Scope: Structured adaptive mesh refinement (SAMR) techniques
can enable cutting-edge simulations of problems governed by
conservation laws. The approach aims at preserving the high
computational performance of uniform grids on a
hierarchically adapted non-uniform mesh. The course will
describe the mathematical background of the typically used
finite volume discretizations for hyperbolic gas dynamics
(see below for the SAMR refinement of an expanding
three-dimensional shock wave), 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 algorithms for elliptic and
parabolic problems and higher-order SAMR methods will also
be covered. A discussion of presently available SAMR
software and a practical exercise with the AMROC framework
will complete the short course.

Topics to be covered include:

   1. Finite volume methods
          * Shock-capturing schemes
          * Higher-order discretizations
          * Possible mesh adaptation approaches
   2. Structured AMR for hyperbolic problems
          * The recursive algorithm with time-space refinement
          * Flux-correction, grid generation
          * Higher-order interpolation
          * Distributed memory parallelization
   3. Complex hyperbolic structured AMR applications
          * Consideration of non-Cartesian geometries
          * Shock-induced combustion
          * Fluid-structure interaction
          * Combressible turbulence
   4. Further topics
          * Using the SAMR approach for geometric multigrid
methods
          * Discussion of available SAMR software
          * Practical implementation considerations
          * Demonstration of the SAMR framework AMROC
   5. Overlapping grids
          * Spatial approximations
          * Interpolation
   6. A++/P++ arrays
          * Serial and parallel array classes for C++
   7. Overture classes
          * Graphics
          * Geometry, grids and grid functions
          * Operators and boundary conditions
          * Sparse equation solvers and multigrid
          * AMR
   8. Grid generation
          * Component and grid generation
          * CAD and CAD repair
          * Overlapping grid generation
   9. Overture primer examples
  10. Composite Grid (CG) solvers
          * cgins: incompressible flow
          * cgcns: compressible flow
          * cgsm: elastic wave equation
          * cgmx: Maxwell's equations
          * cgmp: multi-physics solver
  11. Hands-on demonstration

Working Plan: The lectures on the theory will be
complemented by hands-on computational practicals during the
afternoons. The participants may bring their own laptops
(must operate on linux) to do the practicals and to connect
to the server. Instructions on essential software and how to
acquire it will be given at registration. We are able to
provide a number of laptops for the duration of the course.
There will be additional seminars which will demonstrate the
application of the short course topic in industrial and
academic practice.

Who should attend: The course is suitable for researchers
and practitioners from industry, research institutions and
consultancy organizations, doctoral students and
post-doctoral research fellows.