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:

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:

See Spectral super-resolution 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 two-dimensional quasi-static crack growth simulations for details.