Eric Michielssen

My research develops fast algorithms for partial differential equations arising in computational electromagnetics and wave physics. I focus on algorithmic ideas that make large simulations feasible and reliable in practice. The goal is to make previously intractable simulations routine, reducing computation times from days to hours and enabling analysis of structures orders of magnitude larger than classical methods permit. Core contributions include extensions of fast multipole methods to layered media and complex materials, the plane wave time domain algorithm and related blocked FFT schemes for transient integral equations, Calderón preconditioners that resolve dense-mesh breakdown and low-frequency ill-conditioning, and butterfly-based direct solvers for high-frequency systems where iterative methods fail. The emphasis is on methods that behave predictably across frequency, discretization, and material complexity. More recent work extends Wigner-Smith time delay theory to Maxwell's equations, enabling fast frequency sweeps within method-of-moments frameworks and providing a unified view across wave and ray descriptions. Current directions include adaptive direct solvers for Helmholtz problems, time-domain methods with improved stability for nonlinear and time-varying systems, and applications in time-varying metamaterials and advanced packaging. Throughout, the aim is to connect applied mathematics and computational science to engineering problems where accurate electromagnetic modeling matters.

• 1999 International Union of Radio Scientists – United States National Committee Henry G. Booker Fellow
• 1999 International Union of Radio Scientists Issac Koga Gold Medal Awardee
• 2002 IEEE Fellow
• 2014 IEEE AP-S Chen-To Tai Distinguished Educator Award
• 2018 IEEE AP-S Sergei A. Schelkunoff Award
• 2020 Applied Computational Electromagnetics Society CEM Award
• 2020 IEEE AP-S Mittra-Harrington Computational Electromagnetics Award
• 2022 IEEE AP-S R.W.P. King Paper Award

• D. S. Weile and E. Michielssen, "Genetic algorithm optimization applied to electromagnetics: A review," IEEE Transactions on Antennas and Propagation, vol. 45, no. 3, pp. 343–353, Mar. 1997.
• B. Shanker, A. A. Ergin, M. Lu, and E. Michielssen, "Fast analysis of transient electromagnetic scattering phenomena using the multilevel plane wave time domain algorithm," IEEE Transactions on Antennas and Propagation, vol. 51, no. 3, pp. 628–641, Mar. 2003.
• F. P. Andriulli, K. Cools, I. Bogaert, and E. Michielssen, "On a well-conditioned electric field integral operator for multiply connected geometries," IEEE Transactions on Antennas and Propagation, vol. 61, no. 4, pp. 2077–2087, Apr. 2013.
• H. Guo, Y. Liu, J. Hu, and E. Michielssen, "A butterfly-based direct integral-equation solver using hierarchical LU factorization for analyzing scattering from electrically large conducting objects," IEEE Transactions on Antennas and Propagation, vol. 65, no. 9, pp. 4742–4750, Sep. 2017.
• U. R. Patel and E. Michielssen, "Wigner–Smith time delay matrix for electromagnetics: Computational aspects for radiation and scattering analysis," IEEE Transactions on Antennas and Propagation, vol. 69, no. 7, pp. 3995–4010, Jul. 2021.