We consider the minimization problem with strictly convex, possibly nondifferentiable, separable cost and linear constraints. The dual of this problem is an unconstrained minimization problem with differentiable cost which is well suited for solution by parallel methods based on Gauss-Seidel relaxation. We show that these methods yield the optimal primal solution and, under additional assumptio...

A distributive Gauss–Seidel relaxation based on the least squares commutator is devised for the saddle-point systems arising from the discretized Stokes equations. Based on that, an efficient multigrid method is developed for finite element discretizations of the Stokes equations on both structured grids and unstructured grids. On rectangular grids, an auxiliary spacemultigridmethod using onemu...

In this letter, we propose a fast numerical solution for the steady state radiative transfer equation in order to calculate the path loss due to light absorption and scattering in various type of underwater channels. In the proposed scheme, we apply a direct non-uniform method to discretize the angular space and an upwind type finite difference method to discretize the spatial space. A Gauss-Se...

This talk corresponds to the paper 8] with the same name. 1 Motivation Multigrid solves a set of simultaneous linear equations optimally. That is the time and space used by the multigrid computation are proportional to N, the number of unknowns. In reality the performance of any computation is not just dictated by how many operations performed. The order of the operations and the layout of data...

We construct a formal connection on the Aomoto complex of an arrangement of hyperplanes, and use it to study the Gauss-Manin connection for the moduli space of the arrangement in the cohomology of a complex rank one local system. We prove that the eigenvalues of the Gauss-Manin connection are integral linear combinations of the weights which define the local system.