Publications

Refereed Journal Articles by Year:     (Ordered roughly by completion and submission, not necessarily by appearance.)

[ 2023-Present ] [ 2019-2022 ] [ 2015-2018 ] [ 2012-2014 ] [ 2009-2011 ] [ 2006-2008 ] [ 2003-2005 ] [ 2000-2002 ] [ 1993-1999 ]

NOTE: Most of the articles below have also been posted at [ arXiv.org ]. You can also go directly to the [ arXiv.org site ]. (Here is a temporary page by [ area ] for discussion.)

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

Refereed Journal Articles by Number and Year:
Year No. Authors, Title. Journal where Appearing, Other Information.
Present
-to- 2023 		A100 M. Holst, D. Maxwell, and G. Tsogtgerel, A Scaling Approach to Elliptic Theory for Geometrically-Natural Differential Operators with Sobolev-Type Coefficients. Submitted for publication (73 pages).
[ PDF  | arXiv:2306.15842 [math.AP] ]
A99 T. Fernando, M. Licht, and M. Holst, Finite Element Methods for Linear Maxwell's Equations in Bianisotropic Media Permitting Polarization Fields and Magnetic Currents. Submitted for publication (6 pages).
[ PDF  | arXiv:2212.11930 [physics.comp-ph] ]
A98 M. Holst, V. Kungurtsev, and S. Mukherjee, A Note on Optimal Tokamak Control for Fusion Power Simulation. Submitted for publication (24 pages).
[ PDF  | arXiv:2211.08984 [physics.plasm-ph] ]
A97 J. Dilts and M. Holst, When do Spacetimes have Constant Mean Curvature Slices? Submitted for publication (11 pages).
[ PDF  | arXiv:1710.03209 [gr-qc] ]
A96 A. Behzadan and M. Holst, Rough Solutions of the Einstein Constraint Equations on Asymptotically Flat Manifolds without Near-CMC Conditions. Submitted for publication (82 pages).
[ PDF  | arXiv:1504.04661 [gr-qc] ]
A95 M. Holst and C. Meier, Non-Uniqueness of Solutions to the Conformal Formulation. Submitted for publication (34 pages).
[ PDF  | arXiv:1210.2156 [gr-qc] ]
A94 M. Holst, M. Licht, and Z. Lyu, Newest Vertex Bisection over General Triangulations. Submitted for publication (28 pages).
[ PDF ]
A93 J. Dilts, M. Holst, T. Kozareva, and D. Maxwell, Numerical Bifurcation Analysis of the Conformal Method. Submitted for publication to Annales Henri Poincare (22 pages).
[ PDF  | arXiv:1710.03201 [gr-qc] ]
A92 M. Holst and M. Licht, Geometric Transformation of Finite Element Methods: Theory and Applications. Applied Numerical Mathematics, 192 (2023), pp. 389-413 (24 pages).
[ PDF  | Journal  | arXiv:1809.10354 [math.NA] ]
2022
-to- 2019 		A91 M. Holst, D. Maxwell, and R. Mazzeo, Conformal Fields and the Structure of the Space of Solutions of the Einstein Constraint Equations. Advances in Theoretical and Mathematical Physics, 26 (2022), No. 5, pp. 1157-1201 (45 pages).
[ PDF  | Journal  | arXiv:1711.01042 [gr-qc] ]
[442p] A90 M. Holst, H. Hu, J. Lu, J. Marzuola, D. Song, and J. Weare, Symmetry Breaking in Density Functional Theory due to Dirac Exchange for a Hydrogen Molecule. Journal of Nonlinear Science, 32 (2022), No. 6, pp. 1-40 (40 pages).
[ PDF  | Journal  | arXiv:1902.03497 [math-ph] ]
A89 A. Behzadan and M. Holst, On the Space of Locally Sobolev-Slobodeckij Functions. Journal of Function spaces, Volume 2022, Article 9094502 (2022), pp. 1-30 (30 pages).
[ PDF  | Journal  | arXiv:1806.02188 [math.AP] ]
A88 A. Behzadan and M. Holst, On Certain Geometric Operators Between Sobolev Spaces of Sections of Tensor Bundles on Compact Manifolds Equipped with Rough Metrics. Contemporary Mathematics, 3 (2022), pp. 89-140 (52 pages).
[ PDF  | Journal  | arXiv:1704.07930v2 [math.AP] ]
A87 A. Behzadan and M. Holst, Sobolev-Slobodeckij Spaces on Compact Manifolds, Revisited. Mathematics, 10 (2022), pp. 522:1-103 (103 pages).
[ PDF  | Journal  | arXiv:1704.07930v3 [math.AP]  ]
