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Written works authored by Michael Holst
Color key used for article numbers:
- green
= accepted or published.
- magenta
= submitted and in review.
- black
= preprint or report.
Journal Articles
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Year
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No.
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Authors of Paper, Title of Paper.
Journal where Appearing, Other Information.
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2008
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65
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E. Bylaska, M. Holst, and J. Weare,
Adaptive Multilevel Finite Element Methods for
Solving the Electronic Schroedinger Equation.
Preprint.
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64
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M. Holst, G. Nagy, and O. Sarbach,
Stability reversal in fluid models of black strings
for high space dimensions.
Preprint.
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63
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L. Chen and M. Holst,
Mesh Adaptation Based on Optimal Delaunay Triangulation.
Preprint.
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62
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D. Estep, M. Holst, and A. Malqvist,
A Posteriori Error Analysis for Elliptic Problems with
Rough Data.
Preprint.
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61
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M.A. Ebrahimi and M. Holst and E. Lunasin,
The Navier-Stokes-Voight Model for Image Inpainting.
Preprint.
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60
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M. Holst and G. Tsogtgerel,
Adaptive Finite Element Approximation of Nonlinear Geometric PDE.
Preprint.
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59
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B. Aksoylu, S. Bond, and M. Holst,
Numerical Solution of the Poisson-Boltzmann Equation
with Optimal Complexity Methods.
Preprint.
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58
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M. Holst and Y. Zhou,
Adaptive Finite Element Approximation of
Coupled Finite Element-Boundary Element Methods.
Preprint.
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57
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M. Holst,
Analysis and Convergent Adaptive Solution of the
Einstein Constraint Equations (Plenary Paper).
Proceedings of the Eighteeth International Conference on
Domain Decomposition Methods, Jerusalem, Israel,
January 2008.
Preprint.
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2007
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56
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M. Holst and G. Tsogtgerel,
Convergent Adaptive Finite Element Approximation of the Einstein Constraints.
Preprint.
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55
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B. Aksoylu, D. Bernstein, S. Bond and M. Holst,
Generating initial data in general relativity
using adaptive finite element methods.
Submitted to Class. Quantum Grav.
(Paper at arXiv:0801.3142 [gr-qc])
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54
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O. Korobkin, B. Aksoylu, M. Holst, E. Pazos, and M. Tiglio,
Solving the Einstein constraints on
multi-block triangulations using finite elements.
Submitted to J. Comput. Phys.
(Paper at arXiv:0801.1823 [gr-qc])
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53
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S. Bond, M. Holst, Z. Yu, and Y. Zhou,
Practical adaptive finite element modeling techniques for the
Poisson-Boltzmann equation.
Preprint.
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52
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M. Holst, G. Nagy, and G. Tsogtgerel,
Far-from-constant mean curvature solutions of Einstein's constraint
equations with positive Yamabe metrics.
Physical Review Letters, Vol. 100 (2008), No. 16, pp. 161101-1--161101-4.
(Paper at arXiv:0802.1031 [gr-qc])
(Paper at APS)
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51
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M. Holst, G. Nagy, and G. Tsogtgerel,
Rough Solutions of the Einstein Constraints
on closed manifolds without near-CMC conditions.
Submitted for publication.
(Paper at arXiv:0712.0798 [gr-qc])
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50
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M. Holst, J. Kommemi, and G. Nagy,
Rough Solutions of the Einstein Constraint Equations
with Nonconstant Mean Curvature.
Submitted for publication.
(Paper at arXiv:0708.3410 [gr-qc])
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49
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T. Hayashi, M.E. Martone, Z. Yu, A. Thor, M. Doi,
M. Holst, M.H. Ellisman, and M. Hoshijima,
Three-dimensional reconstruction reveals new details
of membrane systems for calcium signaling in the heart.
Submitted to Journal of Cell Biology.
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48
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Z. Yu, M. Holst, T. Hayashi, C. Bajaj,
M. Ellisman, J.A. McCammon, and M. Hoshijima,
Multiscale geometric modeling of ventricular myocytes:
bridging the gap between imaging and simulation.
