Animations
Surface plasmon waves
An incident time harmonic transverse magnetic wave, in a medium with
unit permittivity, is scattered from a homogeneous dielectric cylinder
with sharp edges. The permittivity of the cylinder is 1.1838, with
limit taken from above in the complex plane. The total magnetic field
is shown:
See On a
Helmholtz transmission problem in planar domains with corners
for details.
Singularity spectra
The effective permittivity of a staggered array of square
cylinders. The area fraction of squares goes up to almost 0.5. The
permittivity ratio (squares/background) ranges from 6 to 1, with
limits taken from above in the complex plane:

Staggered.mpeg (540 x 720
pixels, mpeg4, 22MB).

Staggered.gif (360 x 480
pixels, gif, 3.6MB). [press "Esc" to interrupt and click "reload
current page" to resume]
The effective permittivity of a square array of square cylinders. The
area fraction of squares ranges from 0 to 0.99. The permittivity ratio
(squares/background) ranges from 6 to 1, with limits taken from above
in the complex plane:

Square.mpeg (540 x 720
pixels, mpeg4, 7.7MB).

Square.gif (360 x 480
pixels, gif, 2.0MB). [press "Esc" to interrupt and click "reload
current page" to resume]
See
Spectral superresolution in metamaterial composites for
details.
Laplace's equation
Laplace's equation is solved in real time on a polygonal
domain. Piecewise constant Dirichlet boundary conditions are imposed.
The numerical techniques used are described in A robust and accurate solver of Laplace's
equation with general boundary conditions on general domains in the
plane and in references therein.
Crack propagation
See A
higher order scheme for twodimensional quasistatic crack growth
simulations for details.