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Computational Electromagnetics with the RBF-FD Method

Andrej Kolar-Požun, Gregor Kosec

Abstract

One of the most popular methods employed in computational electromagnetics is the Finite Difference Time Domain (FDTD) method. We generalise it to a meshless setting using the Radial Basis Function generated Finite Difference (RBF-FD) method and investigate its properties on a simple test problem.

Computational Electromagnetics with the RBF-FD Method

Abstract

One of the most popular methods employed in computational electromagnetics is the Finite Difference Time Domain (FDTD) method. We generalise it to a meshless setting using the Radial Basis Function generated Finite Difference (RBF-FD) method and investigate its properties on a simple test problem.
Paper Structure (8 sections, 6 equations, 3 figures)

This paper contains 8 sections, 6 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Methods
  3. The FDTD algorithm
  4. The RBF-FD Method
  5. Our Meshless FDTD Generalisation
  6. Problem setup
  7. Results
  8. Conclusions

Figures (3)

  • Figure 1: Solution snapshots for both the FDTD and RBF-FD methods. In the $\Delta s = 0.5$ case we have hidden the irrelevant nodes. A zoomed-in portion of the snapshot is shown for the $n=100$ case.
  • Figure 2: Different stencils and their corresponding stability limit Courant numbers. The center node is marked with a square and the node colours correspond to the RBF-FD weights $w_y$ for $\partial_y$.
  • Figure 3: Solution snapshots at $n=150$ and the normalised Fourier component magnitudes, plotted for various stencil sizes. $\omega$ and $k$ are the temporal and spatial frequency indices respectively. The speed of light is shown with a black line.