Kein Folientitel - PowerPoint PPT Presentation

1 / 47
About This Presentation
Title:

Kein Folientitel

Description:

Title: Kein Folientitel Author: Biro Last modified by: asusnotebook Created Date: 2/6/2000 6:29:22 PM Document presentation format: On-screen Show Company – PowerPoint PPT presentation

Number of Views:130
Avg rating:3.0/5.0
Slides: 48
Provided by: Biro150
Category:
Tags: folientitel | kein

less

Transcript and Presenter's Notes

Title: Kein Folientitel


1
Finite Elements in Electromagnetics2. Static
fields
Oszkár Bíró IGTE, TU Graz Kopernikusgasse 24Graz,
Austria email biro_at_igte.tu-graz.ac.at
2
Overview
  • Maxwells equations for static fields
  • Static current field
  • Electrostatic field
  • Magnetostatic field

3
Maxwells equations for static fields
4
Static current field (1)
n voltages between the electrodes are given
or
or
n currents through the electrodes are given
i 1, 2, ..., n
5
Symmetry
Static current field (2)
GE0 may be a symmetry plane
A part of GJ may be a symmetry plane
6
Interface conditions
Static current field (3)
Tangential E is continuous
Normal J is continuous
7
Network parameters (ngt0)
Static current field (4)
n1
U1 is prescribed and
or
I1 is prescribed and
ngt1
or
i 1, 2, ..., n
i 1, 2, ..., n
8
Static current field (5)
Scalar potential V
9
Static current field (6)
Boundary value problem for the scalar potential V
10
Static current field (7)
Operator for the scalar potential V
11
Static current field (8)
Finite element Galerkin equations for V
i 1, 2, ..., n
12
High power bus bar
13
Finite element discretization
14
Current density represented by arrows
15
Magnitude of current density represented by colors
16
Static current field (9)
Current vector potential T
17
Static current field (10)
Boundary value problem for the vector potential T
18
Static current field (11)
Operator for the vector potential T
19
Static current field (12)
Finite element Galerkin equations forT
i 1, 2, ..., n
20
Current density represented by arrows
21
Magnitude of current density represented by colors
22
Electrostatic field (1)
n voltages between the electrodes are given
or
n charges on the electrodes are given
i 1, 2, ..., n
on n1 electrodes GE GE0GE1GE2 ... GEi ...
GEn
on the boundary GD
23
Electrostatic field (2)
Symmetry
GE0 may be a symmetry plane
A part of GD (s0) may be a symmetry plane
24
Electrostatic field (3)
Interface conditions
Tangential E is continuous
Special case s0
Normal D is continuous
25
Electrostatic field (4)
Network parameters (ngt0)
n1
U1 is prescribed and
or
Q1 is prescribed and
ngt1
or
i 1, 2, ..., n
i 1, 2, ..., n
26
Electrostatic field (5)
Scalar potential V
27
Electrostatic field (6)
Boundary value problem for the scalar potential V
28
Electrostatic field (7)
Operator for the scalar potential V
29
Electrostatic field (8)
Finite element Galerkin equations for V
i 1, 2, ..., n
30
380 kV transmisson line
31
380 kV transmisson line, E on ground
32
380 kV transmisson line, E on ground in presence
of a hill
33
Magnetostatic field (1)
n magnetic voltages between magnetic walls are
given
or
or
n fluxes through the magnetic walls are given
i 1, 2, ..., n
on n1 magn. walls GE GE0GE1GE2 ... GEi
... GEn
on the boundary GB
34
Magnetostatic field (2)
Symmetry
GH0 (K0) may be a symmetry plane
A part of GB (b0) may be a symmetry plane
35
Magnetostatic field (3)
Interface conditions
Special case K0
Tangential H is continuous
Normal B is continuous
36
Magnetostatic field (4)
Network parameters (ngt0), J0
n1
Um1 is prescribed and
or
Y1 is prescribed and
ngt1
or
i 1, 2, ..., n
i 1, 2, ..., n
37
Magnetostatic field (5)
Network parameter (n0), b0, K0, J?0
Inductance
38
Magnetostatic field (6)
Scalar potential F, differential equation
39
Magnetostatic field (7)
Scalar potential F, boundary conditions
40
Magnetostatic field (8)
Boundary value problem for the scalar potential F
Full analogy with the electrostatic field
41
Magnetostatic field (9)
Finite element Galerkin equations for F
i 1, 2, ..., n
42
Magnetostatic field (10)
In order to avoid cancellation errors in computing
T0 should be represented by means of edge
elements
since
and hence T0 and gradF (n) are in the same
function space
43
Magnetostatic field (11)
Magnetic vector potential A
44
Magnetostatic field (12)
Boundary value problem for the vector potential A
45
Magnetostatic current field (13)
Operator for the vector potential A
46
Magnetostatic field (14)
Finite element Galerkin equations for A
i 1, 2, ..., n
47
Magnetostatic field (15)
Consistence of the right hand side of the
Galerkin equations
Write a Comment
User Comments (0)
About PowerShow.com