JICS Compact course: 07/25/11 - 07/29/11

Structured Adaptive Mesh Refinement Methods - Theory, Implementation and Application

Ralf Deiterding, Rahul Sampath
Computer Science and Mathematics Division, ORNL

Structured adaptive mesh refinement (SAMR) techniques aim at preserving the high computational performance achievable on uniform grids on a hierarchically adapted non-uniform mesh. The course will describe the mathematical background of the typi-cally used discretizations, detail the employed algorithms, and summarize practically relevant applications and their implementation on modern parallel computers. Advanced topics such as using the SAMR approach for implementing geometric multigrid algo-rithms for elliptic problems and parallelization on massively parallel systems will also be covered. A discussion of presently available SAMR software and a practical exercise with the AMROC framework will complete the short course.

Outline:

1. Fundamentals: Hyperbolic problems
   • Finite volume schemes
   • Discussion of mesh adaptation approaches
2. Structured AMR for hyperbolic problems
   • The recursive algorithm with time-space refinement
   • Distributed memory parallelization
3. Complex hyperbolic structured AMR applications
   • Consideration of non-Cartesian geometries
   • Shock-induced combustion
   • Fluid-structure interaction
4. Structured AMR for elliptic problems
   • Adaptive geometric multigrid algorithms
   • A parallel adaptive multigrid method for image registration
5. Further topics
   • Available implementations
   • Exercise with the SAMR framework AMROC

This course is intended for summer students of Applied Mathematics and Computational Sciences. If you want to participate, please send email to deiterdingr@ornl.gov to allow us a headcount.

Course material

Location: JICS, Bldg. 5100, Room 134

daily Monday 07/25/11 to Friday 07/29/11, 1:00pm-2:30pm

Friday 07/29/11, 3:00pm-4:30pm, practical exercise (Linux/Unix laptop required)

Level 2

Level 3

Level 4