Numerical Analysis and Scientific Computing

People
Research
Seminar
Graduate Program
Computing Resources

Industrial Mathematics Program

People

Faculty

Constantin Bacuta, Assistant Professor

Multilevel finite element theory; applications in incompressible flows and electromagnetism.

Richard Braun, Professor

Nonlinear BVPs and free boundary problems in fluid mechanics and materials science.

Tobin Driscoll, Associate Professor

High-order and spectral methods for differential equations; radial basis functions; numerical conformal mapping.

George Hsiao, Professor

Boundary integral equations, finite element methods. Applications in elasticity.

Russell Luke, Assistant Professor

Numerical Optimization, projection algorithms, with applications to image and signal processing and inverse problems

Peter Monk, Professor

Finite element methods, applications in computational electromagnetism and inverse problems.

Lou Rossi , Associate Professor

Lagrangian methods and fluid dynamics.

Gilberto Schleiniger, Associate Professor

Fluid flow: Transonic and viscoelastic flows.

Shangyou Zhang, Associate Professor

Finite element methods, multigrids.

Graduate Students

Research
There are a wide range of scientific computing and numerical analysis activities in our department. Research ranges from basic numerical analysis (finite element, boundary element and finite difference convergence theory) and fast methods (multigrid) to applications in materials science (foam evolution, phase transformations in crystalline alloys, approximation of microstructure, visco-elastic phenomena) and electromagnetism (scattering, inverse scattering and ferromagentism). Graduate students are welcome!

Can you hear the shape of a drum?
Here are two isospectral drums of different shapes.
(Pictures due to T. Driscoll)

Seminar
Numerical analysis and scientific computing presentations are often featured in the Applied Mathematics seminar series. This seminar series is currently organized by Dr. Pelesko and Dr. Schleiniger.

Graduate Program
Students wishing to study numerical analysis or scientific computing usually enroll in the Applied Mathematics graduate program (see The Graduate Program web pages for more details). There are a number of courses specifically intended for students interested in this area as well as topics courses. For example

M611 -- Introduction to Numerical Analysis and Scientific Computation I

M612 -- Intro to Numerical Methods for Partial Differential Equations

M838 -- Numerical Methods for Partial Differential Equations

Students in Applied Mathematics are also encouraged to take courses outside the department. Courses in engineering and computer science can build on the foundations offered above. Other courses in the Mathematical Sciences Department of interest to students of Numerical Analysis and Scientific Computing include

M616 -- Introduction to Applied Mathematics I
M617 -- Introduction to Applied Mathematics II
M694 -- Methods of Optimization
M806 -- Functional Analysis
M807 -- Complex Analysis
M810 -- Asymptotic and Perturbation Methods
M812 -- Inverse Problems
M835 -- Partial Differential Equations I
M836 -- Partial Differential Equations II

Funding
Besides the usual university and departmental funding for TAs and fellows some students are also supported directly by companies.

Computing Resources
The Department operates several computers for the support of research computing. All faculty and graduate students involved with scientific computing have personal workstations.

Click here for a comprehensive list of the department's computing resources

©2004, Department of Mathematical Sciences Last Modified: October 13, 2004 Comments? E-Mail Webmaster (www@math.udel.edu)

©2004, Department of Mathematical Sciences
Last Modified: October 13, 2004
Comments? E-Mail Webmaster (www@math.udel.edu)