Efficient solvers for nonlinear time-periodic eddy current problems

Bachinger, Florian; Langer, Ulrich; Schöberl, Joachim

doi:10.1007/s00791-006-0023-z

Cited by 36 publications

(32 citation statements)

References 22 publications

(34 reference statements)

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“…This method is called the multiharmonic or harmonic balance finite element method. It has been shown in [4] that the convergence of the Fourier approximation is generally of order N −1 (where N is the number of Fourier terms considered in the truncation) but can be much faster for simple harmonic excitations [5] [6].…”

Section: Introductionmentioning

confidence: 99%

Automatic derivation of multiharmonic formulations for nonlinear electromechanical problems with time dependent mesh deformation

Halbach¹,

Geuzaine²

2016

2016 17th International Conference on Thermal, Mechanical and Multi-Physics Simulation and Experiments in Microelectronics and

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Section: Introductionmentioning

confidence: 99%

Automatic derivation of multiharmonic formulations for nonlinear electromechanical problems with time dependent mesh deformation

Halbach¹,

Geuzaine²

2016

2016 17th International Conference on Thermal, Mechanical and Multi-Physics Simulation and Experiments in Microelectronics and

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“…Time-periodic problems appear typically in special physical situations, for example, in eddy current simulations [1], or when periodic forcing is used, like for periodically forced reactors, see [28,30]. The numerical simulation of time-periodic problems is a special area of research, since the time-periodicity modifies the problem structure and solution methods significantly; see, for example, [4,25,27].…”

Section: Introductionmentioning

confidence: 99%

Analysis of Two Parareal Algorithms for Time-Periodic Problems

Gander¹,

Jiang²,

Song³

et al. 2013

SIAM J. Sci. Comput.

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Abstract. The parareal algorithm, which permits us to solve evolution problems in a time parallel fashion, has created a lot of attention over the past decade. The algorithm has its roots in the multiple shooting method for boundary value problems, which in the parareal algorithm is applied to initial value problems, with a particular coarse approximation of the Jacobian matrix. It is therefore of interest to formulate parareal-type algorithms for time-periodic problems, which also couple the end of the time interval with the beginning, and to analyze their performance in this context. We present and analyze two parareal algorithms for time-periodic problems: one with a periodic coarse problem and one with a nonperiodic coarse problem. An interesting advantage of the algorithm with the nonperiodic coarse problem is that no time-periodic problems need to be solved during the iteration, since on the time subdomains, the problems are not time-periodic either. We prove for both linear and nonlinear problems convergence of the new algorithms, with linear bounds on the convergence. We also extend these results to evolution partial differential equations using Fourier techniques. We illustrate our analysis with numerical experiments, both for model problems and the realistic application of a nonlinear cooled reverse-flow reactor system of partial differential equations.

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“…On the other hand the size of the nonlinear system is multiplied by N h compared to the time-domain approach. (Note that the convergence of the Fourier approximation is generally of order N −1 h [22], but can be much faster for simple excitations [17,23]). …”

Section: Multiharmonic Finite Element Formulationmentioning

confidence: 99%

Steady-state, nonlinear analysis of large arrays of electrically actuated micromembranes vibrating in a fluid

Halbach

Geuzaine

2017

Engineering with Computers

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This paper describes a robust and efficient method to obtain the steady-state, nonlinear behaviour of large arrays of electrically actuated micromembranes vibrating in a fluid. The nonlinear electromechanical behavior and the multiple vibration harmonics it creates are fully taken into account thanks to a multiharmonic finite element formulation, generated automatically using symbolic calculation. A domain decomposition method allows to consider large arrays of micromembranes by efficiently distributing the computational cost on parallel computers. Two-and three-dimensional examples highlight the main properties of the proposed method.

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Efficient solvers for nonlinear time-periodic eddy current problems

Cited by 36 publications

References 22 publications

Automatic derivation of multiharmonic formulations for nonlinear electromechanical problems with time dependent mesh deformation

Automatic derivation of multiharmonic formulations for nonlinear electromechanical problems with time dependent mesh deformation

Analysis of Two Parareal Algorithms for Time-Periodic Problems

Steady-state, nonlinear analysis of large arrays of electrically actuated micromembranes vibrating in a fluid

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