Jacob B SchroderEmail: 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 and the Parallel Time Integration with Multigrid (XBraid) 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 both classical spatial multigrid solvers and on parallel-in-time methods using a multigrid reduction strategy. Regarding classical spatial multigrid, Jacob focuses on improving the parallel efficiency of algebraic multigrid methods and also on basic multigrid research such as new adaptive multigrid methods. Jacob's parallel-in-time work applies a multigrid reduction scheme to the time dimension and allows for parallelization of traditional time-stepping methods. This work allows one to circumvent the sequential time integration bottleneck and to take advantage of the coming massive increase in concurrency at exascale.
Areas: Numerical analysis, computational science, high performance computing
Keywords: Iterative methods, preconditioning, multigrid, numerical PDEs, high-order, parallel computing, parallel-in-time
Selected Publications
- T. A. Manteuffel, L. N. Olson, J. B. Schroder, B. S. Southworth, A Root-node based algebraid multigrid method, Copper Mountain Special Section, SIAM J. Sci. Comput. (submitted), (2016). LLNL-JRNL-695797.
- A. Bienz, R.D. Falgout, W. Gropp, L.N. Olson, and J.B. Schroder, Reducing Parallel Communication in Algebraic Multigrid Through Sparsification, SIAM J. Sci. Comput., (to appear). LLNL-JRNL-673388. Supplementary material.
- R. D. Falgout, T. A. Manteuffel, B. O’Neill, and J. B. Schroder, Multigrid reduction in time for nonlinear parabolic problems, Copper Mountain Special Section, SIAM J. Sci. Comput. (submitted), (2016). LLNL-JRNL-692258.
- V. Dobrev, Tz. Kolev, N. A. Petersson, and J. B. Schroder, Two-level convergence theory for parallel-in-time multigrid, Copper Mountain Special Section, SIAM J. Sci. Comput. (submitted), (2016). LLNL-JRNL-692418.
- R.D. Falgout, T.A. Manteuffel, J.B. Schroder and B. Southworth, Parallel-in-time for moving meshes, Technical Report. LLNL-TR-681918.
- C. Ketelsen, T. Manteuffel and J. B. Schroder, Least-Squares Finite-Element Discretization of the Neutron Transport Equation in Spherical Geometry, SIAM J. Sci. Comput., pp. 71-89. 37 (2015). LLNL-JRNL-656198.
- R. D. Falgout, A. Katz, Tz. V. Kolev, J. B. Schroder, A. Wissink and U. M. Yang, Parallel Time Integration with Multigrid Reduction for a Compressible Fluid Dynamics Application, Technical Report. LLNL-JRNL-663416.
- R. D. Falgout, S. Friedhoff, Tz. V. Kolev, S. P. MacLachlan, and J. B. Schroder. Parallel Time Integration with Multigrid, SIAM J. Sci. Comput., pp. 635-661. 36 (2014). LLNL-JRNL-645325.
- R. D. Falgout and J. B. Schroder. Non-Galerkin Coarse Grids for Algebraic Multigrid. SIAM Journal on Scientific Computing, pp. 309-334. 36 (2014). LLNL-JRNL-641635.
- 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.
- J. B. Schroder. Smoothed Aggregation Solvers for Anisotropic Diffusion. Numer. Linear Algebra Appl. pp. 296–312. 19 (2012).
- 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.
- 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.
- L. N. Olson and J. B. Schroder. Components of a More Robust Multilevel Solver for Emerging Architectures and Complex Applications. In SciDAC 2011 (2011).
- J. B. Schroder. Generalizing smoothed aggregation-based algebraic multigrid. Ph.D. Thesis. University of Illinois at Urbana-Champaign, Department of Computer Science, 2010.
- L. N. Olson and J. B. Schroder. Smoothed aggregation for Helmholtz problems. Numer. Linear Algebra Appl., 17:361-386, 2010.
- 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.
- 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).
- 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.
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.
XBraid is a C/MPI implementation of the multigrid reduction in time (MGRIT) approach. It is a non-intrusive, scalable and parallel library for multigrid in time.
Presentations
- Multigrid Reduction in Time: Recent Theoretical Results. Fourteenth Copper Mountain Conference on Iterative Methods. Copper Mountain, Colorado. March 22, 2016.
- Multigrid Reduction in Time (MGRIT): A Flexible and Scalable Approach to Parallel-in-Time. Monash Workshop on Numerical PDEs. February 17, 2016.
- Multigrid Reduction in Time (MGRIT): An Overview. Fourth Workshop on Parallel-in-Time Integration. Dresden, Germany. May 27, 2015.
- A General Purpose Parallel-in-Time Approach. SIAM Conference on Computational Science and Engineering (CS&E). Salt Lake City, Utah. March 18, 2015.
- Multigrid Reduction in Time: A Flexible and Non-Intrusive Method. Third Workshop on Parallel-in-Time Integration. Juelich, Germany. May 27, 2014.
- Theoretical Advances Regarding Non-Galerkin Coarse Grid Operators for AMG. Thirteenth Copper Mountain Conference on Iterative Methods, Copper Mountain, Colorado. April 9, 2014.
- Non-Galerkin Coarse-Grid Operators for Parallel Algebraic Multigrid. Sixteenth Copper Mountain Conference on Multigrid Methods, Copper Mountain, Colorado. March 19, 2013.
- Energy-Minimization Interpolation for Adaptive Algebraic Multigrid. SIAM Conference on Applied Linear Algebra, Valencia, Spain. June 18–22, 2012.
- Non-Galerkin Coarse-Grid Operators for Parallel Algebraic Multigrid. Twelfth Copper Mountain Conference on Iterative Methods, Copper Mountain, Colorado. March 27, 2012.
- PyAMG Tutorial. Twelfth Copper Mountain Conference on Iterative Methods, Copper Mountain, Colorado. March 28, 2012.
- A General Energy-Minimization Strategy for Interpolation in Algebraic Multigrid. Seventh International Congress on Industrial and Applied Mathematics, Vancouver, Canada. July 21, 2011.
- PyAMG Tutorial. Fifteenth Copper Mountain Conference on Multigrid Methods, Copper Mountain, Colorado. March 31, 2011.
- Smoothed Aggregation Solvers for Anisotropic Diffusion. Fifteenth Copper Mountain Conference on Multigrid Methods, Copper Mountain, Colorado. March 28, 2011.
- Generalizing Smoothed Aggregation-Based Algebraic Multigrid. Tech-X Corporation, Boulder, Colorado. July 29, 2010.
- A General Interpolation Strategy for Algebraic Multigrid Using Energy Minimization. Eleventh Copper Mountain Conference on Iterative Methods, Copper Mountain, Colorado. April 5, 2010.
- Smoothed Aggregation Multigrid for Helmholtz Problems. Fourteenth Copper Mountain Conference on Multigrid Methods, Copper Mountain, Colorado. March 23, 2009.
- A General Strength-of-Connection Concept in AMG. Tenth Copper Mountain Conference on Iterative Methods, Copper Mountain, Colorado. April 7, 2008.
- Stability and Load Balancing in a NASA Global Circulation Model. Southeast ACM Conference, Gatlinburg, Tennessee. November 22, 2003.