Mathematical and Numerical Modelling in Electrical Engineering Theory and Applications

1. Front Matter

   Pages i-xiii

   PDF

2. Introduction

   • Michal Křížek, Pekka Neittaanmäki

   Pages 1-3

3. Mathematical modelling of physical phenomena

   • Michal Křížek, Pekka Neittaanmäki

   Pages 4-11

4. Mathematical background

   • Michal Křížek, Pekka Neittaanmäki

   Pages 12-53

5. Finite elements

   • Michal Křížek, Pekka Neittaanmäki

   Pages 54-97

6. Conjugate gradients

   • Michal Křížek, Pekka Neittaanmäki

   Pages 98-120

7. Magnetic potential of transformer window

   • Michal Křížek, Pekka Neittaanmäki

   Pages 121-129

8. Calculation of nonlinear stationary magnetic field

   • Michal Křížek, Pekka Neittaanmäki

   Pages 130-147

9. Steady-state radiation heat transfer problem

   • Michal Křížek, Pekka Neittaanmäki

   Pages 148-161

10. Nonlinear anisotropic heat conduction in a transformer magnetic core

    • Michal Křížek, Pekka Neittaanmäki

    Pages 162-196

11. Stationary semiconductor equations

    • Michal Křížek, Pekka Neittaanmäki

    Pages 197-208

12. Nonstationary heat conduction in a stator

    • Michal Křížek, Pekka Neittaanmäki

    Pages 209-222

13. The time-harmonic Maxwell equations

    • Michal Křížek, Pekka Neittaanmäki

    Pages 223-235

14. Approximation of the Maxwell equations in anisotropic inhomogeneous media

    • Michal Křížek, Pekka Neittaanmäki

    Pages 236-250

15. Methods for optimal shape design of electrical devices

    • Michal Křížek, Pekka Neittaanmäki

    Pages 251-276

16. Back Matter

    Pages 277-300

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Mathematical modeling plays an essential role in science and engineering. Costly and time consuming experiments (if they can be done at all) are replaced by computational analysis. In industry, commercial codes are widely used. They are flexible and can be adjusted for solving specific problems of interest. Solving large problems with tens or hundreds of thousands unknowns becomes routine. The aim of analysis is to predict the behavior of the engineering and physical reality usually within the constraints of cost and time. Today, human cost and time are more important than computer cost. This trend will continue in the future. Agreement between computational results and reality is related to two factors, namely mathematical formulation of the problems and the accuracy of the numerical solution. The accuracy has to be understood in the context of the aim of the analysis. A small error in an inappropriate norm does not necessarily mean that the computed results are usable for practical purposes.

• Algebra
• Approximation
• Hilbert space
• Maxwell's equations
• electrical engineering
• functional analysis
• linear algebra
• linearity
• modeling
• numerical analysis
• numerical methods
• operator
• partial differential equation
• partial differential equations

• Academy of Sciences, Prague, Czech Republic

  Michal Křížek

• University of Jyväskylä, Jyväskylä, Finland

  Pekka Neittaanmäki

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