Study And Application By Non Uniform Mesh FDTD

Since Maxwell developed the Maxwell curl equation which reveals that the whole macroscopic electromagnetic phenomenon followed the universal law in the nature in the1873, the electromagnetic field theory has always been the focus of extensive and more deeply research in the all fields. In other words, all the electromagnetic problems may eventually become to solve problem by Maxwell curl equation under the premise of a given electromagnetic. With the rapid development of the software and the computer memory and the depth study and the continuous innovation of the computational electromagnetic, the computational electromagnetic theory becomes the mainstream computational electromagnetic method to solve the complex structures of the electromagnetic problems. The computational electromagnetic method is a comprehensive discipline which contains to the electromagnetic field theory, the numerical optimization algorithm and the computer science has been widely research and application in the millimeter wave and microwave communication, the biology, the nonlinear chaotic electromagnetic problem and the nanoelectronics.The Finite Difference Time Domain (FDTD) in the electromagnetic field as the one of the three numerical calculation methods has its unique properties and advantages to simulate the complex model of the electromagnetic problems. The FDTD method uses the Maxwell’s equations to simulation the electromagnetic engineering problems with the computers directly, so this method has extensive research and application in the recent years. In this theory, we derived from the discrete equations of the non uniform grid finite difference time domain method in the finite difference time domain method and discussed and improved the mesh method in the non-uniform grid finite difference time domain method.First of all, we briefly describe the basic theory of the FDTD method, including the FDTD method’s discrete equations, the numerical stability, the numerical dispersion characteristic and the absorbing boundary conditions. Using the convolution perfectly matched layer absorbing boundary condition of the FDTD method to simulate to the electric dipole source to discuss the advantage and the disadvantage.Second, the whole calculation domain was divided into the coarse and the dine grid. Setting a putative magnetic field component and using the linear interpolation method, we solve the physical numerical reflection phenomenon in the interface between coarse and fine grid where it may happen when the mesh size change suddenly. Compare the simulation result which using the non-uniform mesh FDTD method to simulate the microstrip patch antenna with the measured values to illustrate the advantages and the disadvantages of the non-uniform mesh FDTD method.Finally, introduce the adaptive grid expansion factor into the gradient mesh division method to change the grid size in the whole calculation domain when the extension factor is changing. This method avoids to the reflection error and the calculation error and improves the calculation accuracy and the computational efficiency. What’s more, we use the method to simulate the rectangular patch antenna, the planar inverted-F antenna and the microstrip low-pass filter. The simulation results show that the method is effective to simulate the process of the propagation of the electromagnetic waves.