Application of p-multigrid to discontinuous galerkin formulations of the poisson equation

AIAA Journal

Volumn 44, Issue 3, 2006, Pages 566-575

  Helenbrook, Brian T ^a,c,d   Atkins, H L ^b,d,e  

^a CLARKSON UNIVERSITY   (United States)

^b NASA LANGLEY RESEARCH CENTER   (United States)

^c Mechanical and Aeronautical Engineering Department   (United States)

^d AIAA   (United States)

^e Aerospace Technologist   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

GALERKIN FORMULATIONS; GAUSS-SEIDEL RELAXATION; LINE RELAXATION METHOD; TWO-DIMENSIONAL PROBLEMS;

GALERKIN METHODS; ISOTOPES; MATRIX ALGEBRA; PROBLEM SOLVING; RELAXATION PROCESSES;

POISSON EQUATION;

EID: 33645402156     PISSN: 00011452     EISSN: None     Source Type: Journal    
DOI: 10.2514/1.15497     Document Type: Conference Paper

References (19)

1. Rönquist, E. M., and Patera, A. T., "Spectral Element Multigrid. I. Formulation and Numerical Results," Journal of Scientific Computing, Vol. 2, No. 4, 1987, pp. 389-406.
2. Maday, Y., and Munoz, R., "Spectral Element Multigrid Part 2: Theoretical Justification," ICASE, Technical Rept. 88-73, 1988.
3. Helenbrook, B. T., "A Two-Fluid Spectral Element Method," Computer Methods in Applied Mechanics and Engineering, Vol. 191, Nos. 3-5, 2001, pp. 273-294.
4. Brooks, A. N., and Hughes, T. J. R., "Streamline Upwind/Petrov-Galerkin Formulations for Convection Dominated Flows with Particular Emphasis on the Incompressible Navier-Stokes Equations," Computer Methods in Applied Mechanics and Engineering, Vol. 32, Nos. 1-3, 1982, pp. 199-259.
5. Fischer, P. F., and Lottes, J. W., "Hybrid Multigrid/Schwarz Algorithms for the Spectral Element Method," Journal of Scientific Computing, Vol. 24, No. 1, 2005, pp. 45-78.
6. Fidkowski, K., "A High-Order Discontinuous Galerkin Multigrid Solver for Aerodynamic Applications," M.S. Thesis, Massachusetts Inst. of Technology, Cambridge, MA, June 2004.
7. Oliver, T. A., "Multigrid Solution for High-Order Discontinuous Galerkin Discretizations of the Compressible Navier-Stokes Equations," M.S. Thesis, Massachusetts Inst. of Technology, Cambridge, MA, Aug. 2004.
8. Fidkowski, K. J., Oliver, T. A., Lu, J., and Darmofal, D. L., "p-Multigrid Solution of High-Order Discontinuous Galerkin Discretizations of the Compressible Navier-Stokes Equations," Journal of Computational Physics, Vol. 207, No. 1, 2005, pp. 92-113.
9. Helenbrook, B. T., Atkins, H. L., and Mavriplis, D. J., "Analysis of p-Multigrid for Continuous and Discontinuous Finite Element Discretizations," AIAA Paper 2003-3989, June 2003.
10. Reed, W. H., and Hill, T. R., "Triangular Mesh Methods for the Neutron Transport Equation," Los Alamos National Lab., Technical Rept. LA-UR-73-479, Los Alamos, NM, 1973.
11. Bassi, F., and Rebay, S., "A High-Order Accurate Discontinuous Finite Element Method for the Numerical Solution of the Compressible Navier-Stokes Equations," Journal of Computational Physics, Vol. 131, No. 2, 1997, pp. 267-279.
12. Arnold, D. N., Brezzi, F., Cockburn, B., and Marini, L. D., "Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems," SIAM Journal on Numerical Analysis, Vol. 39, No. 5, 2002, pp. 1749-1779.
13. Brezzi, F., Manzini, M., Marini, D., Pietra, P., and Russo, A., "Discontinuous Finite Elements for Diffusion Problems," Francesco Brioschi (1824-1897) Convegno di Studi Matematici. Incontro di Studio, No. 16, Istituto Lombardo di Scienze e Lettere, 1999, pp. 197-217.
14. Cockburn, B., and Shu, C.-W., "The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems," SIAM Journal on Numerical Analysis, Vol. 35, No. 6, 1998, pp. 2440-2463.
15. Douglas, J., Jr., and Dupont, T., "Interior Penalty Procedures for Elliptic and Parabolic Galerkin Methods," Computing Methods in Applied Sciences, Vol. 58, Lecture Notes in Physics, Springer-Verlag, Berlin, 1976.
16. Bassi, F., Rebay, S., Mariotti, G., Pedinotti, S., and Savini, M., "A High-Order Accurate Discontinuous Finite Element Method for Inviscid and Viscous Turbomachinery Flows," Proceedings of the 2nd European Conference on Turbomachinery, Fluid Dynamics, and Thermodynamics, edited by R. Decuypere and G. Dibelius, Technologisch Inst., Antwerp, Belgium, 1997, pp. 99-108.
17. Atkins, H. L., and Shu, C.-W., "Quadrature-Free Implementation of Discontinuous Galerkin Method for Hyperbolic Equations," AIAA Journal, Vol. 36, No. 5, 1998, pp. 775-782.
18. Hughes, T. J. R., The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, Prentice-Hall, Englewood Cliffs, NJ, 1987, p. 433.
19. Atkins, H. L., and Shu, C.-W., "Analysis of Preconditioning and Relaxation Operators for the Discontinuous Galerkin Method Applied to Diffusion," AIAA Paper 2001-2554, June 2001.