Screen (Maxwell’s Equations)

This example solves time-harmonic Maxwell’s equations. It describes an electromagnetic wave that hits a thin screen under the angle of 45 degrees, causing a singularity at the tip of the screen. The strength of the singularity makes this example rather difficult.

Model problem

Equation solved: Time-harmonic Maxwell’s equations

(1)

Domain of interest is the square missing the edge that connects the center with the midpoint of the left side. It is filled with air:

Boundary conditions

Tangential component of solution taken from known exact solution (essential BC).

Exact solution

This is rather complicated in this case - see the file definitions.cpp.

Sample solution

Real part of :

Real part of :

Imaginary part of :

Imaginary part of :

Convergence comparisons

Final mesh (h-FEM with linear elements):

Note that the polynomial order indicated corresponds to the tangential components of approximation on element interfaces, not to polynomial degrees inside the elements (those are one higher).

Final mesh (h-FEM with quadratic elements):

Final mesh (hp-FEM):

DOF convergence graphs:

CPU time convergence graphs: