scholarly journals An Adaptive Wavelet Method for the Chemical Master Equation

2010 ◽  
Vol 31 (6) ◽  
pp. 4373-4394 ◽  
Author(s):  
Tobias Jahnke
Keyword(s):  
Master Equation ◽  
Chemical Master Equation ◽  
Wavelet Method ◽  
Adaptive Wavelet ◽  
Adaptive Wavelet Method

A Dynamic Adaptive Wavelet Method for Solution of the Schrodinger Equation

2015 ◽  
Vol 06 (01) ◽  
pp. 1450001 ◽  
Author(s):  
Ratikanta Behera ◽  
Mani Mehra
Keyword(s):  
Schrödinger Equation ◽  
Computational Efficiency ◽  
Schrodinger Equation ◽  
Computational Cost ◽  
Two Dimensional ◽  
Wavelet Method ◽  
Adaptive Wavelet ◽  
One Dimensional ◽  
Grid Adaptation ◽  
Adaptive Wavelet Method

In this paper, we present a dynamically adaptive wavelet method for solving Schrodinger equation on one-dimensional, two-dimensional and on the sphere. Solving one-dimensional and two-dimensional Schrodinger equations are based on Daubechies wavelet with finite difference method on an arbitrary grid, and for spherical Schrodinger equation is based on spherical wavelet over an optimal spherical geodesic grid. The method is applied to the solution of Schrodinger equation for computational efficiency and achieve accuracy with controlling spatial grid adaptation — high resolution computations are performed only in regions where a solution varies greatly (i.e., near steep gradients, or near-singularities) and a much coarser grid where the solution varies slowly. Thereupon the dynamic adaptive wavelet method is useful to analyze local structure of solution with very less number of computational cost than any other methods. The prowess and computational efficiency of the adaptive wavelet method is demonstrated for the solution of Schrodinger equation on one-dimensional, two-dimensional and on the sphere.

scholarly journals An Adaptive Wavelet Method for Solving High-Dimensional Elliptic PDEs

2009 ◽  
Vol 30 (3) ◽  
pp. 423-455 ◽  
Author(s):  
Tammo Jan Dijkema ◽  
Christoph Schwab ◽  
Rob Stevenson
Keyword(s):  
High Dimensional ◽  
Elliptic Pdes ◽  
Wavelet Method ◽  
Adaptive Wavelet ◽  
Adaptive Wavelet Method

The Application of Adaptive Wavelet Method to Multi-Dimensional Limiting Process for Enhancement of Computational Efficiency

2011 ◽  
Author(s):  
Hyungmin Kang ◽  
Kyunghyun Park ◽  
Dongho Lee ◽  
Kyuhong Kim ◽  
Seunghwan Park ◽  
...  
Keyword(s):  
Computational Efficiency ◽  
Interpolation Method ◽  
Higher Order ◽  
High Order ◽  
Computational Time ◽  
Numerical Accuracy ◽  
Wavelet Method ◽  
Adaptive Wavelet ◽  
Computational Fluid Dynamics Cfd ◽  
Adaptive Wavelet Method

An adaptive wavelet method is applied in order to enhance the computational efficiency of enhanced Multi-dimensional Limiting Process (e-MLP) without deterioration of the numerical accuracy of original Computational Fluid Dynamics (CFD) scheme. For this purpose, higher order of adaptive wavelet method is constructed including higher order of wavelet decomposition and modified thresholding. Besides, the locations of crucial features such as shock, vortex core, etc. are automatically and accurately searched in the CFD dataset through wavelet transformation. Only on these locations, high order spatial interpolation scheme with e-MLP are performed; in the other locations, interpolation method is utilized to compute residual values, which reduces the computational time of flux evaluation. This high order adaptive wavelet method was applied to unsteady Euler flow computations such as shock-vortex interaction problem. Throughout these processes, it was verified that computational efficiency was enhanced with preservation of numerical accuracy of CFD solver.

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