Gauss' Adaptive Relaxation for the Multilevel Solution
of Partial Differential Equations on Sparse Grids

C. Pflaum and U. Rüde Institut für Informatik Technische Universität München D-80290 München Germany


In combination with the multilevel principle, relaxation methods are among the most efficient numerical solution techniques for elliptic partial differential equations. Typical methods used today are derivations of the Gauss-Seidel or Gauss-Jacobi method. Recently it has been recognized that in the context of multilevel algorithms, the original method suggested by Gauss has specific advantages. For this method the iteration is concentrated on unknowns where fast convergence can be obtained by intelligently monitoring the residuals. We will present this algorithm in the context of a sparse grid multigrid algorithm. Using sparse grids the dimension of the discrete approximation space can be reduced additionally.

Contributed October 20, 1993.