Simulating an audio beam: A second‐generation wavelet collocation method to numerically solve the Khokhlov–Zabalotskaya–Kuznetsov equation

2001 ◽  
Vol 109 (5) ◽  
pp. 2365-2365
Author(s):  
Kelvin C. M. Lee ◽  
Yew‐Hin Liew ◽  
Woon‐Seng Gan
Keyword(s):  
Collocation Method ◽  
Second Generation ◽  
Wavelet Collocation Method ◽  
Second Generation Wavelet

An Adaptive Wavelet Collocation Method for Solution of the Convection-Dominated Problem on a Sphere

2018 ◽  
Vol 15 (08) ◽  
pp. 1850080
Author(s):  
Ratikanta Behera ◽  
Mani Mehra
Keyword(s):  
Numerical Simulation ◽  
Collocation Method ◽  
Second Generation ◽  
Efficient Computation ◽  
Adaptive Wavelet ◽  
Spherical Wavelets ◽  
Collocation Points ◽  
Wavelet Collocation Method ◽  
Uniform Grids ◽  
Convection Dominated

In this paper, we present a numerical simulation of a convection-dominated problem using adaptive wavelet collocation method. This is based on second-generation spherical wavelets on a recursively refined spherical geodesic grid. The power lies in the fact that they only require small number of coefficients to represent this problem more accurately, which allows compression and efficient computation. In contrast with other approximate schemes, this approach reduced the number of collocation points used by factors of many orders of magnitude when compared to uniform grids of equivalent resolution. Numerical results demonstrate the efficiency of our approach.

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