Rene Plasser, Gergely Koczka and Oszkár Bíró
A transformer model is used as a benchmark for testing various methods to solve 3D nonlinear periodic eddy current problems. This paper aims to set up a nonlinear magnetic circuit…
Abstract
Purpose
A transformer model is used as a benchmark for testing various methods to solve 3D nonlinear periodic eddy current problems. This paper aims to set up a nonlinear magnetic circuit problem to assess the solving procedure of the nonlinear equation system for determining the influence of various special techniques on the convergence of nonlinear iterations and hence the computational time.
Design/methodology/approach
Using the T,ϕ-ϕ formulation and the harmonic balance fixed-point approach, two techniques are investigated: the so-called “separate method” and the “combined method” for solving the equation system. When using the finite element method (FEM), the elapsed time for solving a problem is dominated by the conjugate gradient (CG) iteration process. The motivation for treating the equations of the voltage excitations separately from the rest of the equation system is to achieve a better-conditioned matrix system to determine the field quantities and hence a faster convergence of the CG process.
Findings
In fact, both methods are suitable for nonlinear computation, and for comparing the final results, the methods are equally good. Applying the combined method, the number of iterations to be executed to achieve a meaningful result is considerably less than using the separated method.
Originality/value
To facilitate a quick analysis, a simplified magnetic circuit model of the 3D problem was generated to assess how the different ways of solutions will affect the full 3D solving process. This investigation of a simple magnetic circuit problem to evaluate the benefits of computational methods provides the basis for considering this formulation in a 3D-FEM code for further investigation.
Details
Keywords
Gergely Koczka and Gerald Leber
The simplified modeling of many physical processes results in a second-order ordinary differential equation (ODE) system. Often the damping of these resonating systems cannot be…
Abstract
Purpose
The simplified modeling of many physical processes results in a second-order ordinary differential equation (ODE) system. Often the damping of these resonating systems cannot be defined in the same simplified way as the other parameters due to the complexity of the physical effects. The purpose of this paper is to develop a mathematically stable approach for damping resonances in nonlinear ODE systems.
Design/methodology/approach
Modifying the original ODE using the eigenvalues and eigenvectors of a linearized state leads to satisfying results.
Findings
An iterative approach is presented, how to modify the original ODE, to achieve a well-damped solution.
Practical implications
The method can be applied for every physical resonating system, where the model complexity prevents the determination of the damping.
Originality/value
The iterative algorithm to modify the original ODE is novel. It can be used on different fields of the physics, where a second-order ODE is describing the problem, which has only measured or empirical damping.
Details
Keywords
Gergely Koczka and Oszkár Bíró
The purpose of the paper is to show the application of the fixed‐point method with the T, Φ‐Φ formulation to get the steady‐state solution of the quasi‐static Maxwell's equations…
Abstract
Purpose
The purpose of the paper is to show the application of the fixed‐point method with the T, Φ‐Φ formulation to get the steady‐state solution of the quasi‐static Maxwell's equations with non‐linear material properties and periodic excitations.
Design/methodology/approach
The fixed‐point method is used to solve the problem arising from the non‐linear material properties. The harmonic balance principle and a time periodic technique give the periodic solution in all non‐linear iterations. The optimal parameter of the fixed‐point method is investigated to accelerate its convergence speed.
Findings
The Galerkin equations of the DC part are found to be different from those of the higher harmonics. The optimal parameter of the fixed‐point method is determined.
Originality/value
The establishment of the Galerkin equations of the DC part is a new result. The method is first used to solve three‐dimensional problems with the T, Φ‐Φ formulation.
Details
Keywords
Gergely Koczka, Stefan Außerhofer, Oszkár Bíró and Kurt Preis
The purpose of the paper is to present a method for efficiently obtaining the steady‐state solution of the quasi‐static Maxwell's equations in case of nonlinear material…
Abstract
Purpose
The purpose of the paper is to present a method for efficiently obtaining the steady‐state solution of the quasi‐static Maxwell's equations in case of nonlinear material properties and periodic excitations.
Design/methodology/approach
The fixed‐point method is used to take account of the nonlinearity of the material properties. The harmonic balance principle and a time periodic technique give the periodic solution in all nonlinear iterations. Owing to the application of the fixed‐point technique the harmonics are decoupled. The optimal parameter of the fixed‐point method is determined to accelerate its convergence speed. It is shown how this algorithm works with iterative linear equation solvers.
Findings
The optimal parameter of the fixed‐point method is determined and it is also shown how this method works if the equation systems are solved iteratively.
Originality/value
The convergence criterion of the iterative linear equation solver is determined. The method is used to solve three‐dimensional problems.