46. Advancing Parabolic Operators in Thermodynamic MHD models: Explicit Super Time-Stepping Versus Implicit Schemes with Krylov Solvers
Authors: Ronald Caplan (Predictive Science Inc)Zoran Mikic (Predictive Science Inc)Jon Linker (Predictive Science Inc)Roberto Lionello (Predictive Science Inc)
Abstract: We explore the performance/scaling of using explicit super time-stepping (STS) algorithms versus implicit schemes with Krylov solvers for integrating parabolic operators in thermodynamic MHD models of the solar corona.
Specifically, we compare the second-order Runge-Kutta Legendre (RKL2) method with implicit backward Euler computed using the preconditioned conjugate gradient (PCG) solver with both a point-Jacobi and a non-overlapping domain decomposition ILU0 preconditioner. The algorithms are used to integrate anisotropic Spitzer thermal conduction and artificial kinematic viscosity at time-steps much larger than the explicit Euler limit.
A key component of the comparison is the use of a real-world simulation on large HPC systems, with special attention placed on the parallel scaling of the algorithms. It is shown that, for the specific problem and model used, the RKL2 method generally surpasses the implicit method with PCG solvers in performance and scaling, but suffers from accuracy limitations in some localized regions of the grid.
Two-page extended abstract: pdf