Optimize Differential Equations for HPC

I need help breathing new life into a set of legacy differential-equation models that drive core scientific research in my lab. The algorithms themselves are solid, but they were written for hardware that is now generations behind today’s multi-core CPUs and GPU-accelerated clusters. My goal is to refactor, parallelise, and profile the existing code so it scales efficiently on modern high-performance computing architectures without changing the underlying mathematics or the numerical results.

Here is what I am looking for you to deliver:
• A clean, well-structured refactor of the current solver and supporting routines, ready to compile and run on typical HPC nodes (OpenMP or MPI on CPUs, CUDA or HIP on GPUs—use what fits best once you profile).
• Benchmark comparisons that prove speed-ups over the original implementation, including strong and weak scaling plots.
• Clear, concise documentation of the new build process, runtime parameters, and any compiler flags or environment modules required so my team can reproduce the results on our cluster.

Acceptance criteria: identical scientific outputs (within floating-point tolerance) and a demonstrable performance gain that justifies the port. If this sounds like the sort of optimisation challenge you enjoy, let’s discuss the codebase and target architecture in detail.