Optimization of parallel multilevel-Newton algorithms on workstation clusters

Gräb, Robert; Günther, Michael; Wever, Utz; Zheng, Qinghua

doi:10.1007/bfb0024689

Cited by 5 publications

(3 citation statements)

References 4 publications

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“…This relaxation within the Newton scheme corresponds to a monolithic time-stepping scheme although it features parallel evaluations at the Gauß points at the level of the nonlinear solver. The two nested new Newton loops (inner and outer) are a special case of a parallel multilevel Newton scheme as they are used for example in circuit simulation [23]. Let us state the equivalence for the case in which only one inner iteration of a simplified Newton-Raphson scheme is carried out.…”

Section: Monolithic Hmmmentioning

confidence: 99%

Waveform relaxation for the computational homogenization of multiscale magnetoquasistatic problems

Niyonzima

Geuzaine

Schps

2016

Journal of Computational Physics

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This paper proposes the application of the waveform relaxation method to the homogenization of multiscale magnetoquasistatic problems. In the monolithic heterogeneous multiscale method, the nonlinear macroscale problem is solved using the Newton-Raphson scheme. The resolution of many mesoscale problems per Gauß point allows to compute the homogenized constitutive law and its derivative by finite differences. In the proposed approach, the macroscale problem and the mesoscale problems are weakly coupled and solved separately using the finite element method on time intervals for several waveform relaxation iterations. The exchange of information between both problems is still carried out using the heterogeneous multiscale method. However, the partial derivatives can now be evaluated exactly by solving only one mesoscale problem per Gauß point.

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Section: Monolithic Hmmmentioning

confidence: 99%

Waveform relaxation for the computational homogenization of multiscale magnetoquasistatic problems

Niyonzima

Geuzaine

Schps

2016

Journal of Computational Physics

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“…• A performance model for parallel MLN is described in [88]. It can be used for dynamically adopting numerical parameters of the MLN method -like the maximal number of inner iterations -to the computer-and network-configuration and its actual load.…”

Section: M) (151)mentioning

confidence: 99%

Modelling and Discretization of Circuit Problems

Günther

Feldmann

Maten

2005

Handbook of Numerical Analysis

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“…To apply multigrid methods in global optimization is not a new idea [5,6]. A survey on this topic can be referred to [3].…”

Section: Introductionmentioning

confidence: 99%

A mixed strategy of combining evolutionary algorithms with multigrid methods

Kang

2009

International Journal of Computer Mathematics

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Multigrid methods have been proven to be an efficient approach in accelerating the convergence rate of numerical algorithms for solving partial differential equations. This paper investigates whether multigrid methods are helpful to accelerate the convergence rate of evolutionary algorithms for solving global optimization problems. A novel multigrid evolutionary algorithm is proposed and its convergence is proven. The algorithm is tested on a set of 13 well-known benchmark functions. Experiment results demonstrate that multigrid methods can accelerate the convergence rate of evolutionary algorithms and improve their performance.

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Optimization of parallel multilevel-Newton algorithms on workstation clusters

Cited by 5 publications

References 4 publications

Waveform relaxation for the computational homogenization of multiscale magnetoquasistatic problems

Waveform relaxation for the computational homogenization of multiscale magnetoquasistatic problems

Modelling and Discretization of Circuit Problems

A mixed strategy of combining evolutionary algorithms with multigrid methods

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