Michael Holst directs the MCP Research Group, which is a
collection of research scientists, postdocs, doctoral students,
masters students, and undergraduate students from the
Mathematics and Physics Departments at UCSD.
Other CCoM faculty are often involved in the research.
The group is supported by NSF, DOE, NIH, DOD, and other funding awards for
research projects in several areas of computational mathematics
and mathematical physics.
The research areas covered by the group include:
General Research Areas:
Numerical Analysis,
Applied Analysis,
Partial Differential Equations,
Mathematical Physics.
Specific Areas of Interest:
Adaptive Finite Element Methods,
Geometric PDE,
Biophysics,
General Relativity.
The group has active on-going research projects and
publishes in the following areas:
The MCP group meets in subgroups for research discussions
at various times during the week, and also takes part in the weekly
CCoM
and
CSME
seminars.
The research program of the group centers around mathematical and/or numerical
analysis problems in partial differential equations (PDE), usually involving
PDE systems arising in either biophysics (PDE models of biological systems)
or astrophysics (PDE problems in general relativity).
Our analysis-oriented research involves the intersection
of ideas and techniques from nonlinear PDE, linear and nonlinear functional
analysis, differential geometry, and global nonlinear analysis.
Our numerical analysis-oriented research typically involves a further
combination of these techniques with modern approximation theory,
iterative algorithms for linear and nonlinear equations,
finite element-type numerical methods, and modern parallel computers.
Our simulation-based work often involves the use and/or development of
The Finite Element ToolKit (FETK).
Graduate students in the group usually pursue their M.S. and/or Ph.D. degrees
in the Mathematics or Physics Departments with Michael Holst,
with a formal Specialization in Computational Science
through the graduate
Program in Computational Science,
Mathematics, and Engineering (CSME).
Current and former MCP senior research scientists working with Holst:
Daniel Reynolds
(Ph.D. 2003, Computational and Applied Mathematics, Rice University;
now at SMU)
Gabriel Nagy
(Ph.D. 1995, Theoretical Physics, University of Cordoba, Argentina;
now at Michigan State University)
Olivier Sarbach (Ph.D. 2000, Mathematical Physics, ETH;
now at University Michoacana)
Ivar Stakgold (Ph.D. 1949, Harvard; Emeritus Professor of Mathematical Sciences, University Delaware)
Herb Keller (Ph.D. 1954, NYU; Emeritus Professor of Applied Mathematics, Caltech)
Current and former MCP postdoctoral researchers working with Holst:
Ari Stern (Ph.D. 2008, Applied and Computational Mathematics, Caltech)
Yunrong Zhu (Ph.D. 2008, Mathematics, Penn State University)
Current and former MCP postdoctoral researchers working with Holst:
Current and former MCP undergraduate students working with Holst:
