Krylov Methods for Magnetohydrodynamic Simulations

Mayya Tokman, California Institute of Technology

This poster will discuss the use of Krylov methods in magnetohydrodynamic simulations. These methods use nonlinear exponential propagation to perform time evolution and approximate the action of the right-hand-side differential operator and its Jacobian by projections to the Krylov subspace via the Arnoldi process. The primary advantage of Krylov methods is that they allow one to compute the evolution of equations using a time step which exceeds the CFL limit imposed by the fast modes in the system.

Another advantage of the method is the use of Krylov subspace projections to propagate the right-hand-side differential operator, which avoids the inversion of large complex matrices and makes the method highly parallelizable. We will describe this numerical technique and discuss its performance for the applications in plasma physics.

Abstract Author(s): Mayya Tokman, D. Meiron, P. Bellan