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Research Information for Michael Holst
General Research Areas:
Applied Analysis,
Computational Mathematics,
Partial Differential Equations,
Mathematical Physics.
Specific Areas:
Adaptive Finite Element Methods,
Geometric PDE,
Biophysics,
General Relativity.
Bio/CV: Here is a brief bio
and a curriculum vitae.
The Mathematical and Computational Physics Group (MCP)
The MCP research group is a subset of people (research scientists, postdocs,
graduate, and undergraduate students) from the
Center for Computational Mathematics (CCoM)
that do research with Michael Holst.
Sometimes Randy Bank and other CCoM faculty are also involved in the research.
The group is supported by NSF, DOE, NIH, DOD, and other funding awards for
research projects in the general areas of computational mathematics
and mathematical physics.
The group has active on-going research projects and
publishes in the following areas:
- Numerical Analysis and Approximation Theory
[10,
15,
17,
24,
25,
26,
29,
30,
33,
37,
38,
52,
53]
- Nonlinear Functional Analysis and Nonlinear PDE
[13,
39,
47,
48,
54]
- Geometric PDE/Global Nonlinear Analysis/General Relativity
[12,
24,
31,
47,
48,
53,
54]
- Navier-Stokes, Euler, MHD
[13,
54,
55]
- Electrostatics/Solvation Models in Biophysics
[3,
4,
5,
6,
10,
11,
19,
20,
21,
22,
23,
38,
44,
51,
52]
- Diffusion and Elasticity Models in Physics/Biophysics
[1,
27,
32,
34,
35,
36,
40,
41,
45,
46]
- Computational Geometry and Mesh Generation Algorithms
[14,
42,
43,
49,
50]
- Parallel Computing Algorithm Design and Analysis
[2,
16,
18,
21,
23,
28]
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 Univ.)
- Olivier Sarbach (Ph.D. 2000, Mathematical Physics, ETH;
now at Univ. Michoacana)
- Ivar Stakgold (Ph.D. 1949, Harvard; Emeritus Professor of Mathematical Sciences, Univ. 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)
-
Ryan Szypowski (Ph.D. 2008, Mathematics, UCSD)
-
Evelyn Lunasin (Ph.D. 2007, Mathematics, UC Irvine;
now at University of Arizona)
-
Gantumur Tsogtgerel (Ph.D. 2006, Mathematics, Utrecht;
now at McGill University)
-
Yongcheng Zhou (Ph.D. 2006, Mathematics, Michigan State University;
now at Colorado State University)
-
Zeyun Yu (Ph.D. 2006, Computer Science, UT Austin;
now at Univ. Wisconsin-Milwaukee)
-
Yuhui Cheng (Ph.D. 2007, Physical Chemistry, UCSD)
-
-
BenZhuo Lu (Ph.D. 2002, Biophysics,
University of Science and Technology of China)
-
-
Axel Malqvist
(Ph.D. 2005, Applied Mathematics, Chalmers University;
now at Uppsala)
-
Long Chen (Ph.D. 2005, Mathematics, Penn State;
now at UC Irvine)
-
Jennifer Erway (Ph.D. 2006, Mathematics, UCSD;
now at Wake Forest)
- Jason Suen (Ph.D. 2002, Chemical Engineering, MIT;
now at UCLA)
-
Hugh MacMillan (Ph.D. 2001, Mathematics, University of Colorado;
now at Clemson)
-
Steve Bond (Ph.D. 2000, Mathematics, University of Kansas;
now at UIUC)
- Feng Wang (Ph.D. 1997, PSU Mathematics;
now at Oracle)
Current and former MCP graduate students working with Holst:
- Sara Pollock
(mathematics/CSME
graduate student, UCSD)
-
Chris Deotte
(mathematics/CSME
graduate student, UCSD)
- Vyacheslav Kungertsev
(mathematics/CSME
graduate student, UCSD)
- Caleb Meier
(mathematics graduate student, UCSD)
- Alex Bilik
(mathematics/CSME
graduate student, UCSD)
-
Mohammad Ali Ebrahimi
(mathematics/CSME
graduate student, UCSD)
- Jonny Serencsa
(mathematics/CSME
graduate student, UCSD)
-
Danny McAllaster (mathematics graduate student, UCSD)
-
Ryan Szypowski (Ph.D. 2008, UCSD; now at UCSD)
-
Liz Fenwick (Ph.D. 2005, Mathematics, UCSD;
now at Far-Tech, Inc.)
- Kevin Scully (Ph.D. 2003, Mathematics, UCSD;
now at Aerospace Corp.)
-
Kaihsu Tai (Ph.D. 2002, Chemistry, UCSD, joint w/
J.A. McCammon
and
Palmer W. Taylor;
now at Oxford)
-
Nathan Baker (Ph.D. 2001, Chemistry, UCSD, joint w/
J.A. McCammon;
now at Wash. U.)
-
Burak Aksoylu (Ph.D. 2001, Mathematics, UCSD;
now at LSU)
Current and former MCP undergraduate students working with Holst:
- Hayley Miles-Leighton (2009-2010, Mathematics, UCSD; Math Honors Thesis)
- Nicholas Miller (2008-2010, Mathematics, UCSD; Math Honors Thesis)
- Jessica Lee (2009, Mathematics, UC Santa Cruz, Undergraduate Research Student)
- Kathryn Farrell (2008-2009, Mathematics, UCSD; Math Honors Thesis; Silagi Award)
- Cynthia Wood (2008, Mathematics, UCSD; CAMPS Summer Internship)
- Jennifer Webster (2007-2008, Mathematics, UCSD; Math Honors Thesis)
- Erik Eldridge (2007-2008, Computer Science, CSU San Marcos; CTBP Academic Year and Summer Internships)
- Jonathan Kommemi (2006-2008, Mathematics, UCSD; Enrichment/CalIT2 Summer Research Programs, Math Honors Thesis)
- Brian Nguyen (2006, Mathematics, UCSD; CalIT2 Summer Research Program)
- Patrick Sanan (2006, Mathematics, UCSD; Undergraduate Research Student)
- Ronald Page II (2006, Mathematics, UC Berkeley; UC STARS/UC LEADS Summer Research Program)
- Diego Onuchic (2005, Physics, UCSD; Undergraduate Research Student)
- Lucus Onuchic (2004, Mathematics, UCI; Undergraduate Research Student)
- James Noble (2003, Mathematics, UCSD; Math Honors Thesis)
- John Kleint (2002, Mathematics, UCSD; CalIT2 Summer Research Program)
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