About

My research is interdisciplinary. I use tools from discrete calculus, functional analysis, measure theory, differential and computational geometry, and algebraic topology in developing methods for solving PDEs or constructing theoretical frameworks or computational interfaces for various computer science and engineering problems. The areas of my interest are computational fluid dynamics, multi-physics and multi-scale modeling, solid modeling, electromagnetism and interoperability.

I obtained my Ph.D. and M.Sc. in Mathematics from the University of Pittsburgh. My expertise lies in numerical analysis and scientific computing. I have taken my comprehensive exams in finite element analysis, partial differential equations and differential geometry. My M.Sc. thesis concerned the construction of a finite element method for the Stokes problem on rectangular meshes, and my Ph.D. dissertation concerned the construction of finite element methods for the Stokes and Navier-Stokes problems on cubical (with an extension to n-dimensions) and quadrilateral meshes. I have also completed M.Sc. in Electronics & Communication Engineering with a focus on the electromagnetic theory at Istanbul Technical University.

My postdoctoral research at the International Computer Science Institute at the UC Berkeley, concerned building a theoretical and an algorithmic framework for the interoperability between CAD systems based on the interchangeability of their models, and providing mathematical reviews for some of the existing geometry validation tools and techniques.

In my current postdoctoral research, I work on developing NURBS-Enhanced finite elements and building an interface to integrate several geometry and analysis tools.