[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...
[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...
[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...
[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....
[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...
[Illinois] Multigrid Methods Conference
04 Feb 2016 | Workshops
HIGHLIGHTED TOPICSUncertainty QuantificationOptimization and Inverse ProblemsData Mining, Large Graphs, and Markov ChainsNonsymmetric and Indefinite ProblemsKrylov AcceleratorsHybrid Direct-Iterative Linear SolversParallel Multigrid on Multicore Systems and Heterogeneous ArchitecturesTime...
[Illinois] A Massively Parallel Semicoarsening Multigrid for 3D Reservoir Simulation on Multi-core and Multi-GPU Architectures
04 Feb 2016 | Online Presentations | Contributor(s): Abdulrahman Manea
In this work, we have designed and implemented a massively parallel version of the Semicoarsening Black Box Multigrid Solver , which is capable of handling highly heterogeneous and anisotropic 3D reservoirs, on a parallel architecture with multiple GPU’s. For comparison purposes, the...
[Illinois] On the Design of a Finite Element Multigrid Solver for Mimetic Finite Difference Schemes
04 Feb 2016 | Online Presentations | Contributor(s): Carmen Rodrigo
The focus of this work is to study the relation between mimetic finite difference schemes on triangular grids and some finite element methods for two model problems based on curl-rot and grad-div operators. With this purpose, modified Nédélec and Raviart-Thomas finite element...
[Illinois] Least-Squares Finite Element Method and Nested Iteration for Electromagnetic Two-Fluid Plasma Models
04 Feb 2016 | Online Presentations | Contributor(s): Christopher Leibs
Efforts are currently being directed towards a fully implicit, electromagnetic, JFNK-based solver, motivating the necessity of developing a fluid-based, electromagnetic, preconditioning strategy . The two-fluid plasma (TFP) model is an ideal approximation to the kinetic Jacobian. The TFP...
[Illinois] A Multigrid Method for the Self-Adjoint Angular Flux Form of the Radiation-Transport Equation Based on Cellwise Block Jacobi Iteration
04 Feb 2016 | Online Presentations | Contributor(s): Jeffrey Densmore
Cellwise block Jacobi iteration is a technique for radiation-transport calculations in which the angular flux for all directions is solved for simultaneously within a spatial cell with the angular flux in neighboring cells held fixed. Each step of the iteration then involves the inversion of a...
[Illinois] Understanding the Propagation of Silent Data Corruption in Algebraic Multigrid
04 Feb 2016 | Online Presentations | Contributor(s): Jon Calhoun
Sparse linear solvers from a fundamental kernel in high performance computing (HPC). Exascale systems are expected to be more complex than systems of today being composed of thousands of heterogeneous processing elements that operate at near-threshold-voltage to meet power constraints. The...
[Illinois] A Performance Comparison of Algebraic Multigrid Preconditioners on GPUs and MIC
04 Feb 2016 | Online Presentations | Contributor(s): Karl Rupp
Algebraic multigrid (AMG) preconditioners for accelerators such as graphics processing units (GPUs) and Intel's many-integrated core (MIC) architecture typically require a careful, problem-dependent trade-off between efficient hardware use, robustness, and convergence rate in order to...
[Illinois] Monolithic Multigrid Methods for Coupled Multi-Physics Problems
04 Feb 2016 | Online Presentations | Contributor(s): Scott Maclachlan
While block-diagonal and approximate block-factorization preconditioners are often considered for coupled problems, monolithic approaches can offer improved performance, particularly when the coupling between equations is strong. In this talk, we discuss the extension of Braess-Sarazin...
[Illinois] Application of Multigrid Techniques to Magnetic and Electromagnetic Systems
04 Feb 2016 | Online Presentations | Contributor(s): Benjamin Cowan
We discuss the use of multigrid techniques for several novel systems related to electromagnetics. One of these is the magnetostatic problem, in which systems can involve highly anisotropic and nonlinear materials. We describe the linear problems arising in several variations of this problem,...
[Illinois] Geometric Multigrid for MHD Simulations with Nedelec Finite Elements on Tetrahedral Grids
04 Feb 2016 | Online Presentations | Contributor(s): Chris Hansen
The Magneto-HydroDynamic (MHD) model is used extensively to simulate macroscopic plasma dynamics in Magnetic Confinement Fusion (MCF) devices. In these simulations, the span of time scales from fast wave dynamics to the desired evolution of equilibrium due to transport processes is large,...
[Illinois] Parallel Multigrid Preconditioner Based on Automatic 3D Tetradedric Meshes
04 Feb 2016 | Online Presentations | Contributor(s): Frederic Vi
Multigrid methods are efficient for solving large sparse linear systems. Geometric (GMG) and Algebraic Multigrid (AMG) have both their own benefits and limitations. Combining the simplicity of AMG with the efficiency of GMG lead us to the development of an Hybrid Multigrid preconditionner. From...
[Illinois] HPGMG: Benchmarking Computers Using Multigrid
04 Feb 2016 | Online Presentations | Contributor(s): Jed Brown
HPGMG (https://hpgmg.org) is a geometric multigrid benchmark designed to measure the performance and versatility of computers. For a benchmark to be representative of applications, good performance on the benchmark should be sufficient to ensure good performance on most important applications...
[Illinois] A Scalable Algorithm for Inverse Medium Problems with Multiple Sources
04 Feb 2016 | Online Presentations | Contributor(s): Keith Kelly
We consider the problem of acoustic scattering as described by the free-space, time-harmonic scalar wave equation given by (0.1) along with radiation boundary conditions. Here, is a point in , is the source term, and is the wavenumber. Our formulation is based on potential theory....
[Illinois] Support Graph Smoothing Techniques
04 Feb 2016 | Online Presentations | Contributor(s): Alyson Fox
Many tasks in large-scale network analysis and simulation require efficient approximation of the solution to the linear system $ Lx=b$, where $ L$ is a graph Laplacian. However, due to the large size and complexity of scale-free graphs, standard iterative methods do not perform optimally. The...
[Illinois] Task-Graph and Functional Programming Models: The New Paradigm
04 Feb 2016 | Online Presentations | Contributor(s): Ben Bergen
The Message Passing Interface (MPI) is an example of a distributed-memory communication model that has served us well through the CISC processor era. However, because of MPI's low-level interface, which requires the user to manage raw memory buffers, and its bulk-synchronous communication...