PIXIE3D: A Parallel, Implicit, eXtended MHD 3D Code

We report on the development of PIXIE3D, a 3D parallel, fully implicit Newton-Krylov extended MHD code in general curvilinear geometry. PIXIE3D employs a second-order, finite-volume-based spatial discretization that satisfies remarkable properties such as being conservative, solenoidal in the magnetic field to machine precision, non-dissipative, and linearly and nonlinearly stable in the absence of physical dissipation.\footnote{L. Chac\'on, \emph{Comput. Phys. Comm.}, {\bf 163} (3), 143-171 (2004)} PIXIE3D employs fully-implicit Newton-Krylov methods for the time advance. Currently, second-order implicit schemes such as Crank-Nicolson and BDF2 ($2^{nd}$ order backward differentiation formula) are available. PIXIE3D is fully parallel (employs PETSc for parallelism), and exhibits excellent parallel scalability. A parallel, scalable, MG preconditioning strategy, based on physics-based preconditioning ideas,\footnote{L. Chac\'on et al., {\em J. Comput. Phys}. {\bf 178} (1), 15- 36 (2002); {\em J. Comput. Phys.}, {\bf 188} (2), 573-592 (2003)} has been developed for resistive MHD,\footnote{L. Chac\'on, {\em 32nd EPS Conf. Plasma Physics}, Tarragona, Spain, 2005} and is currently being extended to Hall MHD.\footnote{L. Chac\'on et al., {\em 33rd EPS Conf. Plasma Physics}, Rome, Italy, 2006} In this poster, we will report on progress in the algorithmic formulation for extended MHD, as well as the the serial and parallel performance of PIXIE3D in a variety of problems and geometries.