyperbolic PDEs Using Interpolating Wavelets
SIAM Journal on Scientific Computing
Spectral methods for hyperbolic problems
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. VII: partial differential equations
Adaptive High-Order Finite-Difference Method for Nonlinear Wave Problems
Journal of Scientific Computing
Smoothing parameter selection for smoothing splines: a simulation study
Computational Statistics & Data Analysis
Curves and Surfaces for Computer Graphics
Curves and Surfaces for Computer Graphics
An Adaptive Wavelet Collocation Method for Fluid-Structure Interaction at High Reynolds Numbers
SIAM Journal on Scientific Computing
An adaptive multilevel wavelet collocation method for elliptic problems
Journal of Computational Physics
Simultaneous space-time adaptive wavelet solution of nonlinear parabolic differential equations
Journal of Computational Physics
Hi-index | 0.00 |
In this study, an improved wavelet-based adaptive-grid method is presented for solving the second order hyperbolic Partial Differential Equations (PDEs) for describing the waves propagation in elastic solid media. In this method, the multiresolution adaptive threshold-based approach is incorporated with smoothing splines as denoiser of spurious oscillations. This smoothing method is fast, stable, less sensitive to noise, and directly applicable to unequally sampled data. However, the conventional methods can not be directly applied to estimate the smoothing parameters; therefore the optimum ranges are captured through trial-and-error efforts. Here, the spatial derivatives are directly calculated in a non-uniform grid by Fornberg fast method. The derivatives are calculated in 2D simulations, applying antisymmetric end padding method to minimize Gibb's phenomenon, caused by the edge effects. Therefore, stable moving front is achieved. In the realistic source modeling, time dependent thresholding method, introduced here, is an efficient and cost effective adaptive scheme as well. Furthermore, level-dependent thresholding scheme is used to diminish the effects of non-physical long period waves reflected by absorbing boundaries. Finally, several 2D finite, infinite and semi-infinite numerical examples are simulated. These examples have fixed, free and absorbing boundary conditions. Here, the robustness of proposed method is demonstrated.