Improved Nonlinear Solvers in BOUT++

Challenging aspects of large-scale turbulent edge simulations in plasma physics include robust nonlinear solvers and efficient preconditioners. This paper presents recent advances in the scalable solution of nonlinear partial differential equations in BOUT++, with emphasis on simulations of edge localized modes in tokamaks. A six-field, nonlinear, reduced magnetohydrodynamics model containing the fast shear Alfven wave and electron and ion heat conduction along magnetic fields is solved by using Jacobian-free Newton-Krylov (JFNK) methods and nonlinear GMRES (NGMRES). Physics-based preconditioning based on analytic Schur factorization of a simplified Jacobian is found to result in an order of magnitude reduction in runtime over unpreconditioned JFNK, and NGMRES is shown to significantly reduce runtime while requiring only the nonlinear function evaluation. We describe in detail the preconditioning algorithm, and we discuss parallel performance of NGMRES and Newton-Krylov methods using the PETSc library.