Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 
 

 

The fast adaptive composite grid (FAC) method for elliptic equations


Authors: S. McCormick and J. Thomas
Journal: Math. Comp. 46 (1986), 439-456
MSC: Primary 65N20; Secondary 65F10, 65N50
DOI: https://doi.org/10.1090/S0025-5718-1986-0829618-X
MathSciNet review: 829618
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The fast adaptive composite grid (FAC) method is a systematic process for solving differential boundary value problems. FAC uses global and local uniform grids both to define the composite grid problem and to interact for its fast solution. It can with little added cost substantially improve accuracy of the coarse grid solution and is very suitable for vector and parallel computation. This paper develops both the theoretical and practical aspects of FAC as it applies to elliptic problems.


References [Enhancements On Off] (What's this?)

  • [1] D. Bai & A. Brandt, Local Mesh Refinement Multilevel Techniques, Research report, Dept. of Appl. Math., Weizmann Institute of Science, Rehovot, Israel, 1983.
  • [2] R. E. Bank & C. Douglas, "Sharp estimates for multigrid rates of convergence with general smoothing and acceleration," SIAM J. Numer. Anal., v. 4, 1985, pp. 617-633. MR 795944 (86j:65037)
  • [3] M. Berger & T. Jameson, An Adaptive Multigrid Method for the Euler Equations, Lecture Notes in Physics, Proc. 9th Internat. Conf. Numer. Methods in Fluid Dynamics, June, 1984, Saclay, France.
  • [4] M. Berger & J. Oliger, "An adaptive mesh refinement for hyperbolic partial differential equations," J. Comput. Phys., v. 53, 1984, pp. 484-512. MR 739112 (85h:65211)
  • [5] A. Brandt, "Multilevel adaptive solutions to boundary value problems," Math. Comp., v. 31, 1977, pp. 333-390. MR 0431719 (55:4714)
  • [6] F. Chatelin & W. Miranker, "Acceleration by aggregation of successive approximation methods," Linear Algebra Appl., v. 43, 1982, pp. 17-47. MR 656434 (83m:15002)
  • [7] W. G. Gropp, "Local uniform mesh refinement for elliptic partial differential equations," SIAM J. Sci. Statist. Comput., to appear; also available as Res. report no. 278, Dept. of Comput. Sci., Yale University, New Haven, CT, 1983.
  • [8] W. Hackbusch, "Local defect correction method and domain decomposition techniques," in Defect Correction Methods: Theory and Applications (K. Böhmer and H. J. Stetter, eds.), Computing Supplementum 5, Springer-Verlag, Wien, 1984, pp. 89-113. MR 782692 (86e:65146)
  • [9] J. Mandel, S. McCormick & J. Ruge, "An algebraic theory for multigrid methods for variational problems," SIAM J. Numer. Anal. (To appear.) MR 923928 (88m:65054)
  • [10] S. McCormick, A variational theory for multilevel adaptive techniques (MLAT), Proc. Multigrid Conference, Bristol, Sept., 1983, IMAJ.
  • [11] S. McCormick, "Fast adaptive composite grid (FAC) methods," in Defect Correction Methods: Theory and Applications (K. Böhmer and H. J. Stetter, eds.), Computing Supplementum 5, Springer-Verlag, Wien, 1984, pp. 115-121. MR 782693
  • [12] W. Miranker & V. Pan, "Methods of aggregation," Linear Algebra Appl., v. 29, 1980, pp. 231-257. MR 562764 (82d:65036)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65N20, 65F10, 65N50

Retrieve articles in all journals with MSC: 65N20, 65F10, 65N50


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1986-0829618-X
Article copyright: © Copyright 1986 American Mathematical Society

American Mathematical Society