Category: Sponsored Research

Ong Closes Contract from Lawrence Livermore National Laboratory

Benjamin Ong
Associate Professor Benjamin Ong

Benjamin Ong is the principal investigator (PI) on a project that has received a $45,000 research and development contract from the Lawrence Livermore National Laboratory, entitled “Systematic Approaches to Construct Coarse-Grid Operators for Multigrid Reduction in Time.”

Multigrid Reduction in Time (MGRIT) [2] uses multigrid reduction techniques to enable temporal parallelism for solving initial value problems. It is known that the convergence rate of MGRIT [3] depends in part on the choice of time-stepping operators on the fine- and coarse-grid, which we call the fine-grid operator and coarse-grid operator respectively. An “ideal” coarse-grid operator is the fine-grid operator applied to approximate the solution on the coarse time interval.

In practice, the ideal coarse-grid operator is never used as the computational cost destroys any parallel speed-up that could be obtained using MGRIT. Instead, a common choice for a coarse-grid operator is a simple re-discretization of the fine-grid operator, i.e., if a single-step method is used on the fine-grid with time-step size h, then the same single-step method is used on the coarse-grid with time-step size m h, where m is a specified coarsening factor.

Numerical simulations are increasingly important in the study of complex systems in engineering, life sciences, medicine, chemistry, physics, and even non-traditional fields such as social sciences. Dr. Ong is working to solve these large-scale evolution problems on modern supercomputing architectures by using a hierarchy of space-time grids to accelerate the solution on the finest time grid.


Time permitting, Dr. Ong will explore the connection between the proposed sequences of generated coarse-grid operators to those recently proposed by Vargas et al. [4].

[1] Daniel Crane. The Singular Value Expansion for Compact and Non-Compact Operators. PhD thesis, Michigan Technological University, 2020.

[2] R. D. Falgout, S. Friedhoff, Tz. V. Kolev, S. P. MacLachlan, and J. B. Schroder. Parallel time integration with multigrid. SIAM Journal on Scientific Computing, 36(6):C635–C661, 2014.

[3] Andreas Hessenthaler, Ben S. Southworth, David Nordsletten, Oliver RÅNohrle, Robert D. Falgout, and Jacob B. Schroder. Multilevel convergence analysis of multigrid-reduction-in-time. SIAM Journal on Scientific Computing, 42(2):A771–A796, 2020.

[4] David. A. Vargas. A general framework for deriving coarse grid operators for multigrid reduction in time. Technical report, Lawrence Livermore National Laboratory, 2023.

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Mathematical Sciences research ranked in the top 100 nationwide

In the National Science Foundation’s (NSF) latest rankings of universities by total research expenditures, Michigan Tech ranked 116th in the nation among public institutions and Tech’s atmospheric science and oceanography research ranked first in Michigan.

Nationally, atmospheric science research at Michigan Tech ranked 39th in research expenditures and oceanography ranked 53rd. Environmental science also ranked 53rd. Tech’s mechanical engineering research ranked 23rd in the nation, the highest ranking of all research fields at the University.

“Michigan Tech has been growing our capabilities in environmental science through our faculty hiring processes like the strategic faculty hiring initiative, our facility development efforts like the Great Lakes Research Center and in our equipment investments such as the cloud chamber in the Earth, Planetary, and Space Sciences Institute,” said Dave Reed, vice president for research. “NSF’s report reflects the impact of those investments and the significant research role that Michigan Tech is playing both nationally and within Michigan.”

The NSF report covered fiscal year 2015.

Other research areas at Tech that ranked in the top 100 nationwide include:

  • Biomedical engineering, 96th
  • Chemical engineering, 98th
  • Civil engineering, 92nd
  • Electrical engineering, 55th
  • Mechanical engineering, 23rd
  • Materials science and engineering, 61st
  • Mathematical sciences, 75th
  • Business and management, 73rd
  • Humanities, 98th
  • Visual and performing arts, 85th

The NSF report showed that research expenditures at Michigan Tech totaled $69.6 million for fiscal year 2015.