Development of Semi - coarsening Techniques

Departing from Mulder's semi-coarsening technique for rst-order PDEs, the notion of a grid of grids is introduced and a multi-level nite-volume technique for second order elliptic PDEs is developed. Various grid-transfer operators are investigated, in combination with damped Jacobi-relaxation. Convergence rates as they are predicted by Fourier local mode analysis are compared with practical measurements. The wide variety of grids at our disposal leads to the notion of coherent representations of a function on di erent grids. A sawtooth multi-level algorithm is proposed for the case of multiple semi-coarsening. A hierarchical set of basis-functions for nite volumes on sparse grids is brie y discussed. Note: This research was supported by the Brite-EuRam II Aeronautics R & D Programme of the European Communities (Contract No. AER2-CT92-0040). Note: This chapter has been published in Appl. Numer. Math. 19 (1996) 433{ 465.