A Preconditioned Iterative Method for Saddlepoint Problems

1992 ◽  
Vol 13 (3) ◽  
pp. 887-904 ◽  
Author(s):  
Torgeir Rusten ◽  
Ragnar Winther
Keyword(s):  
Iterative Method ◽  
Preconditioned Iterative ◽  
Saddlepoint Problems

scholarly journals A sparse preconditioned iterative method for vibration analysis of geometrically mistuned bladed disks

2009 ◽  
Vol 87 (5-6) ◽  
pp. 342-354 ◽  
Author(s):  
Vladislav Ganine ◽  
Mathias Legrand ◽  
Hannah Michalska ◽  
Christophe Pierre
Keyword(s):  
Iterative Method ◽  
Vibration Analysis ◽  
Bladed Disks ◽  
Preconditioned Iterative

scholarly journals A Preconditioned Iterative Approach for Efficient Full Chip Thermal Analysis on Massively Parallel Platforms

Technologies ◽  
2018 ◽  
Vol 7 (1) ◽  
pp. 1
Author(s):  
George Floros ◽  
Konstantis Daloukas ◽  
Nestor Evmorfopoulos ◽  
George Stamoulis
Keyword(s):  
Integrated Circuits ◽  
Iterative Method ◽  
State Of The Art ◽  
Massively Parallel ◽  
Computationally Efficient ◽  
Linear Solvers ◽  
Massively Parallel Architectures ◽  
3D Integrated Circuits ◽  
Preconditioned Iterative ◽  
Formulation Problem

Efficient full-chip thermal simulation is among the most challenging problems facing the EDA industry today, especially for modern 3D integrated circuits, due to the huge linear systems resulting from thermal modeling approaches that require unreasonably long computational times. While the formulation problem, by applying a thermal equivalent circuit, is prevalent and can be easily constructed, the corresponding 3D equations network has an undesirable time-consuming numerical simulation. Direct linear solvers are not capable of handling such huge problems, and iterative methods are the only feasible approach. In this paper, we propose a computationally-efficient iterative method with a parallel preconditioned technique that exploits the resources of massively-parallel architectures such as Graphic Processor Units (GPUs). Experimental results demonstrate that the proposed method achieves a speedup of 2.2× in CPU execution and a 26.93× speedup in GPU execution over the state-of-the-art iterative method.

scholarly journals A Preconditioned Iterative Method for Solving Systems of Nonlinear Equations Having Unknown Multiplicity

Algorithms ◽  
2017 ◽  
Vol 10 (1) ◽  
pp. 17 ◽  
Author(s):  
Fayyaz Ahmad ◽  
Toseef Bhutta ◽  
Umar Shoaib ◽  
Malik Zaka Ullah ◽  
Ali Alshomrani ◽  
...  
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations ◽  
Systems Of Nonlinear Equations ◽  
Preconditioned Iterative

scholarly journals A numerical investigation of multi space reduced basis preconditioners for parametrized elliptic advection-diffusion equations

2017 ◽  
Vol 8 (1) ◽  
pp. 282-297
Author(s):  
Niccolò Dal Santo ◽  
Simone Deparis ◽  
Andrea Manzoni
Keyword(s):  
Iterative Method ◽  
Numerical Investigation ◽  
Reduced Basis ◽  
Fine Grid ◽  
Current State ◽  
Advection Diffusion ◽  
Numerical Performance ◽  
Preconditioned Iterative ◽  
The Impact

AbstractWe analyze the numerical performance of a preconditioning technique recently proposed in [1] for the efficient solution of parametrized linear systems arising from the finite element (FE) discretization of parameterdependent elliptic partial differential equations (PDEs). In order to exploit the parametric dependence of the PDE, the proposed preconditioner takes advantage of the reduced basis (RB) method within the preconditioned iterative solver employed to solve the linear system, and combines a RB solver, playing the role of coarse component, with a traditional fine grid (such as Additive Schwarz or block Jacobi) preconditioner. A sequence of RB spaces is required to handle the approximation of the error-residual equation at each step of the iterative method at hand, whence the name of Multi Space Reduced Basis (MSRB) method. In this paper, a numerical investigation of the proposed technique is carried on in the case of a Richardson iterative method, and then extended to the flexible GMRES method, in order to solve parameterized advection-diffusion problems. Particular attention is payed to the impact of anisotropic diffusion coefficients and (possibly dominant) transport terms on the proposed preconditioner, by carrying out detailed comparisons with the current state of the art algebraic multigrid preconditioners.

scholarly journals Erratum: Ahmad, F., et al. A Preconditioned Iterative Method for Solving Systems of Nonlinear Equations Having Unknown Multiplicity. Algorithms 2017, 10, 17

Algorithms ◽  
2017 ◽  
Vol 10 (2) ◽  
pp. 55
Author(s):  
Fayyaz Ahmad ◽  
Toseef Bhutta ◽  
Umar Shoaib ◽  
Malik Ullah ◽  
Ali Alshomrani ◽  
...  
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations ◽  
Systems Of Nonlinear Equations ◽  
Preconditioned Iterative
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