Seventeenth Copper Mountain Conference on Multigrid Methods



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  • Uncertainty Quantification
  • Optimization and Inverse Problems
  • Data Mining, Large Graphs, and Markov Chains
  • Nonsymmetric and Indefinite Problems
  • Krylov Accelerators
  • Hybrid Direct-Iterative Linear Solvers
  • Parallel Multigrid on Multicore Systems and Heterogeneous Architectures
  • Time Parallel Methods
  • Iterative Methods in Applications (e.g., Electromagnetics, Energy, Environmental, MHD, Neutronics, Transport/Reaction)

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  • (2016), "Seventeenth Copper Mountain Conference on Multigrid Methods,"

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In This Workshop

  1. Optimal Order Multigrid Preconditioners for Linear Systems Arising in the Semismooth Newton Method Solution Process of a Class of Control-Constrained Problems

    18 Aug 2015 | Online Presentations | Contributor(s): Andrei Draganescu

    In this work we present a new multigrid preconditioner for the linear systems arising in the semismooth Newton method solution process of certain control-constrained, quadratic distributed optimal control problems. Using a piecewise constant discretization of the control space, each semismooth...

  2. Multilevel Solvers for High Resolution Electric Field Calculations

    18 Aug 2015 | Online Presentations | Contributor(s): Andrew Reisner

    High fidelity electric field calculations are a critical component in plasma simulations. In this this talk we consider the problem of a dielectric barrier discharge (DBD) wherein the electric field is calculated to support a compressible flow, thus requiring a highly efficient global solve. The...

  3. Iterative Solution Method for an Implicit Orbit Averaged Particle-in-Cell Model

    18 Aug 2015 | Online Presentations | Contributor(s): Benjamin Sturdevant

    Present kinetic simulations of turbulence in magnetized plasmas employ models from gyrokinetic theory, which is based on a number of ordering assumptions used to reduce the Vlasov-Maxwell system to eliminate high frequency phenomena. Recently, a second order accurate, implicit particle-in-cell...

  4. 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 [1], which is capable of handling highly heterogeneous and anisotropic 3D reservoirs, on a parallel architecture with multiple GPU’s. For comparison purposes, the...

  5. 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...

  6. 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 [1]. The two-fluid plasma (TFP) model is an ideal approximation to the kinetic Jacobian. The TFP...

  7. 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...

  8. 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...

  9. 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...

  10. 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...

  11. 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,...

  12. 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,...

  13. 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...

  14. HPGMG: Benchmarking Computers Using Multigrid

    04 Feb 2016 | Online Presentations | Contributor(s): Jed Brown

    HPGMG ( 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...

  15. 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....

  16. 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...

  17. 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...

  18. A Fast Multigrid Approach for Solving the Helmholtz Equation with a Point Source

    04 Feb 2016 | Online Presentations | Contributor(s): Eran Treister

    Solving the discretized Helmholtz equations with high wave numbers in large dimensions is a challenging task. However, in many scenarios, the solution of these equations is required for a point source. In this case, the problem can be be reformulated and split into two parts: one in a solution...

  19. Compatible Relaxation Based Geometric-Algebraic Multigrid

    04 Feb 2016 | Online Presentations | Contributor(s): Fei Cao

    We develop compatible relaxation algorithms for smoothed aggregation-based multigrid coarsening. In the proposed method, we use the geometry of the given discrete problem on the finest level to coarsen the system together with compatible relaxation to from the sparsity structure of the...

  20. Hub Snub: Removing Vertices with High Degree from Coarse-grid Correction

    04 Feb 2016 | Online Presentations | Contributor(s): Geoffry Sanders

    Network scientists often employ numerical solutions to linear systems as subroutines of data mining algorithms. Due to the ill-conditioned nature of the systems, obtaining solutions with standard iterative methods is often prohibitively costly; current research aims to automatically construct...

  21. On the Preconditioning of a High-Order RDG-based All-Speed Navier-Stokes Solver

    04 Feb 2016 | Online Presentations | Contributor(s): Brian Weston

    We investigate the preconditioning of an all-speed Navier-Stokes solver, based on the orthogonal-basis Reconstructed Discontinuous Galerkin (RDG) space discretization, and integrated using a high-order fully-implicit time discretization method. The work is motivated by applications in Additive...

  22. Is the Ideal Approximation Operator Always "Ideal" for a Particular C/F Splitting?

    04 Feb 2016 | Online Presentations | Contributor(s): Erin Molloy

    Given a coarse grid, the ideal prolongation operator is defined by , where the weight matrix,  , interpolates a set of fine grid variable (-points) from a set of coarse grid variable (-points), and the identity matrix, , represents the injection of -points to and from...

  23. Reducing Communication Costs for Sparse Matrix Multiplication within Algebraic Multigrid

    04 Feb 2016 | Online Presentations | Contributor(s): Grey Ballard

    We consider the sequence of sparse matrix-matrix multiplications performed during the setup phase of algebraic multigrid. In particular, we show that the most commonly used parallel algorithm is often not the most communication-efficient one for all of the matrix multiplications involved. By...

  24. Space-time constrained FOSLS with AMGe upscaling

    04 Feb 2016 | Online Presentations | Contributor(s): Panayot Vassilevski

    We consider time-dependent PDEs discretized in combined space-time domains. We first reduce the PDE to a first order system. Very often in practice, one of the equations of the reduced system involves the divergence operator (in space-time). The popular FOSLS (first order system least-squares)...

  25. Multilevel Markov Chain Monte Carlo for Uncertainty Quantification in Subsurface Flow

    04 Feb 2016 | Online Presentations | Contributor(s): Christian Ketelsen

    The multilevel Monte Carlo method has been shown to be an effective variance reduction technique for quantifying uncertainty in subsurface flow simulations when the random conductivity field can be represented by a simple prior distribution. In state-of-the-art subsurface simulation the...

  26. Discretization of Elliptic Differential Equations Using Sparse Grids and Prewavelets

    04 Feb 2016 | Online Presentations | Contributor(s): Christoph Pflaum

    Sparse grids can be used to discretize second order elliptic differential equations on a d-dimensional cube. Using Galerkin discretization, we obtain a linear equation system with  unknowns. The corresponding discretization error is  in the -norm. A major difficulty in...

  27. High Dimensional Uncertainty Quantification via Multilevel Monte Carlo

    04 Feb 2016 | Online Presentations | Contributor(s): Hillary Fairbanks

    Multilevel Monte Carlo (MLMC) has been shown to be a cost effective way to compute moments of desired quantities of interest in stochastic partial differential equations when the uncertainty in the data is high-dimensional. In this talk, we investigate the improved performance of MLMC versus...

  28. Stable Discretizations and Robust Block Preconditioners for Fluid-Structure Interaction Systems

    04 Feb 2016 | Online Presentations | Contributor(s): Kai Yang

    In our work we develop a family of preconditioners for the linear algebraic systems arising from the arbitrary Lagrangian-Eulerian discretization of some fluid-structure interaction models. After the time discretization, we formulate the fluid-structure interaction equations as saddle point...

  29. 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...

  30. 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...

  31. 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...

  32. Preconditioning for Divergence-Conforming Discretizations of the Stokes Equations

    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....

  33. 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...