This could have been useful for 2019 me, lmao (abstract follows):

The Molecular Theory is a theoretical and computational framework for the study of soft matter (polymers, surfactants, gels, biological membranes, etc). For example, this theory has been used to study polymer self-assembly, biological nanopores and nanoparticles modified by polymers. The objective of this framework is to find the density and chemical state of all molecules (polymers, solvent molecules and/or ions) in each position of the system. To achieve this, the system’s free energy is written down as an approximated functional of these unknown functions. Analytically minimizing the free energy functional provides analytical expressions for the densities and chemical states. These expressions are discretized following a finite differences scheme which results in a coupled non linear equation system. In order to find a solution for this system we have to find a solution vector X such as F(x) = 0 (where F is the set of coupled non linear equations). The solution to this problem is obtained by employing a variant of Newton’s method. The evaluation of F(x) in each iteration of the method is the most taxing part of the whole program (performance wise) because it requires the multiplication and addition of very large sparse matrices. As of today, the storage and computation of these sparse matrixes operations is done employing an in-house compressed format which doesn’t store the null elements, but the real efficiency of the employed routines hasn’t been evaluated for possible optimizations. Additionally, the code employs the MPI standard for parallelizing the computations, but doesn’t implement optimizations for massively parallel architectures.

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eventually I'll try to port it to GPU, if that is even possible or ideal.