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Mesh generation and mesh adaptation for partial differential equations [M6]

The course will offer a top-level overview of various mesh generation and mesh adaptation techniques, with particular emphasis on the production of meshes suitable for the solution of all types of partial differential equations. The course will cover issues of mesh quality, ease of generation and computational efficiency. A series of practical sessions will guide students in developing simple codes implementing a number of these algorithms and allow for hands-on experience of the mesh-generation process.

Topics include:

  1. Introduction and Fundamentals - Definitions, Simple Grids, Grid Classifications).
  2. Curvilinear Grids - Definitions, Analytic Mappings, Interpolation Techniques, PDE Generation Methods
  3. Unstructured Grids - Fundamentals, Delaunay Triangulation, Advancing Front
  4. Combined Grid Approaches - Hybrid Grids, Overlapping Grids, Chimera Grids, Cartesian Cut-Cell Grids
  5. Grid Adaptation Techniques - Motivation, Unstructured Grid Adaptation, Moving Grids
  6. Structured Adaptive Mesh Refinement - Basic Concepts, Flagging and Clustering, Hierarchy Advancement