A fast direct solver for elliptic partial differential equations on adaptively refined meshes

SIAM Journal on Scientific Computing

Volumn 21, Issue 4, 1999, Pages 1551-1566

  Huang, Jingfang ^a   Greengard, Leslie ^a  

^a NEW YORK UNIVERSITY   (United States)

Author keywords

Adaptive mesh refinement; Direct elliptic solvers; Fast Poisson solvers; Potential theory

Indexed keywords

ADAPTIVELY REFINED MESHES; ELLIPTICAL PARTIAL DIFFERENTIAL EQUATIONS; FAST DIRECT SOLVER; POTENTIAL THEORY;

BOUNDARY CONDITIONS; FAST FOURIER TRANSFORMS; FINITE DIFFERENCE METHOD; FINITE ELEMENT METHOD; GEOMETRY; ITERATIVE METHODS; PROBLEM SOLVING;

PARTIAL DIFFERENTIAL EQUATIONS;

EID: 85066163277     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827598346235     Document Type: Article

References (23)

1. A. AVERBUCH, G. BEYLKIN, R. COIFMAN, AND M. ISRAELI, Multiscale inversion of elliptic operators, in Signal and Image Representation in Combined Spaces, A. Averbuch and R. Coifman, eds., Academic Press, New York, 1995, pp. 1-16.
2. A. BRANDT, Multi-level adaptive solutions to boundary value problems, Math. Comp., 31 (1977), pp. 333-390.
3. B. L. BUZBEE, G. H. GOLUB, AND C. W. NEILSON, On direct methods for solving Poisson's equation, SIAM J. Numer. Anal., 7 (1970), pp. 627-656.
4. T. F. CHAN, R. GLOWINSKI, J. PERIAUX, AND O. B. WIDLUND, EDS., Proceedings of the Third International Symposium on Domain Decomposition Methods for Partial Differential Equations, Proceedings in Applied Mathematics 43, SIAM, Philadelphia, 1989.
5. H. CHENG, L. GREENGARD, AND V. ROKHLIN, A fast adaptive multipole algorithm in three dimensions, J. Comput. Phys., 155 (1999), pp. 468-498.
6. G. B. FOLLAND, Introduction to Partial Differential Equations, Princeton University Press, Princeton, NJ, 1976.
7. P. GARABEDIAN, Partial Differential Equations, 2nd ed., Chelsea, New York, 1986.
8. J. A. GEORGE AND J. W. LIU, Computer Solution of Large Sparse Positive Definite Systems, Prentice-Hall, Englewood Cliffs, NJ, 1981.
9. G. H. GOLUB AND C. F. VAN LOAN, Matrix Computations, The Johns Hopkins University Press, Baltimore, MD, 1996.
10. L. GREENGARD AND J.Y. LEE, A direct adaptive Poisson solver of arbitrary order accuracy, J. Comput. Phys., 125 (1996), pp. 415-424.
11. L. GREENGARD AND V. ROKHLIN, A fast algorithm for particle simulations, J. Comput. Phys., 73 (1987), pp. 325-348.
12. R.B. GUENTHER AND J.W. LEE, Partial Differential Equations of Mathematical Physics and Integral Equations, Prentice-Hall, Englewood Cliffs, NJ, 1988.
13. R. W. HOCKNEY, A fast direct solution of Poisson's equation using Fourier analysis, J. Assoc. Comput. Mach., 12 (1965), pp. 95-113.
14. E.N. HOUSTIS AND T.S. PAPATHEODOROU, 'A high-order fast elliptic equation solver, ACM Trans. Math. Software, 5 (1979), pp. 431-441.
15. J.F. HUANG, A Fast Adaptive Solver for Linear Differential Equations Based on Potential Theory, in Iterative Methods in Scientific Computation IV, IMACS Series in Computational and Applied Mathematics 5, 1999.
16. F. JOHN, Partial Differential Equations, 4th ed., Springer-Verlag, New York, 1982.
17. A. MAYO, The fast solution of Poisson's and the biharmonic equations on irregular regions, SIAM J. Numer. Anal., 21 (1984), pp. 285-299.
18. A. MAYO, The rapid evaluation of volume integrals of potential theory on general regions, J. Comput. Phys., 100 (1992), pp. 236-245.
19. A. MCKENNEY, L. GREENGARD, AND A. MAYO, A fast Poisson solver for complex geometries, J. Comput. Phys., 118 (1995), pp. 348-355.
20. G. RUSSO AND J. STRAIN, Fast triangulated vortex methods for the 2D Euler equations, J. Comp. Phys., 111 (1994), pp. 291-323.
21. J. M. SONG AND W. C. CHEW, Fast multipole method solution using parametric geometry, Microwave Opt. Tech. Letters, 7 (1994), pp. 760-765.
22. P. N. SWARZTRAUBER, The methods of cyclic reduction, Fourier analysis and the FACR algorithm for the discrete solution of Poisson's equation on a rectangle, J. Comput. Phys., 15 (1974), pp. 46-54.
23. P. SWARZTRAUBER, AND R. SWEET, Efficient Fortran Subprograms for the Solution of Elliptic Partial Differential Equations, NCAR Technical Note NCAR-TN/IA-109, 1975, pp. 135-137.