A local corrections algorithm for solving poisson's equation in three dimensions

Communications in Applied Mathematics and Computational Science

Volumn 2, Issue 1, 2007, Pages 57-81

  Mccorquodale, Peter ^a   Colella, Phillip ^a   Balls, Gregory T ^b   Baden, Scott B ^c  

^a LAWRENCE BERKELEY NATIONAL LABORATORY   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Adaptive mesh refinement; Domain decomposition; Local corrections; Poisson's equation

Indexed keywords

EID: 85015737642     PISSN: 15593940     EISSN: 21575452     Source Type: Journal    
DOI: 10.2140/camcos.2007.2.57     Document Type: Article

References (20)

1. A. S. Almgren, T. Buttke, and P. Colella, A fast adaptive vortex method in 3 dimensions, J. Comput. Phys. 113 (1994), no. 2, 177-200
2. C. R. Anderson, A method of local corrections for computing the velocity field due to a distribution of vortex blobs, J. Comput. Phys. 62 (1986), 111-123
3. S. B. Baden, Run-time partitioning of scientific continuum calculations running on multiprocessors, Ph.D. thesis, UC Berkeley Computer Science Division, April 1987
4. D. Bai and A. Brandt, Local mesh refinement multi-level techniques, SIAM Journal Sci. Stat. Comput. 8 (1987), 109-134
5. G. T. Balls, A finite difference domain decomposition method using local corrections for the solution of Poisson's equation, Ph.D. thesis, University of California, Berkeley, 1999
6. G. T. Balls and P. Colella, A finite difference domain decomposition method using local corrections for the solution of Poisson's equation, J. Comput. Phys. 180 (2002), no. 1, 25-53
7. A. Brandt, Multilevel adaptive methods for boundary-value problems, Math. Comp. 31 (1977), no. 138, 333-390
8. H. Cheng, J. Huang, and T. J. Leiterman, A fast adaptive solver for the modified Helmholtz equation in two dimensions, J. Comput. Phys. 211 (2006), no. 2, 616-637
9. F. Ethridge and L. Greengard, A new fast-multipole accelerated Poisson solver in two dimensions, SIAM Journal Sci. Comput. 23 (2001), no. 3, 741-760
10. M. Frigo and S. G. Johnson, FFTW: An adaptive software architecture for the FFT, ICASSP Conference Proceedings, vol. 3, ICASSP, 1998, pp. 1381-1384
11. L. Greengard and J.-Y. Lee, A direct adaptive Poisson solver of arbitrary order accuracy, J. Comput. Phys. 125 (1996), no. 2, 415-424
12. L. Greengard and V. Rokhlin, A fast algorithm for particle simulations, J. Comput. Phys. 73 (1987), 325-348
13. R. W. Hockney and J. W. Eastwood, Computer simulation using particles, McGraw-Hill, 1981
14. R. A. James, The solution of Poisson's equation for isolated source distributions, J. Comput. Phys. 25 (1977), no. 2, 71-93
15. H. Johansen and P. Colella, A Cartesian grid embedded boundary method for Poisson's equation on irregular domains, J. Comput. Phys. 147 (1998), no. 2, 60-85
16. O. D. Kellogg, Foundations of potential theory, Dover Publications, 1953
17. K. Lackner, Computation of ideal MHD equilibria, Computer Physics Communications 12 (1976), no. 1, 33-44
18. P. McCorquodale, P. Colella, D. Grote, and J.-L. Vay, A node-centered local refinement algorithm for Poisson's equation in complex geometries, J. Comput. Phys. 201 (2004), 34-60
19. G. H. Shortley and R. Weller, The numerical solution of Laplace's equation, J. Appl. Phys. 9 (1938), 334-348
20. B. F. Smith, P. E. Bjørstad, and W. D. Gropp, Domain decomposition: parallel multilevel methods for elliptic partial differential equations, Cambridge University Press, 2004