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

  author = {M. Griebel and G. W. Zumbusch},
  title = {Parallel Adaptive Subspace Correction Schemes with
		  Applications to Elasticity},
  journal = {Computer Methods in Applied Mechanics and Engineering},
  publisher = {Elsevier},
  address = {Amsterdam, The Netherlands},
  volume = {184},
  year = {2000},
  pages = {303--332},
  ps = { 1},
  pdf = { 1},
  annote = {refereed article,parallel},
  abstract = {In this paper, we give a survey on the three main aspects
		  of the efficient treatment of PDEs, i.e. adaptive
		  discretization, multilevel solution and parallelization. We
		  emphasize the abstract approach of subspace correction
		  schemes and summarize its convergence theory. Then, we give
		  the main features of each of the three distinct topics and
		  treat the historical background and modern developments.
		  Furthermore, we demonstrate how all three ingredients can
		  be put together to give an adaptive and parallel multilevel
		  approach for the solution of elliptic PDEs and especially
		  of linear elasticity problems. We report on numerical
		  experiments for the adaptive parallel multilevel solution
		  of some test problems, namely the Poisson equation and
		  Lam{\'e}'s equation. Here, we emphasize the parallel
		  efficiency of the adaptive code even for simple test
		  problems with little work to distribute, which is achieved
		  through hash storage techniques and space-filling curves.}