Research

Research

The research group in scientific computing works on various problems arising from several exciting applications. Sophisticated numerical methods are developed  and used to solve these problems. Mathematical analysis is used to study convergence rates, qualitative behavior, stability and performance of these numerical methods. Below we list the numerical methods, problems that are being solved, and some applications. Finally, some current projects are discussed.

Numerical Methods and Mathematical Analysis

  • Higher order finite difference methods: ENO/WENO schemes, 
  • Runge-Kutta methods
  • Discontinuous Galerkin methods
  • Spectral element methods and higher order finite element methods
  • Structure preserving discretizations: mixed methods, non-conforming methods, finite volume methods
  • Dispersive analysis of numerical methods
  • A-posteriori error analysis and adaptive methods
  • Multi-scale finite element methods
  • Polynomial chaos techniques
  • Higher order splitting methods for fluid problems
  • Atomistic/continuum coupling methods

Problems/Equations

  • Conservation Laws and Hamilton Jacobi Equations
  • Fluid Dynamics: Complex Fluids, Bio-Fluids, Water waves
  • Solid Mechanics: Linear and nonlinear elasticity, plates and shells structures 
  • Fluid-structure interactions
  • Uncertainty Quantification
  • Kinetic Theory
  • Computational Biology
  • Stochastic PDEs 
  • Fractional PDEs/ non local operators

Applications

  • Semi-conductor devices
  • Study of aneurysms
  • Soft materials coming from various biological applications
  • Cosmology