Structured Mesh Generation: Open-source automatic nonuniform mesh generation for FDTD simulation

Abstract

The finite-difference time-domain (FDTD) method is a numerical technique that is widely used to solve Maxwell's differential equations in the time domain [1]. Both space and time are discretized. Space is discretized into rectangular-shaped elements in two-dimensional (2-D) or cuboid elements in three-dimensional (3-D). Cuboid elements, where the electric fields are located on the edges of the cuboid and the magnetic fields are normal to the faces, are called Yee cells and are the fundamental elements of most FDTD methods [2]. By filling up the problem space with these cells, we obtain a 3-D mesh, where neighboring cells share edges and faces. Each cell has three associated electric and magnetic field components, while the other field components belong to adjacent cells. The properties of each cell are adjusted to represent materials such as dielectrics or conductors by adjusting the constitutive parameters used in the field equations in the corresponding cells, hence forming the geometrical structure of the problem to be solved. For example, Figure 1 shows a sphere and a version of the sphere discretized using cubic elements.