Melvin Leok, Ph.D.

Professor of Mathematics

Director, Computational Science, Mathematics and Engineering
University of California, San Diego

Research Interests

Computational Geometric Mechanics

Applying discrete differential geometry and discrete Lagrangian and Hamiltonian mechanics to the construction of geometric structure-preserving numerical algorithms.

Computational Geometric Control Theory

Construction of real-time digital feedback control of mechanical systems using techniques from geometric control theory and computational geometric mechanics.

Numerical Analysis

Derivation of accurate and efficient numerical schemes with good long-time geometric stability properties by combining geometric integration with adaptive, spectral, and multiscale techniques.

Selected Honors & Education

Recent Awards

  • Newton Award for Transformative Ideas, DoD (2020)
  • Simons Fellowship in Mathematics
  • Kavli Frontiers of Science Fellow, National Academy of Sciences
  • NSF Faculty Early Career Development (CAREER) Award
  • SciCADE New Talent Award

Education

  • Ph.D. Control and Dynamical Systems, Caltech (2004)
  • M.S. Mathematics, Caltech (2000)
  • B.S. Mathematics (with honors), Caltech (2000)

Selected Publications

View Selected Publications & Preprints
Global Formulations of Lagrangian and Hamiltonian Dynamics on Manifolds
(with N. Harris McClamroch and Taeyoung Lee) Monograph published in the Interaction of Mechanics and Mathematics series (Springer).
Publisher Website
Lie Group Spectral Variational Integrators
(with J. Hall), Foundations of Computational Mathematics, 17(1), 199-257, 2017.
arXiv Journal
Spectral Variational Integrators
(with J. Hall), Numerische Mathematik, 130 (4), 681-740, 2015.
arXiv Journal
The Hamilton-Pontryagin Principle and Multi-Dirac Structures for Classical Field Theories
(with J. Vankerschaver, H. Yoshimura), Journal of Mathematical Physics, 53(7), 072903 (25 pages), 2012.
arXiv Journal
General Techniques for Constructing Variational Integrators
(with T. Shingel), Frontiers of Mathematics in China, 7(2), 273-303, 2012.
arXiv Journal
Discrete Poincaré Lemma
(with M. Desbrun, and J.E. Marsden), Appl. Numer. Math. 53 (2-4), 231-248, 2005.
Journal

Contact Information

Email [email protected]
Phone / Fax

Office: +1 (858) 534-2126

Fax: +1 (858) 534-5273

Mailing Address

Department of Mathematics
University of California, San Diego
9500 Gilman Drive, Dept. 0112
La Jolla, CA 92093-0112, USA