One of the great challenges in both scientific research and engineering design is the development of a numerical framework that allows scientists to handle the multiple temporal and higher dimensional spatial scales that play a role in virtually all disciplines. Applying advanced tools from mathematical analysis, my research focuses on developing and delivering advanced numerical tools to address the challenges in important science and engineering applications. Current projects in my group include the fast evaluation of electrostatic and hydrodynamic interactions in biomolecular systems; electromagnetic and acoustic wave propagations in inhomogeneous media; computational tools for integral equation methods; and compressible features in large data sets and their efficient processing in a network setting.