Three mathematics faculty mentored students in Portland State University’s REU this summer

Professors Jay Gopalakrishnan, Mau Nam Nguyen, and Jeffrey Ovall directed students in three projects for Portland State University’s Research Experiences for Undergraduates (REU).

Research Experiences for Undergraduates is a National Science Foundation funded program matching talented students with university research projects across the country. Portland State University’s Computational Modeling Serving the City REU is unique in that the projects benefit the city of Portland. The REU introduces participating students to High Performance Computing (HPC) and provides access to a local HPC cluster through membership in the Portland Institute for Computational Science (PICS).  At the end of the ten-week, full-time program, students present in a public symposium what they learned.

Kiet Tran

Kiet Tran from Santa Rosa Junior College apprenticed under Dr. Gopalakrishnan. The research project was designed to display how mathematics guide the design of improved algorithms for solving complex differential equations. The city partner was a small Portland start-up company called Microstructure Engineering, who’s goal is to develop affordable computational tools for predicting the evolution of microstructural defects in crystalline materials like metals.   The city partner gave Kiet the knowledge of the physics of the problem. The group’s PhD students Dow Drake and Tata Goswami taught Kiet the basics of finite element methods and how to use the PICS supercomputer.

Kiet’s final report:
Modeling the Defects That Exist in Crystalline Structures, Kiet A. Tran

 

Karina Rodriguez

Karina Rodriguez from Heritage University was directed by Dr. Nguyen. The research project developed numerical algorithms accompanied by MATLAB codes to reconstruct images with missing or distorted pixels.  Karina explored further applications to others areas such as medical imaging, missing data recovery, and building movie recommendation systems.

Karina’s final report:
Numerical Algorithms for Solving Nonsmooth Optimization Problems and Applications to Image Reconstructions, Karina Rodriguez

 

Kevin Sweet

Kevin Sweet from Lewis & Clark College was mentored by Dr. Ovall.  The research project focused on development of finite element software for 3D linear elasticity simulations.  He used the PICS supercomputer extensively to write and test his code.  The eventual goal is to produce software that can handle realistic geological models related to phenomena such as landslides, lahars and floods. The community partner for this project was the US Geological Survey.

Kevin’s final report:
Discretization of the Hellinger-Reissner Variational Form of Linear Elasticity Equations, Kevin A. Sweet

Read more about Portland State University’s REU program.