Abstract
We present a technique which solves systems of nonlinear equations. The technique couples two solution methods together, multigrid and Newton-Krylov, producing in a method which efficiently uses the strengths of each technique. A form of distributed relaxation multigrid is used to solve systems of scalar linear equations which are then combined to provide efficient preconditioners for the Newton-Krylov method. This new method can be viewed as an alternative to other nonlinear multigrid solvers. Results will be presented for a steady state fluid flow and transient heat conduction.
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References
Y. Saad and M.H. Schultz. GMRES: A Generalized Minimal Residual Algorithm for Solving Non-Symetric Linear Systems. SIAM Journal of Scientific and Statistical Computing, 7: 856, 1986.
P. N. Brown and Y. Saad. Hybrid Krylov Methods for Non-Linear Systems of Equations. SIAM J. Sci. Stat. Comput., 11: 450–481, 1990.
D.A. Knoll, W.J. Rider, and G.L. Olson. An Efficient Nonlinear Solution Method for Non-Equilibrium Radiation Diffusion. Journal of Quantitative Spectroscopy f4 Radiative Transfer, 63: 15–29, 1999.
D.A. Knoll, G. Lapenta, and J.U. Brackbill. A Multilevel Iterative Field Solver for Implicit, Kinetic, Plasma Simulation. Journal of Computational Physics, vol. 149:pages 377–388, 1999.
D.A. Knoll and V.A. Mousseau. On Newton-Krylov-Multigrid Methods for the Incompressible Navier-Stokes Equations. In preperation for Journal of Computational Physics,1999. LA-UR-99-????
G. de Vahl Davis. Natural Convection of Air in a Square Cavity: A Benchmark Numerical Solution. International Journal of Numerical Methods in Fluids, 3: 249–264, 1983.
V.A. Mousseau, D.A. Knoll, and W.J. Rider. Physics-Based Preconditioning and the Newton-Krylov Method for Non-Equilibrium Radiation Diffusion. Submitted to Journal of Computational Physics,1999. LA-UR-99–4230.
D. A. Knoll and W. J. Rider. A multigrid preconditioned Newton-Krylov method. SIAM Journal of Scientific Computing,accepted. LA-UR-97–4013.
W.J. Rider, D.A. Knoll, and G.L. Olson. A Multigrid Newton-Krylov Method for Multidimensional Equilibrium Radiation Diffusion. Journal of Computational Physics, 152: 164–191, 1999.
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© 2000 Springer-Verlag Berlin Heidelberg
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Mousseau, V.A., Knoll, D.A., Rider, W.J. (2000). A Multigrid Newton-Krylov Solver for Non-linear Systems. In: Dick, E., Riemslagh, K., Vierendeels, J. (eds) Multigrid Methods VI. Lecture Notes in Computational Science and Engineering, vol 14. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58312-4_27
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DOI: https://doi.org/10.1007/978-3-642-58312-4_27
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-67157-2
Online ISBN: 978-3-642-58312-4
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