Pen Publications

Book Projects:
  • I. Stakgold and M. Holst, Green's Functions and Boundary Value Problems. John Wiley & Sons, New York, NY, Third Edition, 888 pages, 2011.
    PDF Preview  | Wiley ]
  • I. Stakgold and M. Holst, Boundary Value Problems: Theory and Applications. (Graduate Text In Preparation), 2013.
    PDF Preview ]
  • D. Estep and M. Holst, Applied Functional Analysis and Adjoint Techniques for Differential Equations. (Graduate Text In Preparation), 2015.
  • M. Holst, Mathematical and Computational Physics. (Monograph In Preparation), 2015.

Published Articles and Books by Research Area:
Published Articles and Books by Year:     (Ordered roughly by completion and submission, not necessarily by appearance.)

[ 2015-Present ] [ 2012-2014 ] [ 2009-2011 ] [ 2006-2008 ] [ 2003-2005 ] [ 2000-2002 ] [ 1993-1999 ]

NOTE: Many of the Articles Below Have Also Been Posted at [ arXiv.org ]. You can also go directly to the [ arXiv.org site ].

Color key used for article numbers:
  • green = accepted or published.
  • magenta = submitted and in review.
  • black = preprint or report.

Published Articles and Books by Number and Year:



Year No. Authors, Title. Journal where Appearing, Other Information.



Present
-to-
105 Y. Zhang, K. Key, J. Ovall, and M. Holst, Parallel goal-oriented adaptive finite element modeling for 3D electromagnetic exploration. Submitted for publication.
PDF ]
2015 104 E. Jurrus, D. Engel, K. Star, K. Monson, J. Brandi, L. Felberg, D. Brookes, L. Wilson, J. Chen, K. Liles, M. Chun, P. Li, T. Dolinsky, R. Konecny, D. Koes, J. Nielsen, T. Head-Gordon, W. Geng, R. Krasny, G. Wei, M. Holst, J. McCammon, and N. Baker, Improve- ments to the APBS biomolecular solvation software suite. Submitted for publication.
PDF  | arXiv:q-bio.BM/1707.00027 ]
103 A. Behzadan and M. Holst, On Certain Geometric Operators Between Sobolev Spaces of Sections of Tensor Bundles on Compact Manifolds Equipped with Rough Metrics. Submitted for publication.
PDF  | arXiv:math.AP/1704.07930 ]
102 A. Behzadan and M. Holst, Multiplication in Sobolev-Slobodeckij Spaces, Revisited. Submitted for publication.
PDF  | arXiv:math.AP/1512.07379 ]
101 A. Behzadan and M. Holst, Rough Solutions of the Einstein Constraint Equations on Asymptotically Flat Manifolds without Near-CMC Conditions. Submitted for publication.
PDF  | arXiv:gr-qc/1504.04661 ]
100 M. Holst and C. Meier, An Alternative Between Non-Unique and Negative Yamabe Solutions to the Conformal Formulation of the Einstein Constraint Equations. Submitted for publication.
PDF  | arXiv:gr-qc/1306.1210 ]
99 J. Erway and M. Holst, Barrier Methods for Critical Exponent Problems in Geometric Analysis and Mathematical Physics. Submitted for publication.
PDF  | arXiv:math.NA/1107.0360 ]
98 M. Holst, G. Tsogtgerel, and Y. Zhu, Local Convergence of Adaptive Methods for Nonlinear Partial Differential Equations. Submitted for publication.
PDF  | arXiv:math.NA/1001.1382 ]
97 R. Bank, M. Holst, R. Szypowski, and Y. Zhu, Finite Element Error Estimates for Critical Growth Semilinear Problems without Angle Conditions. Submitted for publication.
PDF  | arXiv:math.NA/1108.3661 ]
96 M. Holst, A. Mihalik, and R. Szypowski, Convergence and Optimality of Adaptive Mixed Methods on Surfaces. Submitted for publication.
PDF  | arXiv:math.NA/1404.1956 ]
95 M. Holst, A. Mihalik, and R. Szypowski, Convergence and Optimality of Adaptive Methods in the Finite Element Exterior Calculus framework. Submitted for publication.
PDF  | arXiv:math.NA/1306.1886 ]
94 M. Holst, C. Meier, and G. Tsogtgerel, Non-CMC Solutions of the Einstein Constraint Equations on Compact Manifolds with Apparent Horizon Boundaries. Submitted for publication.
PDF  | arXiv:gr-qc/1310.2302 ]
93 M. Holst and C. Tiee, Finite Element Exterior Calculus for Parabolic Evolution Problems on Riemannian Hypersurfaces. Accepted for publication in Journal of Computational Mathematics.
PDF  | arXiv:math.NA/1509.05524 ]
92 A. Gillette, M. Holst, and Y. Zhu, Finite Element Exterior Calculus for Evolution Problems. Journal of Computational Mathematics, Vol. 35, No. 2, 2017, 186–212.
PDF  | arXiv:math.NA/1202.1573 ]
91 M. Holst, O. Sarbach, M. Tiglio, and M. Vallisneri, The Emergence of Gravitational Wave Science: 100 Years of the Development of Mathematical Theory, Detectors, Numerical Algorithms, and Data Analysis Tools. Bull. Amer. Math. Soc., 53 (2016), 513-554 (42 pp).
PDF  | Journal  | arXiv:gr-qc/1607.05251 ]
90 K. Vincent, M. Gonzales, A. Gillette, C. Villongco, S. Pezzuto, J. Omens, M. Holst, and A. McCulloch, High-order interpolation methods for cardiac monodomain simulations. Frontiers in Physiology (2015), Vol. 6, No. 217, 1-9 (9 pp).
PDF  | Journal ]
89 M. Holst, S. Pollock, and Y. Zhu, Convergence of Goal-Oriented Adaptive Finite Element Methods for Semilinear Problems. Comput. Vis. Sci., 17 (2015), No. 1, 43-63 (21 pp).
PDF  | Journal  | arXiv:math.NA/1203.1381 ]
88 M. Holst and S. Pollock, Convergence of Goal-Orientied Adaptive Finite Element Methods for Nonsymmetric Problems. Numer. Meth. Part. Diff. Eq., 32 (2016), No. 2, 1098-2426 (29 pp).
PDF  | Journal  | arXiv:math.NA/1108.3660 ]
87 M. Holst and C. Meier, Non-CMC Solutions to the Einstein Constraint Equations on Asymptotically Euclidean Manifolds with Apparent Horizon Boundaries. Class. Quantum Grav., 32 (2014), No. 2, 1-25 (25 pp).
PDF  | Journal  | arXiv:gr-qc/1403.4549 ]



