Dispersion of time domain wavelet Galerkin method based on Daubechies' compactly supported scaling functions with three and four vanishing moments

2000 ◽  
Vol 10 (4) ◽  
pp. 125-127 ◽  
Author(s):  
M. Fujii ◽  
W.J.R. Hoefer
Keyword(s):  
Galerkin Method ◽  
Time Domain ◽  
Scaling Functions ◽  
Vanishing Moments ◽  
Compactly Supported ◽  
Wavelet Galerkin Method

Moments and Parametrizing Construction for 3-Band Biorthogonal Scaling Coefficients

2013 ◽  
Vol 284-287 ◽  
pp. 3189-3193
Author(s):  
Li Hong Cui ◽  
Yan Zhou ◽  
Bin Huang ◽  
Jian Jun Sun
Keyword(s):  
Symbolic Computation ◽  
Computer Algebra ◽  
Computation Method ◽  
Scaling Functions ◽  
Dual Scaling ◽  
Vanishing Moments ◽  
Compactly Supported ◽  
Orthonormal Wavelets ◽  
Discrete Moments ◽  
The Relationship

Regensburger and Scherzer described a symbolic computation method for moments and filter coefficients of scaling functions and obtained parametrizing compactly supported orthonormal wavelets. Following the idea, we are devoted to a study moments and parameterization construction for 3-band biorthogonal scaling coefficients with several vanishing moments. Firstly, we investigate the relations between filter lengths and symmetry. Then, we prove the relationship between dual continuous moments of 3-band biorthogonal scaling functions in theorem 2. This theorem reveals that the sum of continuous moments of dual scaling functions and is completely determined by the lower discrete moments. And we show the fact that the odd-indexed discrete moments are determined by the smaller even-indexed discrete moments. Finally, a family 3-band biorthogonal scaling coefficients with discrete moments as parameters are explicitly expressed based on computer algebra.

Detailed Multi Canister Release Model of Radionuclides in High Level Radioactive Waste Repository Using Wavelet Galerkin Method

2002 ◽  
Author(s):  
Hesham R. Nasif ◽  
Atsushi Neyama
Keyword(s):  
Radioactive Waste ◽  
Galerkin Method ◽  
Near Field ◽  
Far Field ◽  
High Level Radioactive Waste ◽  
Compactly Supported ◽  
Wavelet Galerkin Method ◽  
Bentonite Buffer ◽  
Buffer Region ◽  
High Level

This work develops a model to calculate the radionuclides release from a repository for high level radioactive waste, taking into account multiple-canister interface. Once the overpack loses its integrity, the waste glass starts to dissolve by porewater in the bentonite buffer. Bentonite is expected to have hydraulic conductivity more than three orders of magnitude less than that of the surrounding rocks. The migrating nuclide from the buffer region is transported in the near field granite host rock, then releases to the far field of the repository. A mass concentration calculation in the far field of the repository is also included in the model. The model is diffusion-advection model. The model is solved using wavelet Galerkin method (WGM). The model is devised to be fast and compact due to the compactly supported property of the Daubechies’ wavelet. Since the scaling functions are compactly supported only a finite number of the connection coefficients are nonzero. The resultant matrix has block diagonal structure, which can be inverted easily. We tested our model for a try of canisters contains 200 canisters. The results show well agreements with the results obtained from the analytic solution with a proper selection of wavelet-dilation order pairs.

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