Subspace Projection Extrapolation Scheme for Transient Field Simulations

Clemens, Markus; Wilke, Markus; Schuhmann, Rolf; Weiland, Thomas

doi:10.1109/tmag.2004.824583

Cited by 30 publications

(24 citation statements)

References 10 publications

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“…the finite elements FE, finite difference FD, or the coupled finite element boundary elements BEM-FEM) commonly produces a large scale systems of nonlinear ordinary differential equations or differential algebraic equations [15]. By applying one of the time integration schemes, the values of the EM field variables can be found and the corresponding magnetic forces and torques can be calculated.…”

Section: Solving the Electromagnetic Field Equationsmentioning

confidence: 99%

Model-Order Reduction of Moving Nonlinear Electromagnetic Devices

et al. 2008

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This dissertation delivers a contribution to the field of order reduction of large-scale nonlinear models of electromagnetic devices. In particular, it enables applying model order reduction techniques to an important class of electromagnetic devices that contain moving components and materials with nonlinear magnetic properties. Such devices include among others rotating electrical machines, electromagnetic valves, electromagnetic solenoids, and electromechanical relays.The presented methods exploits the trajectory piecewise linear (TPWL) approach in approximating the nonlinear dependency of materials properties on the applied magnetic field. Additionally, the model nonlinearity that is caused by the movement of the device components is handled using a novel approach that updates the electromagnetic (EM) field model permanently according to the new components positions.The order of the large-scale electromagnetic field model is reduced by approximating the original electromagnetic field distribution by a linear combination of few virtual field distributions that are found using the proper orthogonal decomposition (POD) approach.The challenge of selecting the number and the position of the linearization points in the TPWL model is tackled using a new approach that considers the change in the magnetic properties of the device materials among all the simulated state-vectors.The new presented methods are extended to enable generating parametric reduced order models of moving nonlinear EM devices. Such models enable a fast and accurate prediction of the behavior of the EM device and its variations that result from changing the values of its design parameters. Additionally, several algorithms for generating an optimal reduction subspace of the parametric model are presented and compared.Finally, an approach for overcoming the challenge of generating reduced order models of EM devices while considering the strong influence of their power electronics driving circuits is introduced and applied to the example of a rotating electrical machine coupled to a power electronics driving circuit.The new methods presented in this work are validated by applying them on the examples of three industrial devices. An electrical transformer, an electromagnetic valve, and a rotating electrical machine. DEDICATIONTo my parents, my wife, and my daughter. ACKNOWLEDGMENTS

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Section: Solving the Electromagnetic Field Equationsmentioning

confidence: 99%

Model-Order Reduction of Moving Nonlinear Electromagnetic Devices

et al. 2008

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“…The truncated models were reduced in height, and the injection rates were reduced proportionally. All versions of model C were tested with steady-state flow rates (tests 3-5) and with randomly fluctuating rates (tests [6][7][8]. In case of steady-state rates, the sum of the injection rates was taken equal to the sum of the production rates, whereas in the case of random rates the averages of injection and production rates where equal.…”

Section: Resultsmentioning

confidence: 99%

Accelerating iterative solution methods using reduced‐order models as solution predictors

Markovinovic

Jansen

2006

Numerical Meth Engineering

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SUMMARYWe propose the use of reduced-order models to accelerate the solution of systems of equations using iterative solvers in time stepping schemes for large-scale numerical simulation. The acceleration is achieved by determining an improved initial guess for the iterative process based on information in the solution vectors from previous time steps. The algorithm basically consists of two projection steps: (1) projecting the governing equations onto a subspace spanned by a low number of global empirical basis functions extracted from previous time step solutions, and (2) solving the governing equations in this reduced space and projecting the solution back on the original, high dimensional one. We applied the algorithm to numerical models for simulation of two-phase flow through heterogeneous porous media. In particular we considered implicit-pressure explicit-saturation (IMPES) schemes and investigated the scope to accelerate the iterative solution of the pressure equation, which is by far the most time-consuming part of any IMPES scheme. We achieved a substantial reduction in the number of iterations and an associated acceleration of the solution. Our largest test problem involved 93 500 variables, in which case we obtained a maximum reduction in computing time of 67%. The method is particularly attractive for problems with time-varying parameters or source terms.

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“…In the numerical tests, this procedure will be denoted as 'restart algorithm'. Finally, the first presented iterative method combines the recurrence formulae (8) and possibly the convergence acceleration method (10). In the application, it will be referred as 'proposed method'.…”

Section: Convergence Accelerationmentioning

confidence: 99%

“…One remarks that the recurrence formulae (19) are rather similar to formula (8) and to the iterative process of Section 2.1, except for the Lagrange multiplier and the pseudo-penalization that had been introduced in [10] to stabilize the result of the perturbation process. We no longer discuss this algorithm that is only the linear version of the one presented in [10].…”

Section: A Variant Based On Homotopy and Perturbationmentioning

confidence: 99%

A solver combining reduced basis and convergence acceleration with applications to non‐linear elasticity

Cadou

Potier‐Ferry²

2009

Numer Methods Biomed Eng

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SUMMARYAn iterative solver is proposed to solve the family of linear equations arising from the numerical computation of non-linear problems. This solver relies on two quantities coming from previous steps of the computations: the preconditioning matrix is a matrix that has been factorized at an earlier step and previously computed vectors yield a reduced basis. The principle is to define an increment in two sub-steps. In the first sub-step, only the projection of the unknown on a reduced subspace is incremented and the projection of the equation on the reduced subspace is satisfied exactly. In the second sub-step, the full equation is solved approximately with the help of the preconditioner. Last, the convergence of the sequences is accelerated by a well-known method, the modified minimal polynomial extrapolation. This algorithm assessed by classical benchmarks coming from shell buckling analysis. Finally, its insertion in path following techniques is discussed. This leads to non-linear solvers with few matrix factorizations and few iterations.

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Subspace Projection Extrapolation Scheme for Transient Field Simulations

Cited by 30 publications

References 10 publications

Model-Order Reduction of Moving Nonlinear Electromagnetic Devices

Model-Order Reduction of Moving Nonlinear Electromagnetic Devices

Accelerating iterative solution methods using reduced‐order models as solution predictors

A solver combining reduced basis and convergence acceleration with applications to non‐linear elasticity

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