Classical finite element methods rely on tessellations composed of straight-edged elements mapped linearly from a reference element on domains which physical boundaries and interfaces are indifferently straight or curved. This geometrical approximation represents a serious hindrance for high order methods, since it limits the accuracy of the spatial discretization to second order. Thus, exploiting an enhanced representation of the geometrical features of a given electromagnetic wave propagation problem is an important issue in the design of high order methods, such as the Discontinuous Galerkin Time-Domain (DGTD) method.

Here, we show the norm of the electric field Fourier transform at a high-order resonance of a 50nm-radius gold spheres dimer with a 4nm gap, without (top) and with (bottom) using curvilinear elements for the discretization of the spheres geometry (meshes are identical).

A 3D curvilinear discontinuous Galerkin time-domain solver for nanoscale light-matter interactions

Jonathan Viquerat, Claire Scheid

Journal of Computational and Applied Mathematics, Vol. 289, pp. 37-50 (2015)

Simulation of electromagnetic waves propagation in nano-optics with a high-order discontinuous Galerkin time-domain method

Jonathan Viquerat