Fast algorithmic frameworks for scientific computing group

Our group's research agenda is focused in providing fast algorithmic frameworks for scientific computing, namely for efficient simulation of physics phenomena and scientific data compression. These frameworks often leverage existing knowledge or structure using fast numerical methods involving the interplay of mathematical analysis, linear algebra, optimization, statistics and high performance computing.

Our work features the numerical solution of boundary value problems for PDEs using well-behaved integral equation formulations. When implemented correctly, this approach can yield considerable advantages (dimensionality reduction, bounded condition number, handling of topological and geometric complexity).

The following are examples of areas of active research with our collaborators:

Large-scale, Multiphysics Particulate and Fluid-Structure Interaction

Research Challenge: how to develop and implement an efficient, black-box physics simulation platforms?

  • Integral Equation (BIE) reformulation of PDEs
  • Fast and accurate Integral kernel evaluation
  • Direct solvers and preconditioners for Integral Equations
  • Optimization-based collision resolution
  • Parallel implementation: Hybrid Open-MP / MPI

Large-scale, Multiphysics Particulate and Fluid-Structure Interaction

Terabytes of simulation data we can’t currently keep

Research Challenge: how to compress data so I can analyze and visualize it quickly, learn from it and keep it long-term?

  • Tensor factorization methods: exploit “data-structure” using low rank matrix approximation
  • Streaming data approach: compress data as it is generated.
  • Learning from compressed data: build surrogate models, apply machine learning (ML) algorithms to compressed representations.             

simulation data layout

Heterogeneous Power Grid Modeling and Simulation

Research Challenge: As we add more Inverter Based Resources (IBR) from renewables, our models and analysis of power grids are becoming obsolete.

  • Current modeling and control paradigms are based on AC, synchronous sources. Models for heterogeneous grids including DC, asynchronous sources are needed.
  • Energy-based modeling that can be automatically and efficiently scaled to simulate and analyze large-scale, complex power grid networks.
  • Fast algorithmic frameworks are needed to integrate the resulting large, stiff multiscale ODE systems.
  • Novel techniques for stability analysis are required to understand the transient and long-term behavior of heterogeneous power grids.