2D Mesh Generator for Electromagnetic Fields Simulation Luciana Firmino, Mario Baldini and Adroaldo Raizer Electromagnetic Compatibility Engineering Group - GEMCO Federal University of Santa Catarina - UFSC Postal Code 88040-970, SC, Brazil luciana.firmino@eel.ufsc.br, mario.baldini@ieee.org, raizer@eel.ufsc.br Abstract—This paper presents an image based mesh generator used to create the two-dimensional environment model for elec- tromagnetic fields simulation with the transmission-line modeling method (TLM). At first, the TLM two-dimension shunt node formulation is briefly introduced. Then, the mesh generator program is described and its functioning is explained. Finally, the validated results are shown and the authors present a brief discussion over the program benefits. I. I NTRODUCTION The Transmission-Line Modeling Method (TLM) [1] is a time-domain differential numerical simulation method first cited by Johns and Beurle [2], created for solving two- dimensional electromagnetic field scattering problems. Since then, TLM has evolved, other formulations were proposed and it has been successfully applied for modeling electromagnetic fields in one, two and three dimensions. Nevertheless, due to its scattering formulation, and to the growing complexity of the problems being analyzed, some- times it is a great challenge to efficiently mesh the environ- ment or objects of interest. Several works have attempted to establish easier ways to deal with this problem, some even have developed different types of mesh grids [3], [4], what only corroborates the importance of this issue to efficiently model the most diverse existing situations. It is not the intention of this paper to explain the TLM method in detail, but an overview of the method should be presented in order to facilitate general understanding. There- fore, the main focus will be directed to the mesh generator itself, then its application and results. II. THE TLM TWO-DIMENSIONAL FORMULATION The TLM method physical basis is the Huygens light propagation principle, stating that a punctual wave source propagates spherically, and each wave acts as a new source, forming a network of spherical wave fronts [5]. Its formulation is established from the analogy between transmission-lines and electromagnetic field theories. The space is modeled by a grid of interconnected transmission-lines in each direction, and the transmission-lines are represented by a combination of equivalent lumped circuit components (see Fig.1). The properties of the materials to be modeled define the parameters of the lumped circuit components. Fig. 1. Two dimensional TLM shunt node. The meshing procedure consists in discretizing space in differential Δl and time in differential Δt respectively, so, the wave propagates at speed v=Δl/Δt. The Δl is chosen as small as possible to reduce the discretization error. A common acceptable value is Δl =0.1λ. The Δt is calculated according to the wave frequency and medium electric properties, so Δt =Δl × ε × μ. The appropriate development of time domain Maxwell’s equations and Kirchhoff’s laws show the relation between electric field and voltage, and also between magnetic field and current, which are: E z = V z /Δl H x = I y /Δl H y = -I x /Δl (1) μ = L d /Δl ε = 2C d + C s /2 σ = G s (2) Having situated the TLM method, the next section defines the main subject of the paper, which is the development of a mesh generator based in bitmap colors identification. III. THE MESH GENERATOR In order to simulate a problem, a color image is created using a generic graphic design program modeling the environ- ment of interest. The the mesh generator receives this image, and converts it into a grid based model, which is later used in the simulation by the TLM program. Each color of the image represents a homogeneous region from the environment being