Research

Scientific Computing

Scientific computing, also called numerical analysis or computational mathematics, is concerned with the design and analysis of algorithms for solving mathematical problems arising in many fields, especially in science and engineering, and with the implementation of such algorithms on high performance computers.

Members of the group conduct research on the development and analysis of numerical techniques for approximating mathematical models of physical systems and on algorithms for solving the resulting equations on high performance computer systems. Specific scientific and engineering applications considered include biological molecular dynamics, materials science, semiconductor simulation, astrophysics, and the design of solid propellant rockets.


Topics

Research topics in Scientific Computing at Illinois include:

  • Iterative solvers and preconditioners for linear systems
  • Mesh-based solvers for finite element structural analysis
  • High-order finite element and spectral element methods
  • Algebraic multigrid solvers and software
  • Nonlinear systems and optimization
  • Discrete exterior calculus
  • Geometric mechanics and control
  • Computational astrodynamics
  • Numerical simulation of astrophysical phenomena
  • Numerical simulation of biomolecules
  • Numerical simulation of electromagnetics
  • Numerical simulation of solid propellant rockets

Projects

Members of the Scientific Computing Group conduct research on the development and analysis of numerical techniques for approximating mathematical models of physical systems and on algorithms for solving the resulting equations on high performance computer systems. Most of the research in the group is motivated directly by various specific applications in science and engineering. Some research projects include:

Software

Software developed by Scientific Computing group members includes:

Seminars

The Scientific Computing group hosts several seminars throughout the academic year, including:

Lab Location & Resources

Scientific Computing maintains a research lab in room 4335 Siebel Center. The lab is equipped with four Sunblade 1500 workstations for general use. Students and faculty affiliated with CSE also have access to the 1536-processor Turing Xserve Cluster and several Sun servers.

Courses

Course Number Course Title Semester Offered
CS 357 Numerical Methods I Fall and Spring
CS 450 Numerical Analysis Fall and Spring
CS 457 Numerical Methods II Spring
CS 554 Parallel Numerical Algorithms Fall, odd years
CS 555 Numerical Methods for PDEs Spring
CS 556 Iterative & Multigrid Methods Fall, even years
CS 558 Topics in Numerical Analysis Irregularly

Learn more about the Scientific Computing Qualifying Exam

Faculty

William Gropp high performance scientific computing, with particular emphasis on parallel computing
Michael Heath numerical analysis and scientific computing: numerical linear algebra and optimization
Luke Olson numerical analysis, scientific computing, large-scale simulation
Anil Hirani numerical analysis, discrete exterior calculus, differential geometry, computational mechanics, computational astrodynamics

 

Scientific Computing Centers & Labs