The mathematical treatment of realistic physics and engineering problems presents a number of difficulties, requiring, in many cases, the numerical solution of linear and nonlinear differential equations of high complexity. It is generally desirable to use numerical methods whose errors decrease rapidly with the refinement of the discretizations – so as to be able to achieve, within the computational infrastructures available, adequate predictions of phenomena and processes of scientific and technological interest. In this talk, we will present recent mathematical methods that have enabled the solution of challenging problems in areas such as fluid dynamics, acoustics, seismology, and electromagnetism. With the goal of achieving an informative description, we will visit some of the mathematical formulations of phenomena in the physical world, we will discuss the central mathematical elements of the new numerical methods, and we will demonstrate their results with a series of practical examples.
Oscar P. Bruno, Biographical Sketch
Dr. Bruno received his Ph.D. degree from the Courant Institute of Mathematical Sciences, New York University. Following graduation, he held a two-year position as Visiting Assistant Professor with the University of Minnesota, and he then joined the faculty of the Georgia Institute of Technology (Georgia Tech), where he served as Assistant and Associate Professor. After a four-year period with Georgia Tech, in 1995 he joined the faculty of the California Institute of Technology (Caltech), where he has served as Professor in the Department of Applied and Computational Mathematics since 1998, and as Executive Officer of that department during 1998-2000. Dr. Bruno’s research interests lie in areas of optics, elasticity and electromagnetism, remote sensing and radar, overall electromagnetic and elastic behavior of materials (solids, fluids, composites materials, multiple-scale geometries), and phase transitions. Dr. Bruno has directed 37 graduate students and postdocs during his career, and his research efforts have resulted in the publication of more than 100 refereed articles, and have been acknowledged by his plenary presentations at many international conferences, his service on editorial boards of important scientific journals, including the SIAM Journal of Applied Mathematics, the SIAM Journal on Scientific Computing, and the Proceedings of the Royal Society of London, and his election to honorary societies, most notably the Council for the Society for Industrial and Applied Mathematics. Dr. Bruno is a recipient of the Sigma-Xi faculty award, the Friedrichs Award for an outstanding dissertation in mathematics, a Young Investigator Award from the National Science Foundation. and a Sloan Foundation Fellowship. Dr. Bruno is a SIAM Fellowship, in the class of 2013, and a National Security NSSEFF Vannevar Bush fellow, in the class of 2016.