In this paper, we propose some algorithms to solve the system of linear equations arising from the finite difference discretization on sparse grids. For this, we will use the multilevel structure of the sparse grid space or its full grid subspaces, respectively.

Finite difference methods (msc 65N06), Solution of discretized equations (msc 65N22), Multigrid methods; domain decomposition (msc 65N55)
Modelling, Analysis and Simulation [MAS]

Sprengel, F. (1999). Some remarks on multilevel algorithms for finite difference discretizationson sparse grids. Modelling, Analysis and Simulation [MAS]. CWI.