New multigrid solver advances in TOPS

New Multigrid Solver Advances in TOPS

In this paper, we highlight new multigrid solver advances in the Terascale Optimal PDE Simulations (TOPS) project in the Scientific Discovery Through Advanced Computing (SciDAC) program. We discuss two new algebraic multigrid (AMG) developments in TOPS: the adaptive smoothed aggregation method (αSA) and a coarse-grid selection algorithm based on compatible relaxation (CR). The αSA method is sho...

Self-correcting Multigrid Solver

A new multigrid algorithm based on the method of self-correction for the solution of elliptic problems is described. The method exploits information contained in the residual to dynamically modify the source term (right-hand side) of the elliptic problem. It is shown that the self-correcting solver is more efficient at damping the short wavelength modes of the algebraic error than its standard ...

Towards a more fault resilient multigrid solver

The effectiveness of sparse, linear solvers is typically studied in terms of their convergence properties and computational complexity, while their ability to handle transient hardware errors, such as bit-flips that lead to silent data corruption (SDC), has received less attention. As supercomputers continue to add more cores to increase performance, they are also becoming more susceptible to S...

Multigrid solver for axisymmetrical 2D fluid equations

We have developed an efficient algorithm for steady axisymmetrical 2D fluid equations. The algorithm employs multigrid method as well as standard implicit discretization schemes for systems of partial differential equations. Linearity of the multigrid method with respect to the number of grid points allowed us to use 256×256 grid, where we could achieve solutions in several minutes. Time limita...

Some Recent Advances in Multigrid Methods 1