Research Group of Prof. Dr. M. Griebel
Institute for Numerical Simulation

  author = {T. Schiekofer and G. W. Zumbusch},
  title = {Software Concepts of a Sparse Grid Finite Difference
  booktitle = {Proceedings of the 14th GAMM-Seminar Kiel on Concepts of
		  Numerical Software},
  year = {1998},
  editor = {W. Hackbusch and G. Wittum},
  series = {Notes on Numerical Fluid Mechanics},
  publisher = {Vieweg},
  address = {Wiesbaden, Germany},
  pages = {11},
  note = {submitted},
  ps = { 1},
  pdf = { 1},
  annote = {refereed,CVD},
  abstract = {Sparse grids provide an efficient representation of
		  discrete solutions of PDEs and are mainly based on specific
		  tensor products of one-dimensional hierarchical basis
		  functions. They easily allow for adaptive refinement and
		  compression. We present special finite difference operators
		  on sparse grids that possess nearly the same properties as
		  full grid operators. Using this approach, partial
		  differential equations of second order can be discretized
		  straightforwardly. We report on an adaptive finite
		  difference research code implementing this on sparse grids.
		  It is structured in an object oriented way. It is based on
		  hash storage techniques as a new data structure for sparse
		  grids. Due to the direct access of arbitrary data
		  traditional tree like structures can be avoided. The above
		  techniques are employed for the solution of parabolic
		  problems. We present a simple space-time discretization.
		  Furthermore a time-stepping procedure for the solution of
		  the Navier Stokes equations in 3D is presented. Here we
		  discretize by a projection method and obtain Poisson
		  problems and convection-diffusion problems.}