Submitted to Journal of Structural Biology.
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2006
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47
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Y. Cheng, C. Chang, Z. Yu, Y. Zhang, M. Sun, T.S. Leyh, M. Holst,
and J.A. McCammon,
Diffusional channeling in the sulfate activating complex:
combined continuum modeling and coarse-grained
Brownian dynamics studies.
Submitted to PLoS Computational Biology.
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46
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M. Holst and A. Malqvist,
Existence of weak solutions to the coupled nonlinear
Joule heating problem.
Submitted to Comm. Math. Sci.
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45
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S. Lu, A. Michailova, J. Saucerman, Y. Cheng Z. Yu, T. Kaiser, W. Li,
R. Bank, M. Holst, A. McCammon, T. Hayashi, M. Hoshijima,
P. Arzberger, and A. McCulloch,
Multi-Scale Modeling of Ventricular Myocytes:
Contributions of structural and functional heterogeneities
to excitation-contraction coupling in the normal and
failing rodent heart.
Accepted for publication in
IEEE Journal on Engineering in Medicine and Biology.
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44
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B. Lu, Y. Zhou, M. Holst, and J.A. McCammon,
Recent Progress in Numerical Methods for the
Poisson-Boltzmann Equation in Biophysical Applications.
Comm. Comput. Phys., Vol. 3 (2008), No. 5, pp. 973--1009.
(Paper at Comm. Comput. Phys.)
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43
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Z. Yu, M. Holst, Y. Cheng, and J.A. McCammon,
Feature-Preserving Adaptive Mesh Generation for Molecular Shape
Modeling and Simulation.
Journal of Molecular Graphics and Modeling,
Vol. 26 (2008), pp. 1370--1380.
(Paper at JMGM)
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42
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Z. Yu, M. Holst, and J.A. McCammon,
High-Fidelity Geometric Modelling for Biomedical Applications.
Accepted for Publication
in Finite Elements in Analysis and Design.
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41
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Y. Zhou, B. Lu, G.A. Huber, M. Holst and J.A. McCammon,
Continuum Simulations of Acetylcholine Consumption by
Acetylcholinesterase: A Poisson-Nernst-Planck Approach.
J. Phys. Chem. B, Vol. 112 (2008), pp. 270--275.
(Paper at JPCB)
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40
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B. Lu, Y. Zhou, G. Huber, S. Bond, M. Holst and J.A. McCammon,
Electrodiffusion: A continuum-modeling frame-work
for biomolecular systems with realistic spatiotemporal resolution.
J. Chem. Phys., Vol. 127 (2007), No. 13, pp. 135102.1--135102.16.
(Paper at J. Chem. Phys.)
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39
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Y. Zhou, M. Holst, and J.A. McCammon,
Nonlinear elastic modeling of macromolecular conformational
change induced by electrostatic forces.
J. Math. Anal. Appl., Vol. 340 (2008), No. 1, pp. 135--164.
(Paper at J. Math. Anal. Appl.)
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2005
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38
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L. Chen, M. Holst, and J. Xu,
The Finite Element Approximation of the
Nonlinear Poisson-Boltzmann equation.
SIAM J. Numer. Anal., Vol. 45 (2007), No. 6, pp. 2298--2320.
(Paper at SIAM)
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37
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L. Chen, M. Holst, and J. Xu,
Convergence and Optimality of Adaptive Mixed Finite Element Methods.
Accepted for Publication
in Math. Comp.
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36
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W. Li, N. Baker, K. Baldridge, J. McCammon, M. Ellisman, A. Gupta,
M. Holst, A. McCulloch, A. Michailova, P. Papadopoulos, A. Olson,
M. Sanner, and P. Arzberger,
National Biomedical Computation Resource (NBCR):
Developing End-to-End Cyberinfrastructure for
Multiscale Modeling in Biomedical Research.
CTWatch Quarterly: Trends and Tools in Bioinformatics
and Computational Biology, Vol. 2 (2006), pp. 6--17.
