Solving 2D diffusion equation using MPI with Claude AI

In this talk, we want to share our experience of using LLMs with Claude AI for solving 2D diffusion equation - a parabolic PDE - numerically in parallel using MPI, a classic model often used in our training courses on parallel computing. Our goal is to see if Claude can act as a capable research assistant and programmer, and at what level. We started by presenting the Claude the mathematical statement of the problem in an image, along with a set of tasks: 1) Literature review; 2) Formulation; 3) Implementation design; 4) Code implementation; 5) Code verification and visualization; 6) Final report. We took a laissez-faire, but guided approach, proceeded with one task at a time. We did not tell Claude what to do or how to do specifically, instead, we ask Claude to come back with ideas and suggestions. We then make decisions based on the findings and recommendations by Claude. In the end, we are very satisfied with the outcome. The performance of Claude has exceeded our expectation. To us Claude appears to be a senior researcher and a professional programmer. Its work can hardly be matched by a graduate student and a junior programmer.