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
Winner of the 2023 SIAM/ACM Prize in Computational Science and Engineering
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