(Paper at CTWatch)
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35
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Y. Cheng, J.K. Suen, D. Zhang, S.D. Bond, Y. Zhang, Y. Song, N.A. Baker,
C.L. Bajaj, M.J. Holst and J.A. McCammon,
Finite Element Analysis of the Time-Dependent Smoluchowski
Equation for Acetylcholinesterase Reaction Rate Calculations.
Biophys. J., Vol. 92 (2007), pp. 3397--3406.
(Paper at Biophys. J.)
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34
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Y. Cheng, J.K. Suen, Z. Radic, S.D. Bond, M.J. Holst and J.A. McCammon,
Continuum simulations of acetylcholine diffusion with
reaction-determined boundaries in neuromuscular junction models.
Biophys. Chem. 127 (2007) 129-139.
(Paper at Biophys. Chem.)
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33
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B. Aksoylu and M. Holst,
Optimality of multilevel preconditioners
for local mesh refinement in three dimensions.
SIAM J. Numer. Anal., Vol. 44 (2006), No. 3, pp. 1005--1025.
(Paper at SIAM)
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2004
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32
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D. Zhang, J. Suen, Y. Zhang, Y. Song, Z. Radic,
P. Taylor, M. Holst, C. Bajaj, N. Baker,
and J. A. McCammon,
Tetrameric Mouse Acetylcholinesterase: Continuum Diffusion Rate Calculations
by Solving the Steady-State Smoluchowski Equation
Using Finite Element Methods.
Biophys. J., Vol. 88 (2005), pp. 1659--1665.
(Paper at Biophys. J.)
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31
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M. Holst, L. Lindblom, R. Owen, H.P. Pfeiffer, M.A. Scheel, and L.E. Kidder,
Optimal Constraint Projection for Hyperbolic Evolution Systems.
Phys. Rev. D, Vol. 70 (2004), No. 8, pp. 084017(1)--084017(17).
(Paper at arXiv:gr-qc/0407011v3)
(Paper at APS)
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30
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D. Estep, M. Holst, and M. Larson,
Generalized Green's Functions and the Effective Domain of Influence.
SIAM J. Sci. Comput., Vol. 26 (2005), No. 4, pp. 1314-1339.
(Paper at SIAM)
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2003
-to-
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29
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B. Aksoylu, S. Bond, and M. Holst,
An Odyssey into Local Refinement and Multilevel Preconditioning III:
Implementation and Numerical Experiments.
SIAM J. Sci. Comput., Vol. 25 (2003), No. 2, pp. 478-498.
(Paper at SIAM)
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1993
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28
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R. Bank and M. Holst,
A New Paradigm for Parallel Adaptive Meshing Algorithms.
SIAM Review, Vol. 45 (2003), No. 2, pp. 291-323.
(Paper at SIAM)
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27
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K. Tai, S. Bond, H. MacMillan, N. Baker, M. Holst, and J. A. McCammon,
Finite element simulations of acetylcholine diffusion in
neuromuscular junctions.
Biophys. J.,
84 (2003), pp. 2234-2241.
(Paper at Biophys. J.)
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26
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M. Holst,
Applications of domain decomposition and partition of unity methods
in physics and geometry (Plenary Paper).
Proceedings of the Fourteenth International Conference on Domain
Decomposition Methods, January 2002, Cocoyoc, Mexico,
I. Herrera, D. Keyes, O. Widlund, and R. Yates, eds.,
Domain Decomposition Methods in Science and Engineering,
Mexico City, Mexico, National Autonomous University
of Mexico (UNAM), June 2003, pp. 63-78.
(Paper at DDM.Org)
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25
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D. Estep, M. Holst, and D. Mikulencak,
Accounting for stability: a posteriori error estimates
for finite element methods based on residuals and variational analysis.
Communications in Numerical Methods in Engineering,
18 (2002), pp. 15-30.
(Paper at Wiley)
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24
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M. Holst,
Adaptive numerical treatment of elliptic systems on manifolds.
Advances in Computational Mathematics,
15 (2001), pp. 139-191.
(Paper at Kluwer)
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23
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N. Baker, D. Sept, S. Joseph, M. Holst, and J. A. McCammon.
