A fast method for solving the heat equation by layer potentials

Journal of Computational Physics

Volumn 224, Issue 2, 2007, Pages 956-969

  Tausch, Johannes ^a  

^a SOUTHERN METHODIST UNIVERSITY   (United States)

Author keywords

Fast Gauss transform; Fast multipole method; Heat equation; Layer potentials

Indexed keywords

CONVOLUTION; DEGREES OF FREEDOM (MECHANICS); HEAT TRANSFER; PARTIAL DIFFERENTIAL EQUATIONS;

BOUNDARY INTEGRAL FORMULATIONS; FAST GAUSS TRANSFORM; FAST METHODS; FAST-MULTIPOLE METHODS; HEAT EQUATION; LAYER POTENTIALS; NUMBER OF DEGREES OF FREEDOM; SPACE AND TIME; TIME CONVOLUTION; TIME STEP;

POLYNOMIAL APPROXIMATION;

EID: 34248581666     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2006.11.001     Document Type: Article

References (13)

1. Atkinson K.E. The Numerical Solution of Integral Equations of the Second Kind (1997), Cambridge University Press
2. Canuto C., Hussaini M.Y., Quarteroni A., and Zhang T.A. Spectral Methods in Fluid Dynamics (1988), Springer
3. Chien D. Numerical evaluation of surface integrals in three dimensions. Math. Comp. 64 (1995) 727-743
4. Dargush G.F., and Banerjee P.K. Application of the boundary element method to transient heat conduction. Int. J. Numer. Meth. Eng. 31 (1991) 1231-1247
5. Greengard L., and Lin P. Spectral approximation of the free-space heat kernel. Appl. Comput. Harmonic Anal. 9 (1999) 83-97
6. Greengard L., and Strain J. A fast algorithm for the evaluation of heat potentials. Comm. Pure Appl. Math. XLIII (1990) 949-963
7. Greengard L., and Strain J. The fast Gauss transform. SIAM J. Sci. Statist. Comput. 12 (1991) 79-94
8. Greengard L., and Sun X. A new version of the fast Gauss transform. Doc. Math. J. DMV Extra Volume ICM 1998 III (1998) 575-584
9. Grigoriev M.M., and Dargush G.F. Higher-order boundary element methods for transient diffusion problems. part I: bounded flux formulation. Int. J. Numer. Meth. Eng. 55 (2002) 1-40
10. Mason J., and Handscomb D. Chebyshev Polynomials (2002), CRC Press
11. McIntyre E.A. Boundary integral solutions of the heat equation. Math. Comp. 46 173 (1986) 71-79
12. Strain J. Fast adaptive methods for the free-space heat equation. SIAM J. Sci. Statist. Comput. 15 1 (1994) 185-206
13. Sun X., and Bao Y. A Kronecker product representation of the fast Gauss transform. SIAM J. Matrix Anal. Appl. 24 3 (2003) 768-786