A cost-effective multigrid projection operator

A Cost-Effective Multigrid Projection Operator

A Cost-eeective Multigrid Projection Operator

A novel heuristic residual analysis is proposed to derive a computationally cost-eeective residual projection operator in multigrid with the ve-point Red-Black Gauss-Seidel relaxation for solving the two dimensional Poisson equation. This optimal residual injection operator is as cheap as the trivial injection operator, but is more eecient than the costly full-weighting operator and achieves ne...

Multicloud: Multigrid convergence with a meshless operator

The primary objective of this work is to develop and test a new convergence acceleration technique we call multicloud. Multicloud is well-founded in the mathematical basis of multigrid, but relies on a meshless operator on coarse levels. The meshless operator enables extremely simple and automatic coarsening procedures for arbitrary meshes using arbitrary fine level discretization schemes. The ...

Operator splitting and multigrid methods

In general we will be searching for methods of solving problems containing terms where the courant condition is too restrictive for practical computation; typical in this regard is the inclusion of diffusion or thermal conduction which contain second derivatives in space implying that time steps must scale as ∆t ∝ 1/(∆x). In this case we can not solve the problems explicitly but rather solve (a...

Operator-based interpolation for bootstrap algebraic multigrid

Bootstrap Algebraic Multigrid (BAMG) is a multigrid-based solver for matrix equations of the form Ax = b. Its aim is to automatically determine the interpolation weights used in algebraic multigrid (AMG) by locally fitting a set of test vectors that have been relaxed as solutions to the corresponding homogeneous equation, Ax = 0, and are then possibly improved later using a multilevel eigensolv...