Sparse-grid finite-volume multigrid for \(3D\)-problems (Q1894151)

This paper introduces a multigrid method based on Haar wavelets, and the method is applied to second-order, elliptic partial differential equations. It is shown that the question of which collection of Haar wavelets to use as a basis has significant influence on the computational efficiency. The paper provides a Fourier analysis of the convergence of the algorithm, and it is shown that \(W\)-cycles are more reliable than \(V\)-cycles for strongly anisotropic elliptic operators.