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

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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.

**[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)**

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DOI:
https://doi.org/10.1090/S0025-5718-1986-0829618-X

Article copyright:
© Copyright 1986
American Mathematical Society