Electrostatics of nanosystems: Application to
microtubules and the ribosome.
Proceedings of the National Academy of Sciences,
98 (2001), pp. 10037-10041.
(Paper at PNAS)
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22
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N. Baker, K. Tai, R. Henchman, D. Sept, A. Elcock, M. Holst, and J. A. McCammon,
Mathematics and Molecular Neurobiology.
Proceedings of the 3rd International Workshop on Methods
for Macromolecular Modeling, New York City, October 12-14, 2000.
In Computational Methods for Macromolecules: Challenges and Applications,
H. Gan and T. Schlick, eds., Springer-Verlag, New York, 2002.
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21
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N. Baker, D. Sept, M. Holst, and J. A. McCammon,
The adaptive multilevel finite element solution of the
Poisson-Boltzmann equation on massively parallel computers.
IBM Journal of Research and Development,
45 (2001), pp. 427-438.
(Paper at IBM)
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20
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N. Baker, M. Holst, and F. Wang,
Adaptive multilevel finite element solution of the
Poisson-Boltzmann equation II: refinement at solvent
accessible surfaces in biomolecular systems.
J. Comput. Chem., 21 (2000), pp. 1343-1352.
(Paper at Wiley)
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19
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M. Holst, N. Baker, and F. Wang,
Adaptive Multilevel Finite Element Solution of the
Poisson-Boltzmann Equation I: Algorithms and Examples.
J. Comput. Chem., 21 (2000), pp. 1319-1342.
(Paper at Wiley)
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18
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R. Bank and M. Holst,
A New Paradigm for Parallel Adaptive Meshing Algorithms.
SIAM J. Sci. Comput., Vol. 22 (2000), No. 4, pp. 1411-1443.
(Paper at SIAM)
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17
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S. Ashby, M. Holst, T. Manteuffel, and P. Saylor,
The role of the inner product in stopping criteria for
conjugate gradient iterations.
BIT, 41 (2001), pp. 26-53.
(Paper at BIT)
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16
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R.E. Bank, M. Holst, B. Mantel, J. Periaux, and C.H. Zhou,
CFD PPLTMG: Using a posteriori error estimates and domain decomposition.
ECCOMAS 98, John Wiley & Sons, New York, NY, 1998.
(Proceedings at Wiley)
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15
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M. Holst and S. Vandewalle,
Schwarz methods: to symmetrize or not to symmetrize.
SIAM J. Numer. Anal., Vol. 34 (1997), No. 2, pp. 699--722.
(Paper at SIAM)
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14
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D. Zorin, M. Holst, and P. Schroeder,
Subdivision-Based Surface Representations.
TeamCAD 97 Workshop, Atlanta, GA, 1997, pp. 35-38.
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13
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M. Holst and E. Titi,
Determining Projections and Functionals for
Weak Solutions of the Navier-Stokes Equations.
Recent Developments in Optimization Theory and Nonlinear Analysis,
Y. Censor and S. Reich, eds., vol 204 of Contemporary mathematics,
Providence, Rhode Island, 1997, American Mathematical Society.
(Book at AMS)
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12
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D. Bernstein and M. Holst,
A 3d finite element solver for the initial-value problem.
Proceedings of the 18th Texas Symposium on Relativistic Astrophysics,
December 16-20, 1996, Chicago, Illinois, A. Olinto, ed.,
World Scientific, 1996.
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11
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M. Holst and F. Saied,
Multigrid and domain decomposition methods for electrostatics problems.
Domain Decomposition Methods in Science and Engineering
(Proceedings of the Seventh International Conference on Domain
Decomposition Methods, October 27-30, 1993,
The Pennsylvania State University)
D. E. Keyes and J. Xu, eds.,
American Mathematical Society,
Providence, 1995.
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10
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M. Holst and F. Saied,
Numerical solution of the nonlinear Poisson-Boltzmann equation:
Developing more robust and efficient methods.
J. Comput. Chem., 16 (1995), pp. 337-364.
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9
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M. Holst and S. Vandewalle,
Schwarz methods: To symmetrize or not to symmetrize.
