An important component of applied mathematics is the construction of mathematical tools to facilitate parsimonious descriptions of phenomena of interest. Such models must then be analyzed and turned into effective computations. Several faculty are active in this broad area. Peter Schröder uses tools from differential geometry for purposes of geometric and physical modeling in the context of computer graphics with an emphasis on structure preservation.
Houman Owhadi is known for his work on homogenization with non-separated scales, multiscale modeling, flow averaging and structure preserving integrators, and the introduction of gamblets (operator adapted wavelets with a game theoretic interpretation). Oscar Bruno studies theoretical problems concerning partial differential equations and integral equations, including regularity theory, characterization of singular behavior, and spectral properties of differential, pseudodifferential and integral operators. Andrew Stuart has interests in stochastic (partial) differential equations, multiscale methods and applications of this methodology in the sciences and engineering. Tom Hou has interests in multiscale analysis and computation and in developing effective computational and analytical methods to study singularity formation in the 3D incompressible Euler and Navier-Stokes equations.