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Wednesday, December 05

An Implicit Maxwell Solver Based on Method of Lines Transpose

Andrew Christlieb, Michigan State University, East Lansing
Computer Science and Mathematics Division Seminar
10:00 AM — 11:00 AM, Joint Institute for Computational Sciences (Building 5100), Auditorium (Room 128)
Contact: Clayton Webster (, 865.574.3649


Fast summation methods have been successfully used in a range of plasma applications. However, in the case of moving point charges, direct application of fast summation methods in the time domain requires the use of retarded potentials. In practices, this means that every time a point charge moves in a simulation, it leaves behind an image charge that becomes a source term for all time. Hence, at each time step the number of points in the simulation grows with the number of particles being simulated.

In this talk, Dr. Christlieb will present a new approach to Maxwell's equations based on the method of lines transpose. The method starts by expressing Maxwell's equations in second order form, and then the time operator is discretized. The resulting implicit system is then solved using integral methods. This process is known as the method of lines transpose. This approach pushes the time history into a volume integral, which does not grow in complexity with time. To efficiently solve the boundary integral, Dr. Christlieb will explain the developed ADI method that is combined with a $O(N)$ solver for the 1D boundary integrals that is competitive with explicit time stepping methods. Because the new method is implicit, this approach does not have a CFL. Further, because the approach is based on an integral formulation, the new method easily encompasses complex geometry with no special modification. Dr. Christlieb will present preliminary results of this method applied to wave propagation and some basic Maxwell examples.

If you would like to meet with Andrew Christlieb, please contact Billy Fields at or Cory Hauck at