This focusing of different research areas on real problems and the diversity of applications of solutions of real problems creates an atmosphere of interaction and cooperation within the department and the university, as well as with other major research institutions. Numerical analysis and scientific computing are active fields of research at Rensselaer. Investigations range from the study of fundamental problems in linear algebra to the development and analysis of numerical schemes for solving particular physical problems. Applications of these studies include reacting flows, shock wave propagation, semiconductor performance, biomathematics, acoustic signal propagation, and incompressible flow in various geometries. This research involves the recovery of internal physical properties of a system from boundary data or spectral data.
Mathematical models are ordinary or partial differential equations.
Current research applies functional analysis, numerical analysis, and optimization to study the nonlinear dependence of the unknown physical quantities on the available data. Applications include geophysics, mechanics, electrical engineering, and bioengineering. This research is concentrated on the theory of dynamical systems and its applications in physics and engineering. Dynamical systems arise as mathematical models in various applications such as mechanics, optics, electric circuits, solid-state physics, fluid dynamics, optimal control, and other fields. The aim of this research is to discover and to explain new and important phenomena found in experimental and numerical studies.