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

  author = { F.~Koster},
  title = { Preconditioners for Sparse Grid Discretizations},
  year = {2001},
  institution = {SFB 256, Universit\"{a}t Bonn, Germany},
  number = {No. 746},
  annote = {unrefereed},
  abstract = {In this paper we deal with preconditioners for sparse grid
		  finite-difference-- and Petrov-Galerkin--discretizations of
		  the Poisson equation. We analyse the Jacobi-preconditioner
		  for the simple setting of non-adaptive grids and periodic
		  boundary conditions. The analysis shows that the resulting
		  condition numbers mainly depend on the underlying tensor
		  product Wavelets. For example, high order
		  Lifting-Interpolets lead to l2-condition numbers which are
		  essentially independent of the finest mesh size. Based on
		  this observation we introduce a so-called
		  Lifting-preconditioner for discretizations which use
		  Interpolets as trial-functions. Numerical examples show the
		  efficiency of the preconditioners for cases which are not
		  covered by our analysis, e.g., adaptive grids.},
  ps = { 1}