ARKODE
Adaptive Runge Kutta solvers for systems of Ordinary Differential Equations
Distributed as part of SUNDIALS (below)
SUNDIALS
SUite of Nonlinear Differential and ALgebraic Solvers
Enzo
Astrophysical adaptive mesh refinement simulation framework
E3SM/HOMME
Energy Exascale Earth System Model
Tempest
Tempest atmosphere / Earth-system model
ParaDiS
Parallel Dislocation Simulator
RKLab
Runge Kutta exploration framework
Recommended Software
Open-source packages that I use or recommend
MFEM
Modular Finite Element Methods
hypre
Scalable multigrid linear solvers
SuperLU
Sparse-direct linear solvers
PETSc
Portable Extensible Toolkit for Scientific Computation
deal.ii
Finite element Differential Equations Analysis Library
FETK
Finite Element ToolKit
Trilinos
Object-oriented large-scale solver framework