I am a Lead Software Engineer at Caltech, working on custom and commodity database backends for gigantic star catalogs and images.

The box below is a simple web application to illustrate Adaptive Mesh Refinement, one of the techniques I use in my projects. When you click on the box, the script will adapt the grid around the point you clicked. You could then use that adapted mesh to solve a physics problem more quickly and accurately than if you used a regular grid.