Computational Mathematics


Crack Detection


An example of an inverse problem is that of determining the size and location of interior cracks in a surface by using nondestructive electrostatic measurements at the edges of the surface. Such cracks may occur, for example, in aging aircraft.


Numerical Conformal Mapping


Conformal mapping allows a complicated region in the plane to be transformed into a simpler region in such a way that important mathematical properties, such as angles between intersecting curves, are preserved. New numerical methods for determining these mappings have been recently developed for difficult regions, such as regions with several holes, as shown. These algorithms are useful tools in a variety of applications such as fluid dynamics, electrostatics, and elasticity.


Numerical Analysis

High performance computing, MHD, free surface/multiphase CFD, with applications in bubbly flows, phase transitions, interfacial instability, shock waves and plasma/tokamak physics.
Efficient numerical schemes for hyperbolic systems and electromagnetic waves, front tracking Quantum computing, adiabatic rapid passage.