Development of semi-coarsening and sparse-grid techniques

Departing from Mulder's semi-coarsening technique for first-order PDEs, the notion of a grid of grids is introduced and a multi-level finite-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 different grids. A sawtooth multi-level algorithm is proposed for the case of multiple semi-coarsening. A generalization of this technique towards Zenger's sparse grids is also investigated. A hierarchical set of basis-functions for finite volumes on sparse grids is briefly discussed.