Tim Meagher PhD Mathematical Sciences Dissertation Defense
Friday, April 27, 2018 - 1:00pm

Ph.D. in Mathematical Sciences Dissertation Defense

A New Finite Difference Time Domain Method to Solve Maxwell's Equations


Timothy Meagher


BS in Mathematics, University of Nevada at Las Vegas, 2008

MS in Mathematics, Portland State University, 2010



Defense date:

Friday, April 27, 2018

Defense Committee Chair:           

Bin Jiang, PhD




Defense Committee

Dacian Daescu, PhD


Cramer Hall room 321


Andres La Rosa, PhD


1721 SW Broadway


James Morris, PhD (OGS)


We have constructed a new Finite Difference Time Domain (FDTD) method in this project. Our new algorithm focuses on the most important and most challenging transverse electric (TE) case. In this case, the electric field is discontinuous across the interface between different dielectric media where the permittivity stays as a constant in each medium. 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. We build the new algorithm 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 with mesh size. 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.