Research

My research interests center around the development and analysis of algorithms for the solution of partial differential equations that arise in engineering and science. I am particularly interested in bringing new tools to bear upon challenging problems that arise in the numerical approximation of pde's. For a brief summary of some of the problems I've worked on click here.

I am also interested in the design and analysis of mesh generation algorithms. Two dimensional mesh generation has evolved to a very satisfactory state. This mesh of New Zealand was generated by Steven Pav, a former Ph.D. student, who analyzed the performance of Ruppert's algorithm when small angles are present in the input. Subsequently we developed algorithms that could accommodate curved input constraints containing zero tangent angles, such as the cusps illustrated in this mesh.

This past decade has witnessed substantial breakthroughs in the analysis of three dimensional mesh generation algorithms. Building upon these developments a former student, Alex Rand, has developed a three dimensional mesh generation code (dir3) capable of meshing an arbitrary "piecewise linear complex". A beta release of this code is available at dir3 website ; you are welcome to download this code and we welcome comments and/or suggestions on your experiences using it.

Selected Publications