Lawrence Livermore National Laboratory

Lawrence Livermore National Laboratory


Jacob B Schroder


Email: schroder2@llnl.gov
Phone: 925-422-1652


Jacob Schroder is a computational mathematician at the Center for Applied Scientific Computing.  The core direction of his research is numerical analysis and scientific computing.  His specific focus is on the numerical solution to partial differential equations (PDEs), iterative solvers for large sparse linear systems, and their associated preconditioning.  He approaches his research both from a software perspective centered on providing these methods to the broader community and also from a theoretical perspective centered on the development of new methods.  He is a member of the Scalable Linear Solvers (hypre) project.

Jacob earned his Ph.D. in computer science from the University of Illinois at Urbana-Champaign under the direction of Prof. Luke Olson.  His dissertation resulted in new methods for smoothed aggregation-based algebraic multigrid
(AMG), which proved effective for a variety of problems, e.g., anisotropic diffusion, Helmholtz, elasticity and Euler flow.  Next, he joined University of Colorado at Boulder for one year as a postdoc under Profs. Thomas Manteuffel and Stephen McCormick.  Jacob joined LLNL in September, 2011.

His current work focuses on improving the parallel efficiency of algebraic multigrid methods and also on basic multigrid research such as new adaptive multigrid methods.  A recent focus is parallel-in-time schemes where a multigrid scheme is applied to to the time dimension and allows for parallelization of traditional time-stepping methods. 


Areas: Numerical analysis, computational science, high performance computing
Keywords: Iterative methods, preconditioning, multigrid, numerical PDEs, high-order, parallel computing, parallel in time

Selected Publications

  1. R.D. Falgout, S. Friedhoff, Tz.V. Kolev, S.P. MacLachlan, and J.B. Schroder. Parallel Time Integration with Multigrid, SIAM J. Sci. Comput., (submitted). LLNL-JRNL-645325.
  2. R. D. Falgout and J. B. Schroder. Non-Galerkin Coarse Grids for Algebraic Multigrid. SIAM Journal on Scientific Computing, (to appear). LLNL-JRNL-641635.
  3. S. Friedhoff, R. Falgout, T. Kolev, S. MacLachlan and J. Schroder. A Multigrid-In-Time Algorithm for Solving Evolution Equations in Parallel. Student paper winner. Sixteenth Copper Mountain Conference on Multigrid Methods, Copper Mountain, Colorado. March, 2013.
  4. J. B. Schroder. Smoothed Aggregation Solvers for Anisotropic Diffusion. Numer. Linear Algebra Appl. pp. 296–312. 19 (2012).
  5. L. N. Olson, J. B. Schroder and R. S. Tuminaro.  A general interpolation strategy for algebraic multigrid using energy minimization.  SIAM J. Sci. Comput., 33:966-991, 2011.
  6. L. N. Olson and J. B. Schroder.  Smoothed aggregation multigrid solvers for high-order discontinuous Galerkin methods for elliptic problems.  J. Comput. Phys., 230:6959-6976, 2011.
  7. L. N. Olson and J. B. Schroder. Components of a More Robust Multilevel Solver for Emerging Architectures and Complex Applications. In SciDAC 2011 (2011).
  8. J. B. Schroder.  Generalizing smoothed aggregation-based algebraic multigrid.  Ph.D. Thesis. University of Illinois at Urbana-Champaign, Department of Computer Science, 2010.
  9. L. N. Olson and J. B. Schroder.  Smoothed aggregation for Helmholtz problems.  Numer. Linear Algebra Appl., 17:361-386, 2010.
  10. L. N. Olson, J. B. Schroder and R. S. Tuminaro.  A new perspective on strength measures in algebraic multigrid.  Numer. Linear Algebra Appl., 17:713-733, 2010.
  11. J. B. Schroder, R. S. Tuminaro and L. N. Olson. Generalized Strength-of-Connection in Algebraic Multigrid. CSRI Summer Proceedings 2007. pp. 12–26. (2007).
  12. V. E. Howle, J. B. Schroder and R. S. Tuminaro. The Effect of Boundary Conditions within Pressure- Convection Diffusion Preconditioners. Sandia National Laboratory Technical Report #2006-4466. July 2006.

Presentations

  1. Multigrid Reduction in Time: A Flexible and Non-Intrusive Method.  Third Workshop on Parallel-in-Time Integration.  May 27, 2014.
  2. Theoretical Advances Regarding Non-Galerkin Coarse Grid Operators for AMG. Thirteenth Copper Mountain Conference on Iterative Methods, Copper Mountain, Colorado. April 9, 2014.
  3. Non-Galerkin Coarse-Grid Operators for Parallel Algebraic Multigrid. Sixteenth Copper Mountain Conference on Multigrid Methods, Copper Mountain, Colorado. March 19, 2013.
  4. Energy-Minimization Interpolation for Adaptive Algebraic Multigrid. SIAM Conference on Applied Linear Algebra, Valencia, Spain. June 18–22, 2012.
  5. Non-Galerkin Coarse-Grid Operators for Parallel Algebraic Multigrid. Twelfth Copper Mountain Conference on Iterative Methods, Copper Mountain, Colorado. March 27, 2012.
  6. PyAMG Tutorial. Twelfth Copper Mountain Conference on Iterative Methods, Copper Mountain, Colorado. March 28, 2012.
  7. A General Energy-Minimization Strategy for Interpolation in Algebraic Multigrid.  Seventh International Congress on Industrial and Applied Mathematics, Vancouver, Canada. July 21, 2011.
  8. PyAMG Tutorial. Fifteenth Copper Mountain Conference on Multigrid Methods, Copper Mountain, Colorado. March 31, 2011.
  9. Smoothed Aggregation Solvers for Anisotropic Diffusion.  Fifteenth Copper Mountain Conference on Multigrid Methods, Copper Mountain, Colorado. March 28, 2011.
  10. Generalizing Smoothed Aggregation-Based Algebraic Multigrid.  Tech-X Corporation, Boulder, Colorado. July 29, 2010.
  11. A General Interpolation Strategy for Algebraic Multigrid Using Energy Minimization.  Eleventh Copper Mountain Conference on Iterative Methods, Copper Mountain, Colorado. April 5, 2010.
  12. Smoothed Aggregation Multigrid for Helmholtz Problems.  Fourteenth Copper Mountain Conference on Multigrid Methods, Copper Mountain, Colorado. March 23, 2009.
  13. A General Strength-of-Connection Concept in AMG.  Tenth Copper Mountain Conference on Iterative Methods, Copper Mountain, Colorado. April 7, 2008.
  14. Stability and Load Balancing in a NASA Global Circulation Model.  Southeast ACM Conference, Gatlinburg, Tennessee. November 22, 2003.

Software

PyAMG is a highly usable open source Python/C++ implementation of both classical algebraic multigrid and smoothed aggregation-based algebraic multigrid solvers.  3,000+ downloads from over 100 countries

Hypre is a benchmark library of high performance preconditioners that features parallel multigrid methods for both structured and unstructured grid problems.