# Mesh Coarsening

GRUMMP provides mesh coarsening capability to enable automatic generation of quality coarse meshes for use with multigrid. The algorithm [10] selects a set of vertices from the fine mesh to retain in the coarse mesh, then removes unwanted vertices one at a time from the fine mesh. This incremental deletion scheme has a robustness advantage over generating a coarse mesh from scratch: incremental deletion always produces a coarse mesh even if it can not remove all the unwanted vertices. The scheme has been designed to coarsen triangulations by a factor of about in dimensions for each coarsening while preserving important geometric and topological features of the fine mesh and producing coarse mesh cells with acceptable shape quality.

Subsections

- Selecting Vertices to Retain in the Coarse Mesh
  - Identification of Apexes and Folds
  - Selection of Points to Include in the Coarse Mesh
- Incremental Vertex Deletion
  - Invoking Vertex Deletion
  - Mesh Post-processing
- Anisotropic Mesh Coarsening
  - Selection of Points in Pseudo-structured Anisotropic Meshes
- Outcomes