A Fast Geometric Multigrid Method for Curved Surfaces

We introduce a geometric multigrid method for solving linear systems arising from variational problems on surfaces in geometry processing, Gravo MG. Our scheme uses point clouds as a reduced representation of the levels of the multigrid hierarchy to achieve a fast hierarchy construction and to extend the applicability of the method from triangle...

Multigrid Methods for Partial Differential Equations Arising From Fluid Flow Problems

In the paper, we present multigrid methods for solving scalar conservation laws and convection diffusion equations that frequently arise from fluid flow problems. For scalar conservation laws, we present monotonicity preserving and total variation diminishing multigrid methods. We generalize the upwind-biased residual restriction and...

Multiscale Methods in Computational Fluid and Solid Mechanics

The basic idea of multiscale methods, namely the decomposition of a problem into a coarse scale and a fine scale, has in an intuitive manner been used in engineering for many decades, if not for centuries. Also in computational science, large-scale problems have been solved, and local data, for instance displacements, forces or velocities, have...

Multiscale Methods in Computational Fluid and Solid Mechanics

The basic idea of multiscale methods, namely the decomposition of a problem into a coarse scale and a fine scale, has in an intuitive manner been used in engineering for many decades, if not for centuries. Also in computational science, large-scale problems have been solved, and local data, for instance displacements, forces or velocities, have...

Towards an algebraic multigrid method for tomographic image reconstruction -- improving convergence of ART

In this paper we introduce a multigrid method for sparse, possibly rank-deficient and inconsistent least squares problems arising in the context of tomographic image reconstruction. The key idea is to construct a suitable AMG method using the Kaczmarz algorithm as smoother. We first present some theoretical results about the correction step and...