Supercomputers, an Invaluable Resource for Science and Engineering

Ismael Herrera Revilla
Department of Geophysics, UNAM, Mexico

Abstract: Supercomputers (SCs) are outstanding among the new computational tools. However, the most powerful SCs are massively parallelized and its application to science and engineering problems poses challenges that have to be overcome to profit effectively from this invaluable resource. Its efficient use requires the application of the most advanced parallel software. In particular, mathematical models of many systems of interest in Engineering and Science are constituted by a great variety of boundary-value problems (BVP) of partial differential equations [1], or systems of such equations, whose methods of solution in parallel have been developed throughout the last thirty years or so. In this keynote lecture a representative sample of such problems of science and engineering is presented together with some novel techniques that permit dealing with them in a unified and efficient manner.

About the speaker: Ismael Herrera Revilla is a Mexican born scientist, who studied chemistry, physics and mathematics as an undergraduate, at the National University of Mexico (UNAM) and did his Ph.D. at Brown University (Division of Applied Mathematics). Very soon after graduating and going back to Mexico, he reached top level positions at UNAM and has remained at the top level of the Mexican Scientific System, ever since. Also, he received the maximum appointment at the National System of Research (SNI), when it was created, in 1984. He has received the three most important scientific awards offered in his country: the "Premio Nacional de Ciencias", offered by the President of Mexico; the "Award for Outstanding Research", of the Mexican Academy of Sciences; and the "Luis Elizondo Award".

In addition, Herrera holds a "Chair of Excellence", at National Council for Science and Technology (CONACYT) -position which is shared by only a handful of scientists-, he is a member of the Advisory Scientific Board to the President of Mexico (Consejo Consultivo de Ciencias) and a founding member of the Board of Governors of the "Mexico-USA Foundation for Science". He has been president of the following scientific associations: the Mexican Science Academy, the National Academy of Engineering, the American Academy of Mechanics (Region III), the Union Geofísica Mexicana and the Asociación Latinoamericana de Hidrología Subterránea. He headed the Mexican Scientific Community when formulating the project that led to the creation of the National Council for Science and Technology and was the first Technical Director of that body. At UNAM, he has been Director of the Institute of Geophysics and of the Institute for Research in Applied Mathematics and Systems; in addition, he has actively participated in research not only as a member of those institutes, but also of the Institutes of Engineering and Mathematics. He has been visiting Professor and delivered conferences at the most important universities of the world. In the USA, he held a Tinker Distinguished Visiting Professorship at the Department of Mathematics and Mathematics Research Center, of the University of Wisconsin, in Madison. At Princeton University, he was appointed member of the Advisory Council of the Department of Civil Engineering and Operations Research, where he stayed eight years, 1985-93 (he was reelected for a second term). At Brown, immediately after graduation, in 1962, he was offered an Assistant Professorship, and later, in 1965, he was offered an Associate Professorship. In addition, in different periods he has been visiting professor at Brown University (Fall of 1964), UCLA, University of Delaware and University of Vermont.

In addition, he received the Distinguished Graduate Alumnus Award 2001, from Brown. His research activities exhibit two main streams: fundamental questions of Applied Mathematics and specific applications to different sciences, including engineering science. Outstanding among his achievements in basic questions is the creation of his Algebraic Theory of Boundary Value Problems (Partial Differential Equations), fundamental analysis tool for numerical methods, that has yielded a good number of numerical schemes such as the Localized Adjoint Method (LAM) and the Eulerian Lagrangian LAM (ELLAM), which has been very effective for the treatment of advection-dominated transport. Also, a Unified Theory of Domain-Decomposition Methods and the Indirect Method (or Trefftz-Herrera Method) stem from it. The Pitman Advanced Publishing Program devoted a book to his algebraic theory -"Boundary Methods: An Algebraic Theory" (1984)-, in the early stages of its development. He is the Mexican Mathematician most cited in the scientific literature. Because of his outstanding contributions to numerical methods for partial differential equations, he was invited by John Wiley to organize, together with George F. Pinder (who was at Princeton at the time), "Numerical Methods for Partial Differential Equations: An International Journal", of which he is a founding Editor; responsibility that he still holds (they were joined by John Whiteman, later on). In Ground-Water Hydrology, he is credited with being a founder of the Aquifer System Theory, together with Shlomo Neuman and P. A. Witherspoon. A fundamental contribution of his, in this field, are the integrodifferential equations for leaky aquifers, sometimes referred as "Herrera's Integrodifferential Equations".

In the Science of Materials, in collaboration with Morton E. Gurtin, he solved the controversy about the existence of wave fronts in viscoelastic materials, and started the development of the corresponding theory. Bernard D. Coleman and Clifford Truesdell joined in this latter effort, later on. The Encyclopedia of Physics (Handbuch der Physik, Springer-Verlag, Non-linear Theories of Mechanics) reproduced these results, in a Section devoted to them. In connection with seismological problems, he obtained the "Herrera's Orthogonality Relations" for Rayleigh waves. In Seismic Engineering, in collaboration with Emilio Rosenblueth, he did the pioneering methodology for predicting the seismic response of sedimentary valleys. Under Herrera's leadership many specific applications have been done in Mexico; just to mention a few: computational models for the building (by pumping) of artificial lakes, at Texcoco Basin (a fundamental piece for protecting Mexico City from flooding), the computational model for the geothermal field of Cerro Prieto, in Northwest Mexico (next to "El Centro", California), in 1980, and the first computational model for the groundwater system of Mexico City (70% of the Mexico City's water supply comes from this source). The study "Mexico City's Water Supply", that he proposed and coordinated for the National Research Council (USA) and the Mexican Academy of Sciences, received the "Miguel Aleman Ecology Prize" (1996). He has also a long and distinguished teaching carrier, associated mainly with the Departments of Science and Engineering, as well as the graduate programs of UNAM (Earth Sciences and Computing Science and Engineering). His contribution to college and graduate education in Mexico, has been quite important. In addition to the many students he has graduated, he organized the graduate programs in Earth Sciences and in Computing Science and Engineering, which have been very successful and have become fundamental pieces of graduate education, at UNAM. His book "Numerical Modeling in Science and Engineering" (John Wiley, 1988), must also be mentioned. He has written more than 200 research papers and has more than 3000 citations.
Back Keynotes