A86 A. Behzadan and M. Holst, Multiplication in Sobolev Spaces, Revisited. Arkiv for Matematik, 59 (2021), pp. 275-306 (32 pages).
[ PDF  | Journal  | arXiv:1512.07379 [math.AP] ]
A85 E. Gawlik, M. Holst, and M. Licht, Local Finite Element Approxmation of Sobolev Differential Forms. ESAIM: Mathematical Modelling and Numerical Analysis, 55 (2021), pp. 2075-2099 (25 pages).
[ PDF  | Journal  | arXiv:2011.00634 [math.NA] ]
A84 P. Rangamani, A. Behzadan, and M. Holst, Local sensitivity analysis of the "membrane shape equation" derived from the Helfrich energy. Mathematics and Mechanics of Solids, 26 (2021), pp. 1-30 (30 pages).
[ PDF  | Journal  | arXiv:2005.12550 [math.NA] ]
A83 C.T. Lee, J.G. Laughlin, N. Angliviel de La Beaumelle, R.E. Amaro, J.A. McCammon, R. Ramamoorthi, M. Holst, and P. Rangamani, 3D mesh processing using GAMer 2 to enable reaction-diffusion simulations in realistic cellular geometries. PLOS Computational Biology, 16 (2020), pp. 1-35 (35 pages).
[ PDF  | Journal  | arXiv:1901.11008 [q-bio.QM] ]
A82 C.T. Lee, J.G. Laughlin, J.B. Moody, R.E. Amaro, J.A. McCammon, M. Holst, and P. Rangamani, An Open Source Mesh Generation Platform for Biophysical Modeling Using Realistic Cellular Geometries. Biophys. J., 118 (2020), pp. 1003-1008 (6 pages).
[ PDF  | Journal  | arXiv:1909.04781 [physics.comp-ph] ]
A81 R. Vasan, M. Rowan, C.T. Lee, G.R. Johnson, P. Rangamani, and M. Holst, Applications and Challenges of Machine Learning to Enable Realistic Cellular Simulations. Frontiers in Physics., 7 (2020), pp. 1-10 (10 pages).
[ PDF  | Journal ] | arXiv:1911.05218 [physics.bio-ph] ]
A80 L.M. Stolerman, M. Getz, S.G. Llewellyn Smith, M. Holst, and P. Rangamani, Stability Analysis of a Bulk-Surface Reaction Model for Membrane-Protein Clustering. Bull. Math. Biol., 82 (2020), pp. 1-34 (34 pages).
[ PDF  | Journal  | arXiv:1908.05214 [q-bio.SC] ]
2018
-to- 2015 		A79 M. Holst, Y. Li, A. Mihalik, and R. Szypowski, Convergence and Optimality of Adaptive Methods for Poisson's Equation in the FEEC framework. J. Comput. Math., 38 (2020), pp. 748-767 (20 pages).
[ PDF  | Journal  | arXiv:math.NA/1306.1886 ]
[292p] A78 C.T. Lee, J.B. Moody, R.E. Amaro, J.A. McCammon, and M. Holst, The Implementation of the Colored Abstract Simplicial Complex and its Application to Mesh Generation. ACM Trans. Math. Software, 45 (2019), pp. 28:1-28:20 (20 pages).
[ PDF  | Journal  | arXiv:math.NA/1807.01417 ]
A77 F. Grogan, M. Holst, L. Lindblom, J.A. McCammon, and R.E. Amaro, Reliability Assessment for Large-Scale Molecular Dynamics Approximations. J. Chem. Phys., 147 (2017), pp. 234106 (15 pages).
[ PDF  | Journal  | arXiv:math.NA/1710.05999 ]
A76 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.A. McCammon, and N. Baker, Improvements to the APBS biomolecular solvation software suite. Protein Sci., 27 (2018), pp. 112-128 (17 pages).
[ PDF  | Journal  | arXiv:q-bio.BM/1707.00027 ]
A75 M. Holst, C. Meier, and G. Tsogtgerel, Non-CMC Solutions of the Einstein Constraint Equations on Compact Manifolds with Apparent Horizon Boundaries. Comm. Math. Phys., 357 (2018), pp. 467-517 (51 pages).
[ PDF  | Journal  | arXiv:gr-qc/1310.2302 ]
A74 M. Holst and C. Tiee, Finite Element Exterior Calculus for Parabolic Evolution Problems on Riemannian Hypersurfaces. Journal of Computational Mathematics, 36 (2018), pp. 792-832 (41 pages).
[ PDF  | Journal  | arXiv:math.NA/1509.05524 ]
A73 A. Gillette, M. Holst, and Y. Zhu, Finite Element Exterior Calculus for Evolution Problems. Journal of Computational Mathematics, 35 (2017), pp. 186–212 (27 pages).
[ PDF  | Journal  | arXiv:math.NA/1202.1573 ]
A72 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), pp. 513-554 (42 pages).
