# All Projects

## Galerkin Difference Approximations: Robust, Efficient, and High-Order Accurate PDE Discretization

*(Computation)*

Galerkin Difference (GD) methods are a new class of finite element approximations based on a Galerkin projection into a piecewise polynomial space described by a set of known basis functions.

## First-order methods for structured large-scale problems

*(Optimization)*

First-order methods (FOMs) or gradient-type methods find a solution of a problem by inquiring gradient and/or function value information. Compared to second-order or even higher-order methods, FOMs generally have much lower per-update complexity and much lower memory requirements.

## Fengyan's Project Page

*(Computation)*

The project introduction will be added shortly.

## High-Order Accurate Partitioned Algorithms for Fluid-Structure Interactions and Conjugate-Heat Transfer

*(Computation)*

Fluid-structure interaction (FSI) problems are important in many areas of engineering and applied science such as modeling of blood flow, flow-induced vibrations of structures, and wave energy devices, and there is significant interest in numerical simulation tools for such problems. Conjugate h

## Chjan's project page

*(Modeling)*

The project introduction will be added shortly.

## Mathematical Neuroscience

*(Modeling)*

This project concerns developing theoretical models of processing taking place in a number of brain areas, mostly early sensory pathways. One set of problems we have addressed concerns the asynchronous steady state of a sparsely, randomly connected neuronal network. Another set of problems add

## Rongjie's Project Page

*(Optimization)*

The project introduction will be added shortly.

## Optimization problems with complementarity constraints

*(Optimization)*

A complementarity constraint requires that one of a pair of variables should be zero. Optimization problems with complementarity constraints are widespread, arising for example in transportation problems, energy optimization, and sparse optimization.

## Rank minimization algorithms

*(Optimization)*

We investigate the use of nonconvex approaches to rank minimization problems, an alternative to widely-used convex approaches such as nuclear norm minimization.

## Modeling and Analysis of Wave Amplification in the Cochlea

*(Modeling)*

The fundamental open question in understanding how we hear concerns the role of a nonlinear feedback mechanism known as the cochlear amplifier.

## Research Training in Mathematical Modeling, Analysis and Computation

*(Modeling)*

This is an interdisciplinary program for undergraduates, graduate students, and postdoctoral associates that integrates modeling, analysis, and computations with contemporary experimental research.

## Advanced Computational Toolkit for Engineered Optical Materials (ACTEOM)

*(Computation)*

ACTEOM is a DARPA funded project, part of the EXTREME program, with the goal of developing an Advanced Computational Toolkit for Engineered Optical Materials (ACTEOM).