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Enabling fast convergence of the iterated penalty Picard iteration with O(1) penalty parameter for incompressible Navier-Stokes via Anderson acceleration [article]

Leo G. Rebholz and Duygu Vargun and Mengying Xiao
2021 arXiv   pre-print
This paper considers an enhancement of the classical iterated penalty Picard (IPP) method for the incompressible Navier-Stokes equations, where we restrict our attention to O(1) penalty parameter, and  ...  Results for several challenging numerical tests are given and show that IPP with penalty parameter 1 and enhanced with AA is a very effective solver.  ...  The Anderson accelerated iterated penalty Picard scheme and its convergence Now we present the Anderson accelerated iterated penalty Picard (AAIPP) algorithm and its convergence properties.  ... 
arXiv:2105.09339v1 fatcat:jwvuhz3lzvhtregp3ku66a2qea

Trends in Algorithms for Nonuniform Applications on Hierarchical Distributed Architectures [chapter]

David E. Keyes
2000 Computational Aerosciences in the 21st Century  
However, disregard for the differential costs of accessing different locations in memory (the "flat memory" model) can put unnecessary amounts of synchronization and data motion on the critical path of  ...  Plenty of examples of architecturally motivated algorithmic adaptations can be given today; we illustrate herein with examples from recent aerodynamics simulations.  ...  He is grateful to Manny Salas and Kyle Anderson, organizers of the "Computational Aerosciences for the 21st Century" workshop for the unnatural impetus to contemplate a computational world 10-20 years  ... 
doi:10.1007/978-94-010-0948-5_6 fatcat:7y2rsfl5frdwhemru5agrzj4ge

The mathematics of finite elements and applications

1989 International Journal of Engineering Science  
This paper describes theory and methods for developing a posteriori error estimates and an adaptive strategy for hp-finite element approximations of the incompressible Navier-Stokes equations.  ...  These techniques are applied to representative transient and steady state problems of incompressible viscous flow. o.. -•des O A~t S, daOr S'!  ...  D SILVESTER and A J WATHEN Efficient preconditioners for incompressible flow Having an efficient Stokes solver is an important requisite of many Navier-Stokes solution algorithms.  ... 
doi:10.1016/0020-7225(89)90012-8 fatcat:z6hknn325re4tbssbqqzmcketa

Singular Perturbations and Time Scales in Guidance and Control of Aerospace Systems: A Survey

D. Subbaram Naidu, Anthony J. Calise
2001 Journal of Guidance Control and Dynamics  
changes very rapidly from zero at the boundary to the value as given by the solution of the Navier-Stokes equation.  ...  The convergence is uniform in 0 <1 <7 for x(t, €), and in any interval 0<?, <1 <7 for z(t, €), and the convergence of z(t, €) will usually be nonuniform at r = 0.  ... 
doi:10.2514/2.4830 fatcat:qdfw6bvvxrawbmxoelk6ioc5uq

Singular perturbations and time scales in guidance and control of aerospace systems - A survey

D. S. Naidu, Anthony J. Calise
2001 Journal of Guidance Control and Dynamics  
changes very rapidly from zero at the boundary to the value as given by the solution of the Navier-Stokes equation.  ...  The convergence is uniform in 0 <1 <7 for x(t, €), and in any interval 0<?, <1 <7 for z(t, €), and the convergence of z(t, €) will usually be nonuniform at r = 0.  ... 
doi:10.2514/3.22603 fatcat:v76ixl3625hg5n7jeu3rzceqwq

Numerical simulation of the flow in model skeletal muscle ventricles

F. Iudicello, F.S. Henry, M.W. Collins, A. Shortland, J.C. Jarvis, R.A. Black, S. Salmons
Proceedings of Computers in Cardiology Conference  
Acknowledgements This work has been supported by grants from the British Heart Foundation. ACKNOWLEDGMENT This work is funded by a grant from the British Heart Foundation.  ...  Lin (1985) has proposed the use of three free parameters to accelerate the convergence of Stone's method.  ...  The convergence can be accelerated by using multiple grid iteration (Forsey and Billing, 1988) .  ... 
doi:10.1109/cic.1993.378425 fatcat:evkssjzbtzgijlzytstp2iiorq

Calculation of the A term of magnetic circular dichroism based on time dependent-density functional theory I. Formulation and implementation

Michael Seth, Tom Ziegler, Arup Banerjee, Jochen Autschbach, Stan J. A. van Gisbergen, Evert J. Baerends
2004 Journal of Chemical Physics  
The results confirmed ͑ that the children demonstrated-in both L1 and L2-better skills in quiet than in noise and ͑2͒ that the childrens fast-mapping skills were positively correlated with their pre-existing  ...  In this present study we examine the effect of noise on fast-mapping skills in L1 ͑Hmong͒ and L2 ͑English͒.  ...  ., Dept. of Otolaryngol., Univ. of Michigan, Ann Arbor, MI 48109-0506, bpfingst@umich.edu͒, and Li Xu ͑Ohio Univ., Athens, OH 45701͒ Head-related transfer functions via the fast multipole accelerated  ... 
doi:10.1063/1.1747828 pmid:15268124 fatcat:hwyfald5a5f4njmw5h7p6vjhnu

Computational and experimental analysis of structure development in two-phase polymer systems [article]

BJ Keestra, Meijer, HEH (Han), Lemstra, PJ (Piet), Anderson, PD (Patrick)
2004
Superscript n denotes time t and n + 1 denotes t + t. A Picard iteration is used to deal with the nonlinearity in c term (i = 1 . . .  ...  Compared to the Navier-Stokes equations, in equation (6.7) only one extra capillary term ρµ∇c appears reflecting the interfacial tension via µ this modification accounts for hydrodynamic interactions  ...  Examples are given in figure B.1. For viscous incompressible Newtonian fluids (Re 1), the Navier-Stokes equation reduces to the Stokes equation: with p the pressure and v the velocity.  ... 
doi:10.6100/ir571758 fatcat:7qorxtpl6bcb7g2ekncxnx4uou