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CasADi is a symbolic framework for numeric optimization implementing automatic differentiation in forward and reverse modes on sparse matrix-valued computational graphs. It supports self-contained C-code generation and interfaces state-of-the-art codes such as SUNDIALS, IPOPT etc. It can be used from C++, Python or Matlab/Octave.
oomph-lib is an object-oriented, open-source finite-element library for the simulation of multi-physics problems. It is developed and maintained by Matthias Heil and Andrew Hazel of the School of Mathematics at The University of Manchester, along with many other contributors.