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In this work we consider a relativistic drift-kinetic model for runawayelectrons along with a Fokker-Planck operator for small-angle Coulombcollisions, a radiation damping operator, and a secondary knock-on (Boltzmann)collision source. We develop a new scalable fully implicit solver utilizingfinite volume and conservative finite difference schemes and dynamic meshadaptivity. A new data management framework in the PETSc library based on thep4est library is developed to enable simulations with dynamic adaptive meshrefinement (AMR), parallel computation, and load balancing. This framework istested through the development of the runaway electron solver that is able todynamically capture both bulk Maxwellian at the low-energy region and a runawaytail at the high-energy region. To effectively capture features via the AMRalgorithm, a new AMR indicator prediction strategy is proposed that isperformed alongside the implicit time evolution of the solution. This strategyis complemented by the introduction of computationally cheap feature-based AMRindicators that are analyzed theoretically. Numerical results quantify theadvantages of the prediction strategy in better capturing features comparedwith nonpredictive strategies; and we demonstrate trade-offs regardingcomputational costs. The full solver is further verified through severalbenchmark problems including manufactured solutions and solutions of physicsmodels. We particularly focus on demonstrating the advantages of using implicittime stepping and AMR for runaway electron simulations.

Scalable Implicit Solvers with Dynamic Mesh Adaptation for a Relativistic Drift-Kinetic Fokker-Planck-Boltzmann Model