scholarly journals Fast solvers of generalized airfoil equation of index 1

2001 ◽  
pp. 498-516
Author(s):  
Gennadi Vainikko
Keyword(s):  
Fast Solvers

scholarly journals A comparison of the performance of depth-integrated ice-dynamics solvers

2021 ◽  
Author(s):  
Alexander Robinson ◽  
Daniel Goldberg ◽  
William H. Lipscomb
Keyword(s):  
Numerical Stability ◽  
Ice Sheet ◽  
Model Performance ◽  
Greenland Ice Sheet ◽  
Grid Resolution ◽  
Ice Dynamics ◽  
Fast Solvers ◽  
Ice Flow ◽  
Hybrid Solver ◽  
Constant Viscosity

Abstract. In the last decade, the number of ice-sheet models has increased substantially, in line with the growth of the glaciological community. These models use solvers based on different approximations of ice dynamics. In particular, several depth-integrated dynamics approximations have emerged as fast solvers capable of resolving the relevant physics of ice sheets at the continen- tal scale. However, the numerical stability of these schemes has not been studied systematically to evaluate their effectiveness in practice. Here we focus on three such solvers, the so-called Hybrid, L1L2-SIA and DIVA solvers, as well as the well-known SIA and SSA solvers as boundary cases. We investigate the numerical stability of these solvers as a function of grid resolution and the state of the ice sheet. Under simplified conditions with constant viscosity, the maximum stable timestep of the Hybrid solver, like the SIA solver, has a quadratic dependence on grid resolution. In contrast, the DIVA solver has a maximum timestep that is independent of resolution, like the SSA solver. Analysis indicates that the L1L2-SIA solver should behave similarly, but in practice, the complexity of its implementation can make it difficult to maintain stability. In realistic simulations of the Greenland ice sheet with a non-linear rheology, the DIVA and SSA solvers maintain superior numerical stability, while the SIA, Hybrid and L1L2-SIA solvers show markedly poorer performance. At a grid resolution of ∆x = 4 km, the DIVA solver runs approximately 15 times faster than the Hybrid and L1L2-SIA solvers. Our analysis shows that as resolution increases, the ice-dynamics solver can act as a bottleneck to model performance. The DIVA solver emerges as a clear outlier in terms of both model performance and its representation of the ice-flow physics itself.

Fast solvers for discrete systems

2015 ◽  
pp. 322-355
Author(s):  
Zhongying Chen ◽  
Charles A. Micchelli ◽  
Yuesheng Xu
Keyword(s):  
Discrete Systems ◽  
Fast Solvers

PAM-OPT™/PAM-SOLID™: Optimization of Transport Vehicle Crash and Safety Design and Forming Processes

1998 ◽  
Author(s):  
E. Haug ◽  
P. Guyon
Keyword(s):  
Sheet Metal Forming ◽  
Process Simulation ◽  
Metal Forming ◽  
Paper Briefly ◽  
Fast Solvers ◽  
Vehicle Crash ◽  
Safety Design ◽  
Transport Vehicle ◽  
Flow Charts ◽  
Vehicle Crashworthiness

Abstract Dynamic simulation solver codes are now extensively used by industry for the design verification of vehicle crashworthiness and for the process simulation of sheet metal forming. The logical next step is to use these by now proven codes for the optimization of the vehicle crash design and of metal forming processes. A step towards this goal has been taken by PSI, and an optimization code, PAM-OPT™, has been written for calling dynamic FE codes of the PAM-SOLID™ family in design and process optimization loops. The code interacts with the user via input, signalling and output files and it calls an interface that interacts with the FE solvers. The paper briefly outlines the properties and various flow charts of the optimizer, depending on single or multiple solvers used in the loop, single or parallel calls and fast solvers. Then the paper reports various applications of PAM-OPT™ in conjunction with the PAM-SFE™, PAM-CRASH™, PAM-SAFE™ and PAM-STAMP™ solvers. An outlook on how to replace the user-written interface with a general keyword-driven interface concludes the paper.

scholarly journals Fast solvers for finite difference approximations for the stokes and navier-stokes equations

1996 ◽  
Vol 38 (2) ◽  
pp. 274-290 ◽  
Author(s):  
Dongho Shin ◽  
John C. Strikwerda
Keyword(s):  
Finite Difference ◽  
Stokes Equations ◽  
Linear Equations ◽  
Computational Effort ◽  
Navier Stokes ◽  
Fast Solvers ◽  
Navier Stokes Equations ◽  
Finite Difference Approximations ◽  
Grid Points ◽  
First Time

AbstractWe consider several methods for solving the linear equations arising from finite difference discretizations of the Stokes equations. The two best methods, one presented here for the first time, apparently, and a second, presented by Bramble and Pasciak, are shown to have computational effort that grows slowly with the number of grid points. The methods work with second-order accurate discretizations. Computational results are shown for both the Stokes equations and incompressible Navier-Stokes equations at low Reynolds number.

scholarly journals Multigrid methods: development of fast solvers

1983 ◽  
Vol 13 (3-4) ◽  
pp. 311-326 ◽  
Author(s):  
P.W. Hemker ◽  
R. Kettler ◽  
P. Wesseling ◽  
P.M. de Zeeuw
Keyword(s):  
Multigrid Methods ◽  
Fast Solvers ◽  
Methods Development

scholarly journals Fast solvers for optimal control problems from pattern formation

2016 ◽  
Vol 304 ◽  
pp. 27-45 ◽  
Author(s):  
Martin Stoll ◽  
John W. Pearson ◽  
Philip K. Maini
Keyword(s):  
Optimal Control ◽  
Pattern Formation ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Fast Solvers
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