DGTD method on curvilinear tetrahedral meshes
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. In this study, we exploit a high order mapping for tetrahedra, and focus on specific nanophotonics setups to assess numerically the gains in terms of accuracy and performance.
Tetrahedral mesh for plasmonic resonance of a gold nanosphere with radius 50 nm. The scatterer (in red) is enclosed by the total field (TF) region (in blue), delimited by the TF/SF interface on which the incident field is imposed. Then we find the scattered field (SF) region (in purple), surrounded by UPMLs (in gray).
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| DGTD method with affine elements |
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| DGTD method with curvilinear elements |
Scattering cross-section of a gold nanosphere obtained with P2 and P3 interpolation of the EM field components, using affine (linear) and curvilinear meshes with various refinement levels
Plasmonic coupling between nanoparticles is at the heart of many applications in nano-optics. We illustrate the coupling of two identical gold nanospheres which are aligned along the polarization direction of the incident field, and the surface-to-surface distance is set to 4 nm. In this configuration, the coupled plasmon resonance induces very intense fields in the gap between the particles. Then, a proper near-field resolution is essential to a good understanding of the properties of such coupled structures. Here, we use P4 polynomial approximation with upwind fluxes and a fourth order low storage Runge Kutta time scheme (LSRK4).
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| DGTD method with affine elements | DGTD method with curvilinear elements |
Near-field visualization of the electric field Fourier transform for a gold nanosphere dimer
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| Absorption cross-section of a gold nanosphere dimer obtained with P4 approximation |
| using affine and curvilinear meshes |
Related publications
J. Viquerat and C. Scheid
A 3D curvilinear discontinuous Galerkin time-domain solver for nanoscale light–matter interactions
J. Comput. Appl. Math., Vol. 289, pp. 35-70 (2015)