- Ph. D., University of Illinois at Urbana-Champaign, 1993
- RESEARCH: Astrophysics/Astronomy
- RESEARCH: Biophysics
- Office Location: 5739 AP&M
- Office Phone: 858-534-4899
- Email: email@example.com
- Administrative Contact:
- Professor Holst's general research background and interests are in a broad
area called computational and applied mathematics; his specific research
areas are in adaptive numerical methods, finite element methods, geometric
partial differential equations (PDE), biophysics, and general relativity.
His research projects center around developing mathematical techniques
(theoretical techniques in PDE and approximation theory) and mathematical
algorithms (numerical methods) for using computers to solve certain types
of mathematical problems called nonlinear PDE. These types of problems
arise in nearly every area of science and engineering; this is just a
reflection of the fact that physical systems that we try to manipulate
(e.g., the flow of air over an airplane wing, or the chemical behavior
of a drug molecule), or build (e.g., the wing itself, or a semiconductor),
or simply study (such as the global climate, or the gravitational field
around a black hole) are described mathematically by nonlinear PDE. In
simple cases, these problems can be simplified so that purely mathematical
techniques can be used to solve them, but in most cases they can only be
solved using sophisticated mathematical algorithms designed for use with
computers. Computational simulation of PDE is now critical to almost all
of science and engineering; the mathematicians provide the mathematical
tools and understanding so that scientists in physics, chemistry, biology,
engineering, and other areas can confidently use the modern techniques of
computational science in the pursuit of new understanding in their fields
of study. To learn more about Professor Holst's particular research
program, please see his webpage: http://ccom.ucsd.edu/~mholst/
- - M. Holst, G. Nagy, and O. Sarbach, Stability reversal in fluid models of black strings for high space dimensions. Preprint.
- - M. Holst, E. Lunasin, and G. Tsogtgerel, Partial Regularity Results for Generalized Navier-Stokes Equations. Preprint.
- - M. Holst, G. Tsogtgerel, and Y. Zhu, Adaptive Finite Element Approximation of Nonlinear Geometric PDE. Preprint.
- - M. Holst, R. Szypowski, and G. Tsogtgerel, The Cauchy Problem of Cosmological Topologically Massive Gravity in 2+1 Dimensions. Preprint.
- - B. Aksoylu, S. Bond, E. Cyr, and M. Holst, Adaptive Solution of the Poisson-Boltzmann Equation using Goal-Oriented Error Indicators. Preprint.
- - M. Holst, J. Ovall, and R. Szypowski, An Efficient, Reliable and Robust Error Estimator for Elliptic Problems in R3. Preprint.
- - M. Holst, G. Tsogtgerel, and Y. Zhu, Convergent Adaptive Finite Element Approximation of the Einstein Constraints. Preprint.
- - L. Chen, M. Holst, J. Xu, and Y. Zhu, Local Multilevel Preconditioners for Elliptic Equations with Jump Coefficients on Bisection Grids. Preprint.
- - L. Chen and M. Holst, Efficient Mesh Optimization Schemes Based on Optimal Delaunay Triangulations. Submitted for publication to Computer Methods in Applied Mechanics and Engineering.
- - Y. Cheng, J. Holst, J.A. McCammon, and A. Michailova, Multiscale Continuum Modeling and Simulation of Biological Processes: From Molecular Electro-Diffusion to Sub-Cellular Signaling Transduction. Submitted for publication.