2014
-to-
86 M. Holst and C. Meier, Non-Uniqueness of Solutions to the Conformal Formulation. Accepted for publication in Annales Henri Poincare.
PDF  | arXiv:gr-qc/1210.2156 ]
2012 85 M. Balasubramanian, E. Arias-Castro, F. Medeiros, D. Kriegman, C. Bowd, R. Weinreb, M. Holst, P. Sample, and L. Zangwill, Detecting Glaucoma Progression from Localized Rates of Retinal Changes in Parametric and Nonparametric Statistical Framework with Type I Error Control. Investigative Ophthalmology and Visual Science, 55 (2014), No. 3, 1684-1695 (12 pp).
Journal ]
84 B. Ayuso de Dios, M. Holst, Y. Zhu, and L. Zikatanov, Multilevel Preconditioners for Discontinuous Galerkin Approximations of Elliptic Problems with Jump Coefficients. Math. Comp., 83 (2014), 1083-1120 (28 pp).
PDF  | Journal  | arXiv:math.NA/1012.1287 ]
83 M. Holst and C. Meier, Generalized Solutions to Semilinear Elliptic PDE with Applications to the Lichnerowicz Equation. Acta Applicandae Mathematicae, 130 (2014), No. 1, 163-203 (41 pp).
PDF  | Journal  | arXiv:gr-qc/1112.0351 ]
82 M. Holst and G. Tsogtgerel, The Lichnerowicz Equation on Compact Manifolds with Boundary. Class. Quantum Grav., 30 (2013), No. 20, 1-31 (31 pp).
PDF  | Journal  | arXiv:gr-qc/1306.1801 ]
81 T. Liao, Y. Zhang, P. Kekenes-Huskey, A. Michailova, M. Holst, J.A. McCammon, Multi-core CPU or GPU-accelerated Multiscale Modeling for Biomolecular Complexes. Mol. Based Math. Biol., July (2013), 1-9 (9 pp).
PDF  | Journal ]
80 M. Holst, R. Szypowski, and Y. Zhu, Two-Grid Methods for Semilinear Interface Problems. Numer. Methods Partial Differential Equations., 29 (2013), No. 5, 1729-1748 (20 pp).
PDF  | Journal  | arXiv:math.NA/1203.0339 ]
79 Z. Gao, Z. Yu, and M. Holst, Feature-preserving surface mesh smoothing via suboptimal Delaunay triangulation. Graphical Models, 75 (2013), No. 1, 23-38 (16 pp).
PDF  | Journal ]
78 L. Chen, M. Holst, J. Xu, and Y. Zhu, Local Multilevel Preconditioners for Elliptic Equations with Jump Coefficients on Bisection Grids. Computing and Visualization in Science, 15 (2012), No. 5, 271-289 (19 pp).
PDF  | Journal  | arXiv:math.NA/1006.3277 ]
77 P. Kekenes-Huskey, Y. Cheng, J. Hake, F. Sachse, J. Bridge, M. Holst, A. McCammon, A. McCulloch, A. Michailova, Modeling effects of L-type Ca2+ current and Na+-Ca2+ exchanger on Ca2+ trigger flux in rabbit myocytes with realistic t-tubule geometries. Frontiers in Physiology, 3 (2012), 1-14 (14 pp).
Journal ]
76 Z. Gao, Z. Yu, and M. Holst, Quality tetrahedral mesh smoothing via boundary-optimized Delaunay triangulation. Computer Aided Geometric Design, 29 (2012), No. 9, 707-721 (15 pp).
PDF  | Journal ]
75 M. Balasubramanian, D. Kriegman, C. Bowd, M. Holst, R. Winreb, P. Sample, and L. Zangwill, Localized Glaucomatous Change Detection within the Proper Orthogonal Decomposition Framework. Invest. Ophthalmol. Vis. Sci., 53 (2012), No. 7, 3615-3628 (14 pp).
Journal ]
74 J. Hake, A. Edwards, Z. Yu, P. Kekenes-Huskey, A. Michailova, A. McCammon, M. Holst, M. Hoshijima, and A. McCulloch, Modeling Cardiac Calcium Sparks in a Three-Dimensional Reconstruction of a Calcium Release Unit. J. Physiol., 590 (2012), No. 18, 4403-4422 (18 pp).
Journal ]
73 M. Holst and A. Stern, Semilinear Mixed Problems on Hilbert Complexes and Their Numerical Approximation. Found. Comput. Math. 12 (2012), No. 3, 363-397 (25 pp).
PDF  | Journal  | arXiv:math.NA/1010.6127 ]
72 M. Holst and A. Stern, Geometric variational crimes: Hilbert complexes, finite element exterior calculus, and problems on hypersurfaces. Found. Comput. Math. 12 (2012), No. 3, 263-293 (21 pp).
PDF  | Journal  | arXiv:math.NA/1005.4455 ]
71 B. Aksoylu, S. Bond, E. Cyr, and M. Holst, Goal-Oriented Adaptivity and Multilevel Preconditioning for the Poisson-Boltzmann Equation. J. Sci. Comput., 52 (2012), No. 1, 202-225 (23 pp).
PDF  | Journal  | arXiv:math.NA/1109.4092 ]
70 M.A. Ebrahimi, M. Holst, and E. Lunasin, The Navier-Stokes-Voight Model for Image Inpainting. IMA J. Appl. Math., doi:10.1093/imamat/hxr069 (2012), 1-26 (26 pp).
PDF  | Journal  | arXiv:math.NA/0901.4548 ]
69 Y. Cheng, P. Kekenes-Kuskey, J. Hake, M. Holst, J.A. McCammon, and A. Michailova, Multiscale Continuum Modeling and Simulation of Biological Processes: From Molecular Electro-Diffusion To Sub-Cellular Signaling Transduction. Comput. Sci. Disc., 5 (2012), 015002-015015 (13 pp).
PDF  | Journal ]
68 R. Bank, M. Holst, O. Widlund, and J. Xu, eds., Proceedings of the Twentieth International Conference on Domain Decomposition Methods, San Diego, California, USA. Springer, Berlin, Germany, 2012.
PDF Preview  | Journal ]
67 B. Ayuso De Dios, M. Holst, Y. Zhu, and L. Zikatanov, Multigrid Preconditioner for Nonconforming Discretization of Elliptic Problems with Jump Coefficients. Proceedings of the Twentieth International Conference on Domain Decomposition Methods, February 2011, San Diego, California, USA, R. Bank, M. Holst, O. Widlund, and J. Xu, eds.
PDF  | Journal  | arXiv:math.NA/1107.2160 ]
66 M. Holst, R. Szypowski, and Y. Zhu, Adaptive Finite Element Methods with Inexact Solvers for the Nonlinear Poisson-Boltzmann Equation. Proceedings of the Twentieth International Conference on Domain Decomposition Methods, February 2011, San Diego, California, USA, R. Bank, M. Holst, O. Widlund, and J. Xu, eds.
PDF  | Journal  | arXiv:math.NA/1107.2143 ]
65 M. Holst and V. Kungurtsev, Numerical Bifurcation Analysis of Conformal Formulations of the Einstein Constraints. Phys. Rev. D. 84 (2011), No. 12, 124038(1)-124038(8) (8 pp).
PDF  | Journal  | arXiv:math.NA/1107.0262 ]



