Most mesh generation software seems to be aimed at building nicely shaped elements for FEM. I'm curious about a different situation:
I need to numerically integrate over an irregular region. I don't need to solve for any unknowns in this region -- just integrate a known function. And I need to integrate over many such regions as fast as possible. My current approach is to mesh the region (using either Triangle or Tetgen, depending on 2d vs 3d) and then perform Gaussian quadrature over each individual tri/tet.
However, I suspect that these meshing algorithms (which are a bottleneck) are doing far more work than necessary for this use case. Differences:
- Small internal angles are fine.
- The occasional zero volume element would be fine -- integrating over a zero volume element will give just zero.
- Nonconforming elements are not a problem.
Essentially, anything goes as long as the mesh covers the whole volume and there is no overlap between cells.
Does anyone know of research that addresses this situation?