Fast summation by interval clustering for an evolution equation with memory

SIAM Journal on Scientific Computing

Volumn 34, Issue 6, 2012, Pages

  McLean, William ^a  

^a UNIVERSITY OF NEW SOUTH WALES   (Australia)

Author keywords

Degenerate kernel approximation; Discontinuous Galerkin method; Fractional diffusion

Indexed keywords

DEGREES OF FREEDOM (MECHANICS); DIFFERENTIAL EQUATIONS; GALERKIN METHODS; PIECEWISE LINEAR TECHNIQUES;

CLUSTERINGS; DEGENERATE KERNEL; DEGENERATE KERNEL APPROXIMATION; DISCONTINOUS GALERKIN METHODS; EVOLUTION EQUATIONS; FAST SUMMATION; FRACTIONAL DIFFUSION; KERNEL APPROXIMATION; MEMORY LOCATIONS; TIME LEVEL;

FINITE ELEMENT METHOD;

EID: 84871563342     PISSN: 10648275     EISSN: 10957200     Source Type: Journal    
DOI: 10.1137/120870505     Document Type: Article

References (13)

1. E. Cuesta, C. Lubich, and C. Palencia, Convolution quadrature time discretization of fractional diffusion-wave equations, Math. Comp., 75 (2006), pp. 673-696
2. W. Deng, Short memory principle and a predictor-corrector approach for fractional differential equations, J. Comput. Appl. Math., 206 (2007), pp. 174-188
3. K. Diethelm, J. M. Ford, N. J. Ford, and M. Weilbeer, Pitfalls in fast numerical solvers for fractional differential equations, J. Comput. Appl. Math., 186 (2006), pp. 42-503
4. K. Diethelm and A. D. Freed, An efficient algorithm for the evaluation of convolution integrals, Comput. Math. Appl., 51 (2006), pp. 51-72
5. N. J. Ford and A. C. Simpson, The numerical solutions of fractional differential equations: Speed verses accuracy, Numer. Algorithms, 26 (2001), pp. 333-346
6. W. Hackbusch and Z. P. Nowak, On the fast matrix multiplication in the boundary element method by panel clustering, Numer. Math., 54 (1989), pp. 463-491
7. J.-R. Li, A fast time stepping method for evaluating fractional integrals, SIAM J. Sci. Comput., 31 (2010), pp. 4696-4714
8. M. Lopez-Fernandez, C. Lubich, and A. Schadle, Adaptive, fast, and oblivious convolution in evolution equations with memory, SIAM J. Sci. Comput., 30 (2008), pp. 1015-1037
9. W. McLean, Regularity of solutions to a time-fractional diffusion equation, ANZIAM J., 52 (2010), pp. 123-138
10. W. McLean and K. Mustapha, Convergence analysis of a discontinuous Galerkin method for a sub-diffusion equation, Numer. Algorithms, 52 (2009), pp. 69-88
11. W. McLean and V. Thomée, Numerical solution via Laplace transforms of a fractional order evolution equation, J. Integral Equations Appl., 22 (2010), pp. 57-94
12. R. Metzler and J. Klafter, The random walk's guide to anomalous diffusion: A fractional dynamics approach, Phys. Rep., 339 (2000), pp. 1-77
13. A. Schädle, M. López-Fern'andez, and C. Lubich, Fast and oblivious convolution quadrature, SIAM J. Sci. Comput., 28 (2006), pp. 421-438