Comparison of discrete exterior calculus and discrete-dipole approximation for electromagnetic scattering

Abstract In this study, we perform numerical computations of electromagnetic fields including applications such as light scattering. We present two methods for discretizing the computational domain. One is the discrete-dipole approximation (DDA), which is a well-known technique in the context of light scattering. The other approach is the discrete exterior calculus (DEC) providing the properties and the calculus of differential forms in a natural way at the discretization stage. Numerical experiments show that the DEC provides a promising alternative for solving the general Maxwell equations.

[1]  Mathieu Desbrun,et al.  HOT: Hodge-optimized triangulations , 2011, SIGGRAPH 2011.

[2]  Maxim A Yurkin,et al.  Convergence of the discrete dipole approximation. I. Theoretical analysis. , 2006, Journal of the Optical Society of America. A, Optics, image science, and vision.

[3]  Alfons G. Hoekstra,et al.  Comparison between discrete dipole and exact techniques , 2006 .

[4]  R. Courant,et al.  On the Partial Difference Equations, of Mathematical Physics , 2015 .

[5]  Maxim A Yurkin,et al.  Convergence of the discrete dipole approximation. II. An extrapolation technique to increase the accuracy. , 2006, Journal of the Optical Society of America. A, Optics, image science, and vision.

[6]  Michael Kahnert,et al.  Light scattering by a cube: Accuracy limits of the discrete dipole approximation and the T-matrix method , 2013 .

[7]  L. Kettunen,et al.  Yee‐like schemes on a tetrahedral mesh, with diagonal lumping , 1999 .

[8]  Alain Bossavit,et al.  Yee-like schemes on staggered cellular grids: a synthesis between FIT and FEM approaches , 2000 .

[9]  Alfons G. Hoekstra,et al.  Comparison between discrete dipole implementations and exact techniques , 2007 .

[10]  Anil N. Hirani,et al.  Discrete exterior calculus , 2005, math/0508341.

[11]  T. Rossi,et al.  Theoretical Considerations on the Computation of Generalized Time-Periodic Waves , 2011, 1105.4095.

[12]  J. Marsden,et al.  Asynchronous Variational Integrators , 2003 .

[13]  Raino A. E. Mäkinen,et al.  SOLUTION OF TIME-PERIODIC WAVE EQUATION USING MIXED FINITE ELEMENTS AND CONTROLLABILITY TECHNIQUES , 2011 .

[14]  R. Glowinski,et al.  Controllability Methods for the Computation of Time-Periodic Solutions; Application to Scattering , 1998 .

[15]  Alfons G. Hoekstra,et al.  The discrete-dipole-approximation code ADDA: Capabilities and known limitations , 2011 .

[16]  Alfons G. Hoekstra,et al.  The discrete dipole approximation: an overview and recent developments , 2007 .

[17]  B. Schutz,et al.  Geometrical Methods of Mathematical Physics , 1998 .

[18]  Jean-Pierre Berenger,et al.  A perfectly matched layer for the absorption of electromagnetic waves , 1994 .

[19]  Tuomo Rossi,et al.  Time-harmonic elasticity with controllability and higher-order discretization methods , 2008, J. Comput. Phys..

[20]  B. Draine,et al.  Discrete-Dipole Approximation For Scattering Calculations , 1994 .

[21]  A. Taflove,et al.  Radar Cross Section of General Three-Dimensional Scatterers , 1983, IEEE Transactions on Electromagnetic Compatibility.