DEMO_XY / gallery 25: inspired by Stack Exchange, (JohnDow's question), version "with ellipse", mesh size: 401 x 401 nodes.

Question on forum Physics/Stack Exchange

https://physics.stackexchange.com/questions/113290/simulate-plot-electrostatic-field

Running program

Windows:
DEMO_XY.exe 25

Linux:
./DEMO_XY.run 25

Problem definition.

Numeric meshes

Each pixel of picture represents one mesh node.

white colour - vacuum
red colour   - electrode 1
green colour - electrode 2 (ellipse)

Visualization of mesh on picture.

Model parameters

mesh size:

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

x_start ==  -200.0 [mm]
x_stop  ==  +200.0 [mm]
y_start ==  -200.0 [mm]
y_stop  ==  +200.0 [mm]

number of iterations

>>> SUCCESS - solution V(x,y) has been found
after 337158 iterations

electrode 1 (red A+B)
(A)
boundary ==  +1
voltage  ==  +9.0 [V]
i_col    ==  181 .. 200
i_row    ==  101 .. 200

(B)
boundary ==  +1
voltage  ==  +9.0 [V]
i_col    ==  101 .. 200
i_row    ==  200 .. 220


electrode 2 (ellipse, green)
boundary   ==  +2
voltage    ==  +0.0   [V]
x_center_1 ==  +50.0  [mm]
y_center_1 ==  +20.0  [mm]
x_center_2 ==  +120.0 [mm]
y_center_2 ==  +60.0  [mm]
R_total    ==  +90.0  [mm]

ellipse equation:

input: point in coordinates(x,y)
       parameters of ellipse - 2 focuses
                                    (x_center_1,
                                     y_center_1,
                                     x_center_2
                                     y_center_2)
                              - the sum of 2 distances to two focal foints (R_total)
		
process:
R_1 = sqrt((x - x_center_1)*(x - x_center_1) + (y - y_center_1)*(y - y_center_1))
R_2 = sqrt((x - x_center_2)*(x - x_center_2) + (y - y_center_2)*(y - y_center_2))

if(R_1 + R_2 <= R_total)
{
    then point on mesh belongs to ellipse
}


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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