Before joining New York Tech, Eduardo Corona, Ph.D., held a James Van Loo Postdoctoral Fellowship at the University of Michigan. He received his Ph.D. in Mathematics from the Courant Institute of Mathematical Sciences (NYU) and his Bachelor of Science in Applied Mathematics from Instituto Tecnologico Autonomo de Mexico (ITAM), Mexico City.
Corona’s work focuses on the development of fast algorithmic frameworks for high-fidelity, large-scale computational physics. This requires the integration of innovative contributions in algorithmic structure, numerical methods and solvers, and high-performance computing tools.
The approach often requires numerical solution of boundary value problems for partial differential equations, which we reformulate as integral equations. This can yield considerable advantages, such as dimensionality reduction, bounded condition number, handling of topological and geometric complexity, and growth conditions.
The work addresses challenges in the development of:
- Integral equation formulation design (Fredholm of second kind)
- Singular and near-singular numerical integration schemes
- Fast summation algorithms (FMM)
- Fast hierarchical solvers (HSS, FMM, tensor train)
- Optimization-based contact resolution
Recent Projects and Research
- General applications of hierarchical compression and direct solution techniques for structured dense matrices
- Electromagnetic scattering from brain stimulation devices
- Acceleration of large-scale soil mechanics (modeled as granular media) with the U.S. Army’s TARDEC and University of Michigan’s Automotive Research Center
- Computational statistics and the acceleration of second-order optimization methods (scientific data compression)
- Simulation of particulate Stokes with applications to:
- Porous media flows;
- Materials self-assembly (MHD flows); and
- Microscopic swimming and cell mechanics (in collaboration with the Flatiron Institute)
Publications
- Yan, W., Corona, E., Malhotra, D., Shelley, M., Veerapaneni, S. “Resolving collisions in Stokes suspensions with an efficient and stable potential-free constrained optimization algorithm.” In preparation, 2018.
- Corona, E., Gorsich, D., Jayakumar, P., Veerapaneni, S. “A tensor train acceleration of non-smooth rigid body dynamics.” Applied Mechanics Reviews, 2018.
- Corona, E., Veerapaneni S. “Boundary integral equation analysis for suspensions of spheres in Stokes flow.” Journal of Computational Physics 362, 2018.
- Corona, E., Gomez, L., Michielssen, E. “Quantized tensor train format for compression of electromagnetic volume integral equations,” submitted to Microwave and Optical Technology Letters, 2017.
- Corona, E., Greengard, L., Rachh, M., Veerapaneni, S. “An integral equation formulation for rigid bodies in Stokes flow in three dimensions.” Journal of Computational Physics 332, 2017.
- Corona, E., Rahimian, A., Zorin, D. “A tensor train-accelerated solver for integral equations in complex geometries.” Journal of Computational Physics 334, 2015.
- Corona, E., Martinsson, P.G., Zorin, D. “HSSC Direct Solver Matlab library for integral equations on 2D boundaries and 2D volume.” Publicly available under a GNU general public license.
- Corona, E., Martinsson, P.G., Zorin, D. “An O(N) direct solver for integral equations on the plane.” Applied and Computational Harmonic Analysis 38 (2), 2015.
Professional Honors and Awards
- James Van Loo Postdoctoral Fellowship, University of Michigan, 2014 to 2018
Courses Taught at New York Tech
- Math 140 (Calculus II)
- Math 310 (Linear Algebra)