Computational Mathematics and Analysis

The AMS computational mathematics group encompasses the pipeline of approximations spanning the more theoretical aspects through to efficient computation. This includes techniques for the solution to deterministic/stochastic partial differential equations (PDEs) that arise in mathematical biology, control theory, fluid dynamics, uncertainty qualification, as well as techniques useful in visualization and computer-aided geometric design.  Emerging areas in the department include mean field games, optimization, and deep learning.

Research Faculty 

Greg Fasshauer

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AMS Department Head

  • Meshfree Approximation Methods
  • Radial Basis Functions
  • Approximation Theory
  • Numerical Solution of PDEs
  • Spline Theory
  • Computer-Aided Geometric Design

Mahadevan Ganesh

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AMS, CS, EE Professor 

  • Stochastic, model reduction and multiscle algorithms
  • Quantification of uncertainties in parallel scientific computing models
  • Free surface nonlinear evolutionary systems with applications.
  • Constructive approximations on spherical surfaces.
  • Fully discrete spectral boundary integral and boundary element methods.
  • Parallel evolutionary computations and analysis.
  • Radial basis functions based numerical schemes for PDEs

Jennifer Ryan

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  • Filtering techniques
  • Higher-order methods for numerical partial differential equations
  • Hyperbolic Conservation Laws

Samy Wu Fung

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  • Inverse Problems, Optimization, Deep Learning
  • Optimal Control, Mean Field Games