An algebraic multigrid method for solving very large electromagnetic systems

Mertens, R; Gersem, Herbert De; Belmans, Ronnie; Hameyer, Kay; Lahaye, Domenico; Vandewalle, Stefan; Roose, Dirk

doi:10.1109/20.717782

Cited by 21 publications

(10 citation statements)

References 5 publications

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“…A considerably faster solution strategy compared to conventional ones is established by using a nested multigrid solver [13], [14]. Thereby, a hierarchy of discretizations represented by…”

Section: Multigrid Solvermentioning

confidence: 99%

Influence of higher harmonics in the end region magnetic field on eddy currents in the stator clamping system of hydro generators

Schmidt

Traxler-Samek

Schwery

2005

IEEE International Conference on Electric Machines and Drives, 2005.

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The reliability of the loss calculation is a very important issue during the electrical design phase of hydro generators. Therefore, the accurate calculation of eddy currents in the stator clamping system is a matter of particular interest with initial design and design optimization. Due to the nonlinear magnetic behaviour of the clamping plate, the eddy current losses in these regions can reach high values and produce local thermal hot-spots. The calculation results obtained from 3D time-harmonic and 3D nonlinear transient finite element analyses of a 450 MVA hydro generator are compared with regard to local and total eddy current losses. Thereby, special attention is given to the influence of higher harmonics in the excitating end region magnetic field.

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“…A considerably faster solution strategy compared to conventional ones is established by using a nested multigrid solver [13], [14]. Thereby, a hierarchy of discretizations represented by…”

Section: Multigrid Solvermentioning

confidence: 99%

Influence of higher harmonics in the end region magnetic field on eddy currents in the stator clamping system of hydro generators

Schmidt

Traxler-Samek

Schwery

2005

IEEE International Conference on Electric Machines and Drives, 2005.

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“…MG approaches entered the field of quasistatic magnetic simulation a few years ago [2], [3]. Nowadays, research in the field is focused toward the development and application of algebraic MG schemes [4]- [6] and MG for 3-D curl-curl operator [7], [8]. Geometrical MG is fully mature to solve the Poisson equation arising from 2-D and 3-D nodal formulations for electro-and magnetostatics.…”

Section: A Multigrid In Electromagnetic Simulationmentioning

confidence: 99%

Full multigrid for magnetostatics using unstructured and non-nested meshes

Gersem

Hameyer²

2001

IEEE Trans. Magn.

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Adaptive mesh refinement and mesh enhancing techniques, commonly applied in electromagnetic finite element simulation, give raise to a hierarchy of nonnested unstructured grids. The application of geometrical multigrid is not straightforward. The prolongation operator is adapted to the particular properties of the mesh refinement. Anti-symmetric boundary conditions and nonlinear material characteristics are incorporated. The numerical experiment performed on the model of a synchronous machine shows optimal convergence for the proposed multigrid scheme whereas the convergence of classical nested multigrid becomes troublesome.Index Terms-Adaptive mesh refinement, finite element methods, iterative solvers, multigrid methods.

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“…This paper deals with solving (3) efficiently. Motivated by previous experience [3], this will be performed by using an algebraic multigrid solver. Algebraic multigrid solvers were orginally developed to treat symmetric positive definite problems.…”

Section: Time-harmonic Magnetic Formulationsmentioning

confidence: 99%

Algebraic multigrid for complex symmetric systems

et al. 2000

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The two dimensional quasistatic time-harmonic Maxwell formulations yield complex Helmholtz equations. Multigrid techniques are known to be efficient for solving the discretization of real valued diffusion equations. In this paper these multigrid techniques are extended to handle the complex equation. The implementation of geometric multigrid techniques can be cumbersome for practical engineering problems. Algebraic multigrid (AMG) techniques on the other hand automatically construct a hierarchy of coarser discretizations without user intervention given the matrix on the finest level. In the linear calculation of an induction motor the use of AMG as precondioner for a Krylov subspace solver resulted in a six-fold reduction of the CPU time compared to an optimized incomplete LU factorization and in a twenty-fold reduction compared to symmetric successive overrelaxation.

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An algebraic multigrid method for solving very large electromagnetic systems

Cited by 21 publications

References 5 publications

Influence of higher harmonics in the end region magnetic field on eddy currents in the stator clamping system of hydro generators

Influence of higher harmonics in the end region magnetic field on eddy currents in the stator clamping system of hydro generators

Full multigrid for magnetostatics using unstructured and non-nested meshes

Algebraic multigrid for complex symmetric systems

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