A fast-adaptive composite grid algorithm for solving the free-space Poisson problem on the cell broadband engine

Fast solvers for Poisson's equation with boundary conditions at infinity are an important building block for molecular dynamics. One issue that arises when this equation is solved numerically is the infinite size of the domain. This prevents a direct solution so that other concepts have to be considered. Within this paper a method is discussed that employs hierarchically coarsened grids to overcome this problem. Special attention has to be paid to the discretization at the grid interfaces. A finite volume approach is used for the same. The resulting set of linear equations is solved using a fast-adaptive composite grid algorithm. Emphasis is put on the implementation of the method on the STI cell broadband engine, a modern multi core processor, that is powerful in floating point operations and memory bandwidth. Code optimization techniques are applied as well as parallelization of the code to get maximum performance on this processor. For validation of the performance test runs are executed and the runtime is analyzed in detail. Copyright © 2010 John Wiley & Sons, Ltd.

Published by

Original source : http://dx.doi.org/10.1002%2Fnla.703...

Smoothness of Nonlinear and Non-Separable Subdivision Schemes. (arXiv:1002.0853v1 [math.NA])

We study in this paper nonlinear subdivision schemes in a multivariate
setting allowing arbitrary dilation matrix. We investigate the convergence of
such iterative process to some limit function. Our analysis is based on some
conditions on the contractivity of the associated scheme for the differences.
In particular, we show the regularity of the limit function, in $L^p$ and
Sobolev spaces.

Published by

Original source : http://arxiv.org/abs/1002.0853...

Convergence and Optimal Complexity of Adaptive Finite Element Methods. (arXiv:1002.0887v1 [math.NA])

In this paper, we study adaptive finite element approximations in a
perturbation framework, which makes use of the existing adaptive finite element
analysis of a linear symmetric elliptic problem. We prove the convergence and
complexity of adaptive finite element methods for a class of elliptic partial
differential equations. For illustration, we apply the general approach to
obtain the convergence and complexity of adaptive finite element methods for a
nonsymmetric problem, a nonlinear problem as well as an unbounded coefficient
eigenvalue problem.

Published by

Original source : http://arxiv.org/abs/1002.0887...