2011
-to-
64 I. Stakgold and M. Holst, Boundary Value Problems: Theory and Applications. John Wiley & Sons, New York, NY, 496 pages, October 2011.
PDF Preview ]
2009 63 D. Estep, M. Holst, and A. Malqvist, Nonparametric Density Estimation for Randomly Perturbed Elliptic Problems III: Convergence, Complexity, and Generalizations. J. Appl. Math. Comput., 38 (2012), 367-387 (20 pp).
PDF  | Journal ]
62 Z. Yu, G. Yao, M. Hoshijima, A. Michailova, and M. Holst, Multi-Scale Modeling of Calcium Dynamics in ventricular Myocytes with Realistic Transverse Tubules. IEEE TBME Letters, Special Issue on Multi-Scale Modeling and Analysis for Computational Biology and Medicine, 58 (2011), No. 10, 2947-2951 (4 pp).
PDF  | Journal ]
61 M. Holst, J. Ovall, and R. Szypowski, An Efficient, Reliable and Robust Error Estimator for Elliptic Problems in R3. Appl. Numer. Math. 61 (2011), No. 5, 675-695 (21 pp).
PDF  | Journal  | Report ]
60 I. Stakgold and M. Holst, Green's Functions and Boundary Value Problems. John Wiley & Sons, New York, NY, Third Edition, 888 pages, February 2011.
PDF Preview  | Wiley ]
59 L. Chen and M. Holst, Efficient Mesh Optimization Schemes Based on Optimal Delaunay Triangulations. Comp. Meth. in Appl. Mech. and Engr. 200 (2010), No. 9-12, 967-984 (18 pp).
PDF  | Journal ]
58 M. Holst, M. Larson, A. Malqvist, and R. Soderlund, Convergence Analysis of Finite Element Approximations of the Joule Heating Problem in Three Spatial Dimensions. BIT 50 (2010), No. 4, 781-795 (15 pp).
PDF  | Journal ]
57 Y. Cheng, Z. Yu, M. Hoshijima, M. Holst, A. McCulloch, J.A. McCammon, A.P. Michailova, Numerical Analysis of Ca2+ Signaling in Rat Ventricular Myocytes with Realistic Transverse-Axial Tubular Geometry and Inhibited Sarcoplasmic Reticulum. PLoS Computational Biology 6 (2010), No. 10, e1000972:1-16 (16 pp).
PDF  | Journal ]
56 B. Lu, M. Holst, J.A. McCammon, and Y. Zhou, Poisson-Nernst-Planck Equations for Simulation of Biomolecular Diffusion-Reaction Processes I: Finite Element Solutions. J. Computational Physics. 229 (2010), 6679-7794 (16 pp).
PDF  | Journal ]
55 M. Holst, J.A. McCammon, Z. Yu, Y. Zhou, and Y. Zhu, Adaptive Finite Element Modeling Techniques for the Poisson-Boltzmann Equation. Comm. Comput. Phys. 11 (2012), No. 1, 179-214 (35 pp).
PDF  | Journal  | arXiv:math.NA/1009.6034 ]
54 M. Holst, E. Lunasin, and G. Tsogtgerel, Analysis of a General Family of Regularized Navier-Stokes and MHD Models. J. Nonlinear Science 20 (2010), No. 5, 523-567 (44 pp).
PDF  | Journal  | arXiv:math.AP/0901.4412 ]
53 O. Korobkin, B. Aksoylu, M. Holst, E. Pazos, and M. Tiglio, Solving the Einstein constraints on multi-block triangulations using finite elements. Class. Quant. Grav. 26 (2009), No. 14, 145007 (28 pp).
PDF  | Journal  | arXiv:gr-qc/0801.1823 ]
52 E. Bylaska, M. Holst, and J. Weare, An Adaptive Finite Element Method for Solving the Exact Kohn-Sham Equation of Density Functional Theory. Journal of Chemical Theory and Computation 5 (2009), No. 4, pp. 937-948.
PDF  | Journal ]
51 Y. Cheng, M. Holst, and J.A. McCammon, Finite Element Analysis of Drug Electrostatic Diffusion: Inhibition Rate Studies in N1 Neuraminidase. Biocomputing 2009: Proceedings of the Pacific Symposium, R.B. Altman, A.K. Dunker, L. Hunter, T. Murray, and T.E. Klein, eds., 2009, pp. 281-292.
PDF  | Journal ]
50 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. J. Cell Sci., Vol. 122 (April, 2009), No. 7, pp. 1005-1013.
PDF  | Journal ]
49 Z. Yu, M. Holst, T. Hayashi, C. Bajaj, M. Ellisman, J.A. McCammon, and M. Hoshijima, Three-Dimensional Geometric Modeling of Membrane-bound Oganelles in Ventricular myocytes: Bridging the Gap between Microscopic Imaging and Mathematical Simulation. Journal of Structural Biology, Vol. 164 (2008), No. 10, pp. 304-313.
PDF  | Journal ]



