[Illinois] Data-Centric Models for Multilevel Algorithms
07 Feb 2016 | Online Presentations | Contributor(s): Samuel Guiterrez
Today, computational scientists must contend with a diverse set of supercomputer architectures that are capable of exposing unprecedented levels of parallelism and complexity. Effectively placing, moving, and operating on data residing in complex distributed memory hierarchies is quickly becoming an intractable problem for developers of parallel scientific software. Because of this, there is an increased desire to explore data-centric task-based programming models because of their ability to...
[Illinois] New FOSLS Formulation of Nonlinear Stokes Flow for Glaciers
07 Feb 2016 | Online Presentations | Contributor(s): Jeffrey Allen
This talk describes two First-order System Least-squares (FOSLS) formulations of the nonlinear Stokes flow used to model glaciers and ice sheets. The first is a Stress formulation and the second a Stress-Vorticity formulation. Both use fluidity, which is the reciprocal of viscosity and avoid the difficulties of infinite viscosity. Coercivity and continuity in appropriate Sobolev norms will be discussed. A Nested Iteration (NI), Newton-FOSLS-AMG approach is employed, in which the majority of...
[Illinois] Non-Blocking Conjugate Gradient Methods for Extreme Scale Computing
07 Feb 2016 | Online Presentations | Contributor(s): Paul Eller
Many scientific and engineering applications use Krylov subspace methods to solve large systems of linear equations. For extreme scale parallel computing systems, the dot products in these methods (implemented using allreduce operations in MPI) can limit performance because they are a synchronization point or barrier. Therefore we seek to develop Krylov subspace methods that avoid blocking allreduce operations and provide greater parallel efficiency.
We present a rearranged preconditioned...
[Illinois] Reducing Communication Costs for Sparse Matrix Multiplication within Algebraic Multigrid
07 Feb 2016 | Online Presentations | Contributor(s): Thomas Benson
Recent years have seen renewed interest in the numerical solution of the Stokes Equations. Of particular interest is the use of inf-sup stable pairs of finite elements for which weak enforcement of the incompressibility condition implies strong enforcement as well, such as with BDMelements. While there have been recent developments in preconditioning methods for the linear systems arising from this discretization, they are nonstandard preconditioning approaches. In this talk, we explore...
[Illinois] Range Decomposition: A Low Communication Algorithm for Solving PDEs on Massively Parallel Machines
07 Feb 2016 | Online Presentations | Contributor(s): Tom Manteuffel
The Range Decomposition (RD) algorithm uses nested iteration and adaptive mesh refinement locally before performing a global communication step. Only several such steps are observed to be necessary before reaching a solution within a small multiple of discretization error. The target application is peta- and exascale machines where traditional parallel numerical PDE communication patterns stifle scalability. The RD algorithm uses a partition of unity to equally distribute the error, and...