[yuriko]

You might also want to look at the Firedrake project [1]

[1] https://firedrakeproject.org/

[InfinityByTen]

Oh ther're tons of those. Here's another: https://freefem.org/

Eventually all of them call LAPACK AND BLAS Fortran stuff written decades ago. Just the problem definition syntax evolves a little in each package.