Abstract
The numerical solution of the time-dependent neutron transport problem in 2-D Cartesian geometry is considered. The problem is described by a coupled system of hyperbolic partial differential equations with the parameters of multiple groups. The system, for given group parameter, is discretized by a discrete ordinate method (SN) in angular direction and adaptive spline wavelet method with alternative direction implicit scheme (SW-ADI) [CZ98] in space-time domain. A parallel two-level hybrid method [SZ04] is used for solving the large-scale tridiagonal systems arising from the SW-ADI-SN discretization of the problem. The numerical results are coincided with theoretical analysis well.
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References
W. Cai and W. Zhang (1998), An adaptive SW-ADI method for 2-D reaction diffusion equations, J. Comput. Phys., Vol.139, No.1, 92–126.
X. Sun and W. Zhang (2004), A parallel two-level hybrid method for Tridiagonal systems and its application to fast Poisson solvers, IEEE Trans. Parallel and Distributed Systems, Vol.15,2, 97–107.
G. Beylkin, R. Coifman and V. Rokhlin (1991), Fast wavelet transforms and numerical algorithms I, comm. Pure Appl. math.44. 141.
I. Daubechies (1988), Orthogonal bases of compactly, comm. Pure Appl. Math. 41. 909.
B. Alpert (1993), A class of bases in L2 for the Sparse representation of intefral operators, SIAM J. Math. Anal.24 (1, 246).
W. Cai and J. Wang (1996), Adaptive multiresolution collocation methods for initial boundary value problems of nonlinear PDEs, SIAM J. Math. Anal. 33(3), 937.
L. Jameson (1994), On the Wavelet-Optimized Finite Difference Method, ICASE Report No. 94-9, NASN CR-191601.
L. Jameson (1995), On the spline-based Wavelet differentiationmatrix, Appl.numer.Math. 17(33), 33.
Y. Maday, V. Perrier, and J. C. Ravel (1991), Adaptive dynamique sur bases d’ondeelettes pour l’approximation d’equatioms aus derivees partielles, C, R. Acad. Sci. Paris 312,405.
J. Froehlich and K. Schneider (1997), An Adaptive wavelet-Vagvelette algorithm for the solution of PDEs, J. Comput. Phy. 130, 174.
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© 2005 Springer-Verlag Berlin Heidelberg
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Zhang, H., Zhang, W. (2005). Adaptive Parallel Wavelet Method for the Neutron Transport Equations. In: Zhang, W., Tong, W., Chen, Z., Glowinski, R. (eds) Current Trends in High Performance Computing and Its Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-27912-1_18
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DOI: https://doi.org/10.1007/3-540-27912-1_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-25785-1
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