Proceedings of the Seventh Copper Mountain Conference
on Multigrid Methods, April 2-7, 1995, Copper Mountain, Colorado,
J. Mandel and S. McCormick, eds.,
NASA Langley Research Center,
1995.
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8
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M. Holst,
Kansas hosts macromolecular modeling workshop.
SIAM News, Vol. 28 (March 1995), No. 3, p. 11.
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7
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M. Holst,
Symposium honors Herbert B. Keller.
SIAM News, Vol. 28 (December 1995), No. 10, p. 3.
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6
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M. Holst, R. Kozack, F. Saied, and S. Subramaniam,
Protein electrostatics: Rapid multigrid-based Newton algorithm for solution
of the full nonlinear Poisson-Boltzmann equation.
J. of Biomol. Struct. & Dyn., 11 (1994), pp. 1437-1445.
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5
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M. Holst, R. Kozack, F. Saied, and S. Subramaniam,
Treatment of electrostatic effects in proteins: Multigrid-based-Newton
iterative method for solution of the full nonlinear Poisson-Boltzmann
equation.
Proteins: Structure, Function, and Genetics, 18 (1994), pp. 231-245.
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4
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M. Holst, R. Kozack, F. Saied, and S. Subramaniam,
Multigrid-based Newton iterative method for solving the full
Nonlinear Poisson-Boltzmann equation.
Biophysical Journal,
66 (1994), pp. A130-A130.
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3
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M. Holst and F. Saied,
Multigrid solution of the Poisson-Boltzmann equation.
J. Comput. Chem., 14 (1993), pp. 105-113.
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2
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F. Saied and M. J. Holst,
Multigrid Methods for Computational Acoustics on
Vector and Parallel Computers.
Computational Acoustics -- Volume 1 (Scattering, Supercomputing and
Propagation),
R. L. Lau, D. Lee, and A. R. Robinson (Editors),
North Holland, pp. 71--80, 1993.
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1
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F. Bodine, M. Holst, and T. Kerkhoven,
The three-dimensional depletion approximation computed with multigrid.
Proceedings of the International Workshop
on Computational Electronics.
Leeds, UK,
North Holland,
1993.
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Theses and Technical Reports
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Info
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No.
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Authors, Title. Other Information.
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19
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B. Aksoylu and M. Holst,
An Odyssey into Local Refinement and Multilevel Preconditioning II:
Stabilizing Hierarchical Basis Methods.
Institute for Computational Engineering and Sciences,
The University of Texas at Austin,
ICES Technical Report 05-04, January 2005.
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18
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B. Aksoylu and M. Holst,
An Odyssey into Local Refinement and Multilevel Preconditioning I:
Optimality of the BPX Preconditioner.
Institute for Computational Engineering and Sciences,
The University of Texas at Austin,
ICES Technical Report 05-03, January 2005.
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17
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B. Aksoylu, S. Bond, and M. Holst,
Implementation and Theoretical Aspects of the BPX
Preconditioner in the Three-Dimensional Local Mesh
Refinement Setting.
Institute for Computational Engineering and Sciences,
The University of Texas at Austin,
ICES Technical Report 04-50, October 2004.
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16
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M. Holst and E. Titi,
Determining Projections and Functionals for
Weak Solutions of the Navier-Stokes Equations.
Technical Report CRPC-96-43,
Applied Mathematics and CRPC,
California Institute of Technology,
1996.
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15
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M. Holst and S. Vandewalle,
Schwarz Methods: to Symmetrize or not to Symmetrize.
Technical Report CRPC-94-13,
Applied Mathematics and CRPC,
California Institute of Technology,
1994.
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14
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M. Holst, R. Kozack, F. Saied, and S. Subramaniam,
Treatment of Electrostatic Effects in Proteins:
Multigrid-based Newton Iterative Method for Solution
of the Full Nonlinear Poisson-Boltzmann Equation.
Technical Report UIUC-BI-MB-93-01,
The Beckman Institute for Advanced Science and Technology,
University of Illinois at Urbana-Champaign,
1993.
