Computational Science & Numerical Analysis
Computational science is a key area related to physical mathematics. The problems of interest in physical mathematics often require computations for their resolution. Conversely, the development of efficient computational algorithms often requires an understanding of the basic properties of the solutions to the equations to be solved numerically. For example, the development of methods for the solution of hyperbolic equations (e.g. shock capturing methods in, say, gas-dynamics) has been characterized by a very close interaction between theoretical, computational, experimental scientists, and engineers.
Department Members in This Field
Faculty
- Laurent Demanet Applied analysis, Scientific Computing
- Alan Edelman Parallel Computing, Numerical Linear Algebra, Random Matrices
- Steven Johnson Waves, PDEs, Scientific Computing
- Pablo Parrilo Optimization, Control Theory, Computational Algebraic Geometry, Applied Mathematics
- Gilbert Strang Numerical Analysis, Partial Differential Equations
- John Urschel Matrix Analysis, Numerical Linear Algebra, Spectral Graph Theory
Instructors & Postdocs
- Pengning Chao Scientific computing, Nanophotonics, Inverse problems, Fundamental limits
- Ziang Chen applied analysis, applied probability, statistics, optimization, machine learning
- Andrew Horning Numerical Analysis, Scientific Computing, Large-Scale And Infinite-Dimensional Spectral Problems
- Adam Kay Hydrodynamic Quantum Analogues
Researchers & Visitors
- Keaton Burns PDEs, Spectral Methods, Fluid Dynamics
- Raphaël Pestourie Surrogate Models, AI, Electromagnetic Design, End-to-end Optimization, Inverse Design
Graduate Students*
- Rodrigo Arrieta Candia Numerical methods for PDEs, Numerical Analysis, Scientific Computing, Computational Electromagnetism
- Mo Chen Optimization, Scientific Computing
- Max Daniels High-dimensional statistics, optimization, sampling algorithms, machine learning
- Sarah Greer Imaging, inverse problems, signal processing
- George Stepaniants Statistical Learning of Differential Equations, Optimal Transport in Biology
- Songchen Tan computational science, numerical analysis, differentiable programming
*Only a partial list of graduate students