Abstract
We propose a new two-level nonlinear additive Schwarz preconditioned inexact Newton algorithm (ASPIN). The two-level nonlinear preconditioner combines a local nonlinear additive Schwarz preconditioner and a global linear coarse preconditioner. Our parallel numerical results based on a lid-driven cavity incompressible flow problem show that the new two-level ASPIN is nearly scalable with respect to the number of processors if the coarse mesh size is fine enough.
The work was partially supported by the Department of Energy, DE-FC02-01ER25479, and by the National Science Foundation, CCR-0219190, ACI-0072089 and CCF-0305666.
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References
Balay, S., Buschelman, K., Gropp, W.D., Kaushik, D., Knepley, M., Mcinnes, L.C., Smith, B.F., Zhang, H.: Portable, Extensible, Toolkit for Scientific Computation(PETSc) home page (2004), http://www.mcs.anl.gov/petsc
Cai, X.-C., Keyes, D.E.: Nonlinearly preconditioned inexact Newton algorithms. SIAM J. Sci. Comput. 24, 183–200 (2002)
Cai, X.-C., Keyes, D.E., Marcinkowski, L.: Nonlinear additive Schwarz preconditioners and applications in computational fluid dynamics. Int. J. Numer. Meth. Fluids 40, 1463–1470 (2002)
Dennis, J., Schnabel, R.: Numerical Methods for Unconstrained Optimization and Nonlinear Equations. SIAM, Philadelphia (1996)
Franca, L.P., Frey, S.L.: Stabilized finite element method: II. The incompressible Navier-Stokes equation. Comput. Methods Appl. Mech. Engrg. 99, 209–233 (1992)
Hwang, F.-N., Cai, X.-C.: A parallel nonlinear additive Schwarz preconditioned inexact Newton algorithm for incompressible Navier-Stokes equations. J. Comput. Phys (2004) (to appear)
Marcinkowski, L., Cai, X.-C.: Parallel performance of some two-level ASPIN algorithms. In: Kornhuber, R., Hoppe, R.H.W., Keyes, D.E., Periaux, J., Pironneau, O., Xu, J. (eds.) Lecture Notes in Computational Science and Engineering, pp. 639–646. Springer, Heidelberg
Shadid, J.N., Tuminaro, R.S., Walker, H.F.: An inexact Newton method for fully coupled solution of the Navier-Stokes equations with heat and mass transport. J. Comput. Phys. 137, 155–185 (1997)
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© 2006 Springer-Verlag Berlin Heidelberg
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Hwang, FN., Cai, XC. (2006). A Combined Linear and Nonlinear Preconditioning Technique for Incompressible Navier-Stokes Equations. In: Dongarra, J., Madsen, K., Waśniewski, J. (eds) Applied Parallel Computing. State of the Art in Scientific Computing. PARA 2004. Lecture Notes in Computer Science, vol 3732. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11558958_37
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DOI: https://doi.org/10.1007/11558958_37
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-29067-4
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