332,975 research outputs found
FINITE ELEMENT METHOD FOR NONLINEAR EDDY CURRENT PROBLEMS IN POWER TRANSFORMERS
An efficient finite element method to take account of the nonlinearity of the magnetic materials
when analyzing three dimensional eddy current problems is presented in this paper. The problem is
formulated in terms of vector and scalar potentials approximated by edge and node based finite element
basis functions. The application of Galerkin techniques leads to a large, nonlinear system of ordinary
differential equations in the time domain.
The excitations are assumed to be time-periodic and the steady state periodic solution is of
interest only. This is represented in the frequency domain as a Fourier series for each finite element
degree of freedom and a finite number of harmonics is to be determined, i.e. a harmonic balance method
is applied. Due to the nonlinearity, all harmonics are coupled to each other, so the size of the equation
system is the number of harmonics times the number of degrees of freedom.
The harmonics would be decoupled if the problem were linear, therefore, a special nonlinear
iteration technique, the fixed-point method is used to linearize the equations by selecting a timeindependent
permeability distribution, the so called fixed-point permeability in each nonlinear iteration
step. This leads to uncoupled harmonics within these steps resulting in two advantages. One is that each
harmonic is obtained by solving a system of algebraic equations with only as many unknowns as there
are finite element degrees of freedom. A second benefit is that these systems are independent of each
other and can be solved in parallel. The appropriate selection of the fixed point permeability accelerates
the convergence of the nonlinear iteration.
The method is applied to the analysis of a large power transformer. The solution of the
electromagnetic field allows the computation of various losses like eddy current losses in the massive
conducting parts (tank, clamping plates, tie bars, etc.) as well as the specific losses in the laminated parts
(core, tank shielding, etc.). The effect of the presence of higher harmonics on these losses is
investigated
FINITE ELEMENT METHOD FOR NONLINEAR EDDY CURRENT PROBLEMS IN POWER TRANSFORMERS
An efficient finite element method to take account of the nonlinearity of the magnetic materials
when analyzing three dimensional eddy current problems is presented in this paper. The problem is
formulated in terms of vector and scalar potentials approximated by edge and node based finite element
basis functions. The application of Galerkin techniques leads to a large, nonlinear system of ordinary
differential equations in the time domain.
The excitations are assumed to be time-periodic and the steady state periodic solution is of
interest only. This is represented in the frequency domain as a Fourier series for each finite element
degree of freedom and a finite number of harmonics is to be determined, i.e. a harmonic balance method
is applied. Due to the nonlinearity, all harmonics are coupled to each other, so the size of the equation
system is the number of harmonics times the number of degrees of freedom.
The harmonics would be decoupled if the problem were linear, therefore, a special nonlinear
iteration technique, the fixed-point method is used to linearize the equations by selecting a timeindependent
permeability distribution, the so called fixed-point permeability in each nonlinear iteration
step. This leads to uncoupled harmonics within these steps resulting in two advantages. One is that each
harmonic is obtained by solving a system of algebraic equations with only as many unknowns as there
are finite element degrees of freedom. A second benefit is that these systems are independent of each
other and can be solved in parallel. The appropriate selection of the fixed point permeability accelerates
the convergence of the nonlinear iteration.
The method is applied to the analysis of a large power transformer. The solution of the
electromagnetic field allows the computation of various losses like eddy current losses in the massive
conducting parts (tank, clamping plates, tie bars, etc.) as well as the specific losses in the laminated parts
(core, tank shielding, etc.). The effect of the presence of higher harmonics on these losses is
investigated
Interpolation Parameter and Expansion for the Three Dimensional Non-Trivial Scalar Infrared Fixed Point
We compute the non--trivial infrared --fixed point by means of an
interpolation expansion in fixed dimension. The expansion is formulated for an
infinitesimal momentum space renormalization group. We choose a coordinate
representation for the fixed point interaction in derivative expansion, and
compute its coordinates to high orders by means of computer algebra. We compute
the series for the critical exponent up to order twenty five of
interpolation expansion in this representation, and evaluate it using \pade,
Borel--\pade, Borel--conformal--\pade, and Dlog--\pade resummation. The
resummation returns as the value of .Comment: 29 pages, Latex2e, 2 Postscript figure
Self-similar Singularity of a 1D Model for the 3D Axisymmetric Euler Equations
We investigate the self-similar singularity of a 1D model for the 3D
axisymmetric Euler equations, which is motivated by a particular singularity
formation scenario observed in numerical computation. We prove the existence of
a discrete family of self-similar profiles for this model and analyze their
far-field properties. The self-similar profiles we find agree with direct
simulation of the model and seem to have some stability
Can Computer Algebra be Liberated from its Algebraic Yoke ?
So far, the scope of computer algebra has been needlessly restricted to exact
algebraic methods. Its possible extension to approximate analytical methods is
discussed. The entangled roles of functional analysis and symbolic programming,
especially the functional and transformational paradigms, are put forward. In
the future, algebraic algorithms could constitute the core of extended symbolic
manipulation systems including primitives for symbolic approximations.Comment: 8 pages, 2-column presentation, 2 figure
Rapid computation of L-functions for modular forms
Let be a fixed (holomorphic or Maass) modular cusp form, with
-function . We describe an algorithm that computes the value
to any specified precision in time
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