2008
-to- 2006
48 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.
PDF  | Journal  | arXiv:gr-qc/0802.1031 ]
47 M. Holst, G. Nagy, and G. Tsogtgerel, Rough Solutions of the Einstein Constraints on closed manifolds without near-CMC conditions. Comm. Math. Phys., Vol. 288 (June 2009), No. 2, pp. 547-613.
PDF  | Journal  | arXiv:gr-qc/0712.0798 ]
46 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. Biophys. J., Vol. 95 (2008), No. 10, pp. 4659-4667.
PDF  | Journal ]
45 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. IEEE Journal on Engineering in Medicine and Biology, Vol. 28 (March-April 2009), No. 2, pp. 46-57.
PDF  | Journal ]
44 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.
PDF  | Journal ]
43 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.
PDF  | Journal ]
42 Z. Yu, M. Holst, and J.A. McCammon, High-Fidelity Geometric Modelling for Biomedical Applications. Finite Elements in Analysis and Design, Vol. 44 (2008), No. 11, pp. 715-723.
PDF  | Journal ]
41 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.
PDF  | Journal ]
40 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.
PDF  | Journal ]
39 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.
PDF  | Journal  | arXiv:math.AP/1001.1371 ]
38 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.
PDF  | Journal  | arXiv:math.NA/1001.1350 ]
37 L. Chen, M. Holst, and J. Xu, Convergence and Optimality of Adaptive Mixed Finite Element Methods. Math. Comp., Vol. 78 (2009), No. 265, pp. 33-53.
PDF  | Journal  | arXiv:math.NA/1001.1353 ]
36 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.
PDF  | Journal ]
35 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.
PDF  | Journal ]
34 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.
PDF  | Journal ]
33 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.
PDF  | Journal  | arXiv:math.NA/1001.1369 ]



