Question 3.17: Solve the same boundary value problem as in the previous exa...
Solve the same boundary value problem as in the previous example but apply a finer mesh shown in the figure below. There are NN = 21 nodes and NE = 24 triangular elements. In addition, plot the equipotential contours and the electric field between the two surfaces.
1) The potential is found by solving the matrix equation (3.78) using there a mesh that is manually generated.
[ V ]_{ u }=-[ S ]_{ u , u }{ }^{-1}[ S ]_{ u , k }[ V ]_{ k } \equiv[ F ][ V ]_{ k } (3.78)
The unknown potentials obtained from the MATLAB program are:
V6 = 5.111 V ; V7 = 5.2222 V ; V8 = 5.7778 V ; V9 = 7.8889 V ; V14 = 5.7778 V ; V17 = 5.2222 V ; V20 = 5.1111 V .
2) The calculated normalized capacitance (C = C0 / ε0) for a unit length of the line is C = 10.8444. The relative error achieved here is smaller than in the previous example.
3) The equipotential contours are plotted below using the ‘contour’ function. The electric field is determined using the ‘gradient’ function and displayed using the ‘quiver’ function.
