This project centered on the organization and support of a coordinated training program for postdoctoral researchers, graduate students and undergraduate students that gave equal emphasis to theory, computation and application — the three cornerstones of modern research in applied mathematics. A fundamental goal of the project was to provide the students and postdoctoral researchers with the intellectual and software tools that they need to engage in cutting-edge research in either a university or industry based environment. The program was designed to fund up to 6 postdoctoral researchers, 10 graduate students, and 3 undergraduate students during the academic year and summer session. These postdocs and students were organized into team-based research groups, with each team being coordinated and mentored by two or more of the Investigators. The Investigators, Randolph Bank (PI), Philip Gill (Co-PI), Michael Holst (Co-PI), Melvin Leok (Co-PI), and David Meyer (Co-PI), are Faculty in the UCSD Mathematics Department, and are also core members of the UCSD Center for Computational Mathematics (CCoM). The research topic of each assembled team will reflect the diverse range of areas in applied mathematics, computational and data science, and mathematical physics that are focus areas of the Investigators. The cross-disciplinary aspects of the training program were enhanced substantially by the interdisciplinary Computational Science, Mathematics, and Engineering (CSME) Doctoral Program at UCSD. The CSME Doctoral Program, the Center for Computational Mathematics, and the interdisciplinary CSME and CCoM Seminars, together form a unique, highly dynamic, interdisciplinary core research training environment for the personnel involved in the program. An outreach program included sponsoring a pair of two day  workshops providing an introduction to the research areas of the groups. Both drew a diverse nationwide audience approximately forty in size consisting of both graduate and undergraduate students.

The five Investigators participate in research programs covering a broad and diverse range of topics in applied mathematics, computational and data science, and mathematical physics. The research teams  assembled around these focus projects: (i) new algorithms for parallel computation with adaptive multilevel finite elements; (ii) optimization with ordinary or partial differential equation constraints; (iii) structure-preserving numerical methods for field theories and interconnected systems; (vi) geometric numerical methods for applications in mathematical physics; and (v) numerical methods for quantum computation. Each focus project involved one of the Investigators as the lead, together with overlapping subsets of the remaining Investigators with the appropriate synergistic background. Students and postdoctoral researchers associated with each project were trained in a vertically and horizontally integrated research environment involving not only the Investigators within the Mathematics Department, but also leading scientists from physics, chemistry, biology, and engineering units at UCSD through interaction with these faculty in the research projects and through their training in the CSME Doctoral Program.

The technology produced by this project  included mathematical algorithms, analyses, and numerical software providing  powerful tools for the exploration of multiscale models in physics, chemistry, biology, engineering and medicine. The results will potentially impact the formulation, analysis and development of methods for critical complex multiscale and multiphysics problems that have a fundamental impact on the US economy. Project-sponsored students and postdocs participated in the application of mathematical sciences to a range of research projects involving such diverse areas as undersea oil exploration, optimal power scheduling, drug design and organ modeling.  At the national level, the project made a positive contribution towards achieving the long range goal  of expanding the work force of well-prepared US citizens, nationals and permanent residents in the mathematical sciences. In addition, the project made an important contribution in the direction of the national priority of nurturing the crucial role of the basic mathematical sciences in interdisciplinary research. 

Last Modified: 09/18/2024
Modified by: Randolph E Bank