2005
-to- 2003
32 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.
PDF  | Journal ]
31 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.
PDF  | Journal  | arXiv:gr-qc/0407011 ]
30 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.
PDF  | Journal ]
29 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.
PDF  | Journal  | arXiv:math.NA/arXiv:1001.1370 ]
28 R. Bank and M. Holst, A New Paradigm for Parallel Adaptive Meshing Algorithms. SIAM Review, Vol. 45 (2003), No. 2, pp. 291-323.
PDF  | Journal ]
27 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.
PDF  | Journal ]
26 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.
PDF  | Journal  | arXiv:math.NA/arXiv:1001.1364 ]



2002
-to- 2000
25 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.
PDF  | Journal ]
24 M. Holst, Adaptive numerical treatment of elliptic systems on manifolds. Advances in Computational Mathematics, 15 (2001), pp. 139-191.
PDF  | Journal  | arXiv:math.NA/1001.1367 ]
23 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.
PDF  | Journal ]
22 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.
PDF  |  Journal ]
21 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.
PDF  | Journal ]
20 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.
PDF  | Journal ]
19 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.
PDF  | Journal ]
18 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.
PDF  | Journal ]
17 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.
PDF  | Journal ]



1999
-to- 1993
16 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.
PDF  | Journal ]
15 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.
PDF  | Journal  | arXiv:math.NA/arXiv:1001.1362 ]
14 D. Zorin, M. Holst, and P. Schroeder, Subdivision-Based Surface Representations. TeamCAD 97 Workshop, Atlanta, GA, 1997, pp. 35-38.
PDF  |  Journal ]
13 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.
PDF  | Journal  | arXiv:math.AP/arXiv:1001.1357 ]
12 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 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 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 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 M. Holst, Kansas hosts macromolecular modeling workshop. SIAM News, Vol. 28 (March 1995), No. 3, p. 11.
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7 M. Holst, Symposium honors Herbert B. Keller. SIAM News, Vol. 28 (December 1995), No. 10, p. 3.
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6 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.
info  |  Journal ]
5 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.
info  |  Journal ]
4 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 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 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 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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Articles in the Popular Press



Info No. Authors, Title. Other Information.



3 M. Holst and T.Y. Hou, Obiturary Story on Herbert Bishop Keller. SIAM News, Vol. 41 (July 2008), No. 6, p. 2.
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2 M. Holst, Kansas hosts macromolecular modeling workshop. SIAM News, Vol. 28 (March 1995), No. 3, p. 11.
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1 M. Holst, Symposium honors Herbert B. Keller. SIAM News, Vol. 28 (December 1995), No. 10, p. 3.
HTML ]




Books Projects and Lecture Notes



Info No. Authors, Title. Other Information.



12 M. Holst, Mathematical and Computational Physics. (Monograph In Preparation), 2015.
11 D. Estep and M. Holst, Applied Functional Analysis and Adjoint Techniques for Differential Equations. (Graduate Text In Preparation), 2015.
10 I. Stakgold and M. Holst, Boundary Value Problems: Theory and Applications. (Graduate Text In Preparation), 2013.
9 I. Stakgold and M. Holst, Green's Functions and Boundary Value Problems. John Wiley & Sons, New York, NY, Third Edition, 888 pages, 2011.
PDF Preview  | Wiley ]
8 M. Holst, Notes on Mathematical and Numerical General Relativity. Lecture notes (Math 259C), 2009.
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7 M. Holst, Computational Multiscale Modeling: Adaptive Methods and FETK with Applications in Biophysics. Lecture notes (from the CTBP and NBCR Summer Workshop at UCSD), 2008.
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6 M. Holst, Nonlinear Functional Analysis: Applications in PDE and Numerical Analysis. Lecture notes (Math 241B), 2007.
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5 M. Holst, Differential Geometry: Applications in Shell Theory and General Relativity. Lecture notes (Math 237AB), 2007.
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4 M. Holst, Approximation Theory: Nonlinear Approximation and Numerical Analysis. Lecture notes (Math 273C), 2005.
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3 M. Holst, Linear Functional Analysis: Applications in PDE and Numerical Analysis. Lecture notes (Math 273AB), 2000.
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2 M. Holst, Matrix Theory: Linear Operators on Finite-Dimensional Vector Spaces. Lecture notes (AMa 104), 1997.
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1 M. Holst, Elliptic Equations: Theory and Finite Element Approximation. Lecture notes (AMa 204A), 1995.
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Theses and Technical Reports



Info No. Authors, Title. Other Information.



19 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 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 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 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 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 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 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 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 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 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 M. Holst, Algebraic Schwarz Theory. Technical Report CRPC-94-12, Applied Mathematics and CRPC, California Institute of Technology, 1994.
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8 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 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 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 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.) 4 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 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 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.) 1 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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