DEMO_XY / gallery 15: Cylindrical capacitor. Mesh size: 401 x 401 nodes.

Running program

Windows:
DEMO_XY.exe 15

Linux:
./DEMO_XY.run 15

Problem definition

Problem taught in secondary school (derivation from Gauss law). This time program has solved Laplace equation for analogous electrode distribution.

Numeric meshes

Each pixel represents one mesh point.

colour white - vacuum
colour red   - outer electrode 1 (U = +0.0 [V])
colour green - inner electrode 2 (U = +1.0 [V])

Visualization of mesh on picture.

Model parameters

mesh size:

number of rows     ==  401
number of columns  ==  401

x ==  -200.0 ... +200.0 [mm]
y ==  -200.0 ... +200.0 [mm]

number of iterations

>>> SUCCESS - solution V(x,y) has been found
after 71149 iterations

electrode 1
boundary ==  +1
voltage  ==  +450.0 [V]
x_center ==  +0.0   [mm]
y_center ==  +0.0   [mm]
radius   >=  +190.0 [mm]

electrode 2
boundary ==  +2
voltage  ==  +1.0  [V]
x_center ==  +0.0  [mm]
y_center ==  +0.0  [mm]
radius   <=  +20.0 [mm]


computation accuracy:
eps ==  1.0E-9 [V]

Computation results

Equipotential lines

Mapping of electrostatic potential [V] to colours

Colormap: grayscale

Colormap: grayscale inverted

Colormap: hot-to-cold

Colormap: hot-to-cold inverted

Colormap: jet

Colormap: jet inverted

Mapping of component x of electric force (E_x) [V/mm] to colours

Important: determinig of exact values of E near electrode surface is generally problematic. These maps have generally illustrative character.

Colormap: grayscale

Colormap: grayscale inverted

Colormap: hot-to-cold

Colormap: hot-to-cold inverted

Colormap: jet

Colormap: jet inverted

Mapping of component y of electric force (E_y) [V/mm] to colours

Important: determinig of exact values of E near electrode surface is generally problematic. These maps have generally illustrative character.

Colormap: grayscale

Colormap: grayscale inverted

Colormap: hot-to-cold

Colormap: hot-to-cold inverted

Colormap: jet

Colormap: jet inverted

Mapping of electric force (E) [V/mm] to colours

algorihm of computation:
E = sqrt(E_x*E_x + E_y*E_y)

Important: determinig of exact values of E near electrode surface is generally problematic. These maps have generally illustrative character.

Colormap: grayscale

Colormap: grayscale inverted

Colormap: hot-to-cold

Colormap: hot-to-cold inverted

Colormap: jet

Colormap: jet inverted

Mapping of square of electric force (E*E == E2) [V2/mm2] to colours

algorithm of computation:
E*E = E_x*E_x + E_y*E_y

Important: determinig of exact values of E near electrode surface is generally problematic. These maps have generally illustrative character.

Colormap: grayscale

Colormap: grayscale inverted

Colormap: hot-to-cold

Colormap: hot-to-cold inverted

Colormap: jet

Colormap: jet inverted

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