Advanced chapters of theoretical electro-engineering.
SPbTU, IE, Prof. A.G. Kalimov 2022
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Lecture 8
Numerical Methods of the
Electromagnetic Field
Modeling
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Classification of the numerical methods
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Classification of the problems
Electromagnetic fields
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Static problems |
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Quasi-static problems |
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High frequency |
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Magnetic |
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Electric |
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field |
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field |
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Conducting |
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Free space |
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Current in the |
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conducting |
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4
Classification of the methods
Methods of the Electromagnetic
field computation
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Differential |
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Integral |
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Hybrid |
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Finite |
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Finite |
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differences |
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elements |
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Finite volumes |
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Integro- |
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Method of |
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differential |
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moments |
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Boundary equations
5
Method of moments
6
Method of moments
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H Hc Hm |
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H Hm Hc |
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H B |
B 0 H 0 M |
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m |
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H 0 H 0 M |
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m |
- Domain occupied by magnetized material. |
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r |
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M ( r 1)H |
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H 0 H 0 M |
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M |
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Hm Hc |
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r 1 |
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Method of moments
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1 |
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M (r ) (r |
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Um (r ) |
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d m |
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m |
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J |
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Hm Um |
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r |
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H m (r ) |
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d m |
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m |
- Domain occupied by magnetized material. |
8
Integral equation of magnetostatics
J |
M |
Bio-Savart Law |
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1 |
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J (r ) |
(r |
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Hc (r ) |
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d c |
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m - Magnetized domain.
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M (r ) |
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M (r ) (r |
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r 1 |
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m |
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d m Hc (r ) |
Main variable– magnetization vector.
9
Discretization of the problem domain
Usual basic elements:
Tetrahedrons;
Prisms;
Parallelepipeds.
Shape:
10