11th GAMM-Workshop on

Multigrid and Hierarchic Solution Techniques


  A. Almendral  
  M. Bader  
  R. Bank  
  M. Bebendorf  
  S. Beuchler  
  D. Braess  
  C. Douglas  
  L. Grasedyck  
  B. Khoromskij  
  R. Kornhuber  
  B. Krukier  
  U. Langer  
  C. Oosterlee  
  G. Pöplau  
  A. Reusken  
  J. Schöberl  
  M.A. Schweitzer  
  S. Serra Capizzano  
  B. Seynaeve  
  D. Smits  
  O. Steinbach  
  R. Stevenson  
  M. Wabro  
  R. Wienands  
  Joachim Schöberl: Hierarchical shape functions based on explicit polynomial extension operators

The goal of this work is the construction of fast iterative solvers for matrix equations arising from high order finite elements. We focus on cheap block-Jacobi and block-Gauss-Seidel iterations, where the blocks are defined by the shape functions associated to edge-, face- and interior-nodes. Of course, the speed of convergence depends on the choice of the shape functions.

We present new shape functions leading to nearly optimal iteration numbers. The construction is based on polynomial extension operators. By the help of symbolic computing we could derive cheap recursion formulas for the efficient computation of the shape functions.

Numerical results for 2D and 3D problems are presented.

  This page was last modified Tue Aug 19 17:21:04 2003 by Ronald Kriemann.   Best viewed with any browser