A New Finite Difference Time Domain Method To Solve Maxwells Equations

Download or read book A New Finite Difference Time Domain Method to Solve Maxwell’s Equations written by and published by . This book was released on 2018 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt: We have constructed a new finite-difference time-domain (FDTD) method in this project. Our new algorithm focuses on the most important and more challenging transverse electric (TE) case. In this case, the electric field is discontinuous across the interface between different dielectric media. We use an electric permittivity that stays as a constant in each medium, and magnetic permittivity that is constant in the whole domain. To handle the interface between different media, we introduce new effective permittivities that incorporates electromagnetic fields boundary conditions. That is, across the interface between two different media, the tangential component of the electric field and the normal component of the electric displacement are continuous. Meanwhile, the magnetic field stays as continuous in the whole domain. Our new algorithm is built based upon the integral version of the Maxwell's equations as well as the above continuity conditions. The theoretical analysis shows that the new algorithm can reach second-order convergence O(∆x2)with mesh size ∆x. The subsequent numerical results demonstrate this algorithm is very stable and its convergence order can reach very close to second order, considering accumulation of some unexpected numerical approximation and truncation errors. In fact, our algorithm has clearly demonstrated significant improvement over all related FDTD methods using effective permittivities reported in the literature. Therefore, our new algorithm turns out to be the most effective and stable FDTD method to solve Maxwell's equations involving multiple media.