Scientific Computing


Marsha J. Berger   Leslie Greengard   Michael L. Overton   Olof B. Widlund   Margaret H. Wright   Denis Zorin

Scientific Computing has a long tradition at the Courant Institute, which was founded by Richard Courant at the dawn of the computer era. Computers were invented in the late 1940's and early 1950's for exactly one purpose: solving hard scientific and engineering problems which required too much numerical computation to do by hand. Now, virtually all branches of science and engineering rely heavily on computing. The traditional two branches of science are theoretical science and experimental science. Computational science is now often mentioned as a third branch of science, complementing theory and experiment. Many faculty at Courant, both in the Computer Science and Mathematics Departments, have strong interests in Scientific Computing, both in specific application areas and in general techniques and analysis that have broad applicability.

Marsha Berger's areas of research include computational fluid dynamics, adaptive methods for the numerical solution of pdes in complex geometries, and large-scale parallel computing. She developed techniques for automatic grid for complex geometries generation, needed, for example, to compute the flow around a full aircraft in three dimensions. Efficient simulation of complex flows require adaptive algorithms which concentrate the computational effort where it is most needed. Marsha Berger collaborates with NASA scientists; their jointly developed software is widely used for modeling of aerodynamic behavior in aviation and space launch vehicle projects.

Leslie Greengard's research is largely concerned with the development of fast and adaptive algorithms for computational problems in biology, chemistry, materials science, medicine, and physics. He is best-known for having developed the fast multipole method (FMM) with V. Rokhlin; the FMM is widely used in electromagnetics, astrophysics, molecular simulations, and fluid dynamics. He currently works on protein design, the analysis of "metamaterials", diffusion in complex geometry, and reconstruction methods for magnetic resonance imaging.

Michael Overton studies numerical algorithms in optimization and linear algebra. One of the primary directions of his work is semidefinite programming, which is linear programming in the space of real symmetric matrices with eigenvalue positivity constraints. Most recently, his research has focused on optimization problems involving eigenvalues and pseudospectra of nonsymmetric matrices, which arise in control applications.

Olof Widlund is interested in numerical algorithms for partial differential equations. He has worked extensively in domain decomposition algorithms for the large linear systems of algebraic equations that arise in many computational continuum mechanics problems, for example in fluid dynamics and elasticity. These algorithms are widely used for solving large-scale problems on parallel and distributed computers. Most recently, Olof Widlund's group has focused its work on FETI-DP and BDDC algorithms for elliptic systems, and on domain decomposition methods for electro-magnetics and mortar finite element methods.

Margaret Wright's work includes two parts: basic research into theory and algorithms in optimization and linear algebra; and solution of real-world optimization problems in science and engineering. In her work, the interplay between research and practice goes in both directions. Solving practical problems effectively demands application of her technical knowledge and skills; and the experience of working on a practical problem often inspires fundamental research that moves in new and unexpected directions.

Denis Zorin's interests span two areas: geometric modeling, with applications in computer graphics and computer-aided geometric design, and scientific computing and numerical algorithms. In geometric modeling, he works on efficient and accurate discretizations of various types of surface optimization problems, high-order representations for surfaces, including manifold-based and subdivision surfaces and applications to interactive surface and mesh manipulation. In numeral algorithms, he is interested in fast algorithms for solving boundary integral equations, arising from linear PDEs and their applications. Current efforts include a a general fast multipole-based solver for 3D nonhomogeneous PDEs and arbitrary geometries, and on fluid-deformable surface interactions for Stokes fluid.

Participating Faculty from other Departments

Yu Chen   Jonathan Goodman   Charles Peskin   Michael Shelley


Related Web Pages

Courant Math and Computing Laboratory   Numerical Analysis Seminar   NYU-Columbia Research and Training Group "Numerical Mathematics for Scientific Computing"

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