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

• Amir Adler
• Laurent Demanet Applied analysis, Scientific Computing
• Alan Edelman Scientific Computing, Numerical Linear Algebra, Random Matrices
• Steven Johnson Waves, PDEs, Scientific Computing
• Lu Lu Scientific Machine Learning
• Pablo Parrilo Optimization, Control Theory, Computational Algebraic Geometry, Applied Mathematics
• Gilbert Strang Numerical Analysis, Partial Differential Equations
• John Urschel Matrix Analysis, Matrix Computations, Spectral Graph Theory

Instructors & Postdocs

• Joseph Berleant Representation theory, Geometric algebra
• Shi Chen Machine Learning, Gradient Flows and Optimization, Inverse Problems
• Rikhav Shah

Researchers & Visitors

• Amir Adler
• Keaton Burns Numerical Methods, Fluid Dynamics
• Lu Lu Scientific Machine Learning

Graduate Students*

• Rodrigo Arrieta Candia Numerical methods for PDEs, Numerical Analysis, Scientific Computing, Computational Electromagnetism
• Diego Chavez Physical Applied Math, Waves
• Charlie Cowen-Breen PDE, machine learning, computer-assisted proofs
• Mara Daniels High-dimensional statistics, optimization, sampling algorithms, machine learning
• David Darrow Applied Math, Fluid Dynamics
• Joonsoo Lee Applied Probability, Optimization
• Evelyne Ringoot High-Performance Computing
• Sarah Snider Physical Applied Mathematics, Computational Geophysical Fluid Dynamics, Turbulence Theory

*Only a partial list of graduate students