Alec Dunton, Department of Applied Mathematics, PhD Candidate

Matrix Methods for Data Compression and Reduced Order Modeling in Large-Scale Simulations

The future of high-performance computing, specifically on future Exascale computers, will presumably see memory capacity and bandwidth fail to keep pace with data generated, for instance, from massively parallel partial differential equation (PDE) systems. Current strategies proposed to address this bottleneck entail the omission of large fractions of data, as well as the incorporation of in situ compression algorithms to avoid overuse of memory. To ensure that post-processing operations are successful, this must be done in a way that a sufficiently accurate representation of the solution is stored. Moreover, in situations where the input/output system becomes a bottleneck in analysis, visualization, etc., or the execution of the PDE solver is expensive, the number of passes made over the data must be minimized. In the interest of addressing this problem, the first work focuses on the utility of pass-efficient, parallelizable, low-rank, matrix decomposition methods in compressing high-dimensional simulation data from turbulent flows. A particular emphasis is placed on using coarse representation of the data -- compatible with the PDE discretization grid -- to accelerate the construction of the low-rank factorization. This includes the presentation of a novel single-pass matrix decomposition algorithm for computing the so-called interpolative decomposition. The methods are described extensively and numerical experiments on two turbulent channel flow data are performed.
 

Results show that these compression methods can enable efficient computation of various quantities of interest in both the carrier and dispersed phases. The next three works highlighted in this talk are extensions of the first project.

Alec Dunton, Department of Applied Mathematics, PhD Candidate

Matrix Methods for Data Compression and Reduced Order Modeling in Large-Scale Simulations

The future of high-performance computing, specifically on future Exascale computers, will presumably see memory capacity and bandwidth fail to keep pace with data generated, for instance, from massively parallel partial differential equation (PDE) systems. Current strategies proposed to address this bottleneck entail the omission of large fractions of data, as well as the incorporation of in situ compression algorithms to avoid overuse of memory. To ensure that post-processing operations are successful, this must be done in a way that a sufficiently accurate representation of the solution is stored. Moreover, in situations where the input/output system becomes a bottleneck in analysis, visualization, etc., or the execution of the PDE solver is expensive, the number of passes made over the data must be minimized. In the interest of addressing this problem, the first work focuses on the utility of pass-efficient, parallelizable, low-rank, matrix decomposition methods in compressing high-dimensional simulation data from turbulent flows. A particular emphasis is placed on using coarse representation of the data -- compatible with the PDE discretization grid -- to accelerate the construction of the low-rank factorization. This includes the presentation of a novel single-pass matrix decomposition algorithm for computing the so-called interpolative decomposition. The methods are described extensively and numerical experiments on two turbulent channel flow data are performed.
 

Results show that these compression methods can enable efficient computation of various quantities of interest in both the carrier and dispersed phases. The next three works highlighted in this talk are extensions of the first project.