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 high-performance computing, iterative solvers for large sparse (non)linear systems, their associated preconditioning, and numerical PDEs. 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 both on 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, thus allowing for the parallelization of serial time-stepping methods. The result is a method that circumvents the sequential time integration bottleneck and takes advantage of the coming massive increase in concurrency at exascale. This approach can even be applied to non-PDE evolution problems, such as powergrid simulations and neural network training.
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, 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.
PyAMG is a highly usable open source Python/C++ implementation of both classical algebraic multigrid and smoothed aggregation-based algebraic multigrid solvers. Thousands of downloads from over a hundred countries.
Hypre is a benchmark library of high performance preconditioners that features parallel multigrid methods for both structured and unstructured grid problems. Thousands of downloads from over a hundred countries.
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. 200+ downloads in the last year.
The Lake City Algebraic Multigrid Summit. University of Colorado at Boulder. 10/2010, 9/2011, 10/2012, 9/2013, 10/2014, 9/2015, 10/2016, 9/2017.