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13
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S. Ashby, M. Holst, T. Manteuffel, and P. Saylor,
The Role of the Inner Product in Stopping Criteria
for Conjugate Gradient Iterations.
Technical Report UCRL-JC-112586,
Lawrence Livermore National Laboratory,
1992.
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12
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M. Holst and F. Saied,
Multigrid Solution of the Poisson-Boltzmann Equation.
Technical Report UIUCDCS-R-92-1744,
Numerical Computing Group,
University of Illinois at Urbana-Champaign,
1992.
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11
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M. Holst,
MCLite: An Adaptive Multilevel Finite Element MATLAB Package
for Scalar Nonlinear Elliptic Equations in the Plane.
UCSD Technical report and guide to the MCLite software package.
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10
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M. Holst,
Some bounds on the number of determining nodes
for weak solutions of the Navier-Stokes equations.
Technical Report CRPC-95-1,
Applied Mathematics and CRPC,
California Institute of Technology,
1995.
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9
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M. Holst,
Algebraic Schwarz Theory.
Technical Report CRPC-94-12,
Applied Mathematics and CRPC,
California Institute of Technology,
1994.
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8
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M. Holst and F. Saied,
A short note comparing multigrid and domain decomposition
for protein modeling equations.
Technical Report CRPC-94-10,
Applied Mathematics and CRPC,
California Institute of Technology,
1994.
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7
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M. Holst,
A robust and efficient numerical method for nonlinear
protein modeling equations.
Technical Report CRPC-94-9,
Applied Mathematics and CRPC,
California Institute of Technology,
1994.
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6
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M. Holst,
The Poisson-Boltzmann equation:
Analysis and multilevel numerical solution.
(Monograph based on the Ph.D. Thesis below).
Applied Mathematics and CRPC,
California Institute of Technology,
1994.
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5
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M. Holst,
Notes on the KIVA-II software and chemically reactive fluid mechanics.
Technical Report UCRL-ID-112019,
Lawrence Livermore National Laboratory,
1993.
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(Ph.D.)
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4
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M. Holst,
Multilevel Methods for the Poisson-Boltzmann Equation.
PhD Thesis,
Numerical Computing Group,
University of Illinois at Urbana-Champaign,
October 1993.
(Published as Technical Report UIUCDCS-R-93-1821.)
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3
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M. Holst and F. Saied,
Parallel Performance of some Multigrid Solvers
for Three-Dimensional Parabolic Equations.
Technical Report UIUCDCS-R-91-1697,
Numerical Computing Group,
University of Illinois at Urbana-Champaign,
1991.
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2
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M. Holst and F. Saied,
Vector Multigrid: An Accuracy and Performance Study.
Technical Report UIUCDCS-R-90-1636,
Numerical Computing Group,
University of Illinois at Urbana-Champaign,
1990.
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(M.S.)
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1
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M. Holst,
CgCode: Software for solving linear systems
with conjugate gradient methods.
MS Thesis,
Numerical Computing Group,
University of Illinois at Urbana-Champaign,
May 1990.
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Books and Lecture Notes
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Info
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No.
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Authors, Title. Other Information.
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7
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M. Holst,
Numerical Methods for Nonlinear Elliptic Differential Equations: Part III
(Volume author: Klaus Boehmer).
Three chapters, 2008.
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6
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M. Holst,
Nonlinear Functional Analysis: Applications in
PDE and Numerical Analysis.
Lecture notes, 2007.
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5
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M. Holst,
Differential Geometry: Applications in
Shell Theory and General Relativity.
Lecture notes, 2007.
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4
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M. Holst,
Approximation Theory: Nonlinear Approximation and Numerical Analysis.
Lecture notes, 2005.
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3
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M. Holst,
Linear Functional Analysis: Applications in PDE and Numerical Analysis.
Lecture notes, 2000.
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2
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M. Holst,
Matrix Theory: Linear Operators on Finite-Dimensional Vector Spaces.
Lecture notes, 1997.
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1
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M. Holst,
Elliptic Equations: Theory and Finite Element Approximation.
Lecture notes, 1995.
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