[ PDF  | Journal  | arXiv:gr-qc/1607.05251 ]
A71 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, 6 (2015), pp. 1-9 (9 pages).
[ PDF  | Journal ]
A70 M. Holst, S. Pollock, and Y. Zhu, Convergence of Goal-Oriented Adaptive Finite Element Methods for Semilinear Problems. Comput. Vis. Sci., 17 (2015), pp. 43-63 (21 pages).
[ PDF  | Journal  | arXiv:math.NA/1203.1381 ]
A69 M. Holst and S. Pollock, Convergence of Goal-Orientied Adaptive Finite Element Methods for Nonsymmetric Problems. Numer. Meth. Part. Diff. Eq., 32 (2016), pp. 1098-2426 (29 pages).
[ PDF  | Journal  | arXiv:math.NA/1108.3660 ]
2014
-to- 2012 		A68 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), pp. 1-25 (25 pages).
[ PDF  | Journal  | arXiv:gr-qc/1403.4549 ]
[378p] A67 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), pp. 1684-1695 (12 pages).
[ Journal ]
A66 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), pp. 1083-1120 (28 pages).
[ PDF  | Journal  | arXiv:math.NA/1012.1287 ]
A65 M. Holst and C. Meier, Generalized Solutions to Semilinear Elliptic PDE with Applications to the Lichnerowicz Equation. Acta Applicandae Mathematicae, 130 (2014), pp. 163-203 (41 pages).
[ PDF  | Journal  | arXiv:gr-qc/1112.0351 ]
A64 M. Holst and G. Tsogtgerel, The Lichnerowicz Equation on Compact Manifolds with Boundary. Class. Quantum Grav., 30 (2013), pp. 1-31 (31 pages).
[ PDF  | Journal  | arXiv:gr-qc/1306.1801 ]
A63 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), pp. 1-9 (9 pages).
[ PDF  | Journal ]
A62 M. Holst, R. Szypowski, and Y. Zhu, Two-Grid Methods for Semilinear Interface Problems. Numer. Methods Partial Differential Equations., 29 (2013), pp. 1729-1748 (20 pages).
[ PDF  | Journal  | arXiv:math.NA/1203.0339 ]
A61 Z. Gao, Z. Yu, and M. Holst, Feature-preserving surface mesh smoothing via suboptimal Delaunay triangulation. Graphical Models, 75 (2013), pp. 23-38 (16 pages).
[ PDF  | Journal ]
A60 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), pp. 271-289 (19 pages).
[ PDF  | Journal  | arXiv:math.NA/1006.3277 ]
A59 P. Kekenes-Huskey, Y. Cheng, J. Hake, F. Sachse, J. Bridge, M. Holst, J.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), pp. 1-14 (14 pages).
[ Journal ]
A58 Z. Gao, Z. Yu, and M. Holst, Quality tetrahedral mesh smoothing via boundary-optimized Delaunay triangulation. Computer Aided Geometric Design, 29 (2012), pp. 707-721 (15 pages).
[ PDF  | Journal ]
A57 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), pp. 3615-3628 (14 pages).
[ Journal ]
A56 J. Hake, A. Edwards, Z. Yu, P. Kekenes-Huskey, A. Michailova, J.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), pp. 4403-4422 (18 pages).
[ Journal ]
A55 M. Holst and A. Stern, Semilinear Mixed Problems on Hilbert Complexes and Their Numerical Approximation. Found. Comput. Math. 12 (2012), pp. 363-397 (25 pages).
[ PDF  | Journal  | arXiv:math.NA/1010.6127 ]
A54 M. Holst and A. Stern, Geometric variational crimes: Hilbert complexes, finite element exterior calculus, and problems on hypersurfaces. Found. Comput. Math. 12 (2012), pp. 263-293 (21 pages).
[ PDF  | Journal  | arXiv:math.NA/1005.4455 ]
A53 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), pp. 202-225 (23 pages).
[ PDF  | Journal  | arXiv:math.NA/1109.4092 ]
A52 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), pp. 1-26 (26 pages).
[ PDF  | Journal  | arXiv:math.NA/0901.4548 ]
A51 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), pp. 015002-015015 (13 pages).
[ PDF  | Journal ]
A50 M. Holst and V. Kungurtsev, Numerical Bifurcation Analysis of Conformal Formulations of the Einstein Constraints. Phys. Rev. D. 84 (2011), pp. 124038(1)-124038(8) (8 pages).
[ PDF  | Journal  | arXiv:math.NA/1107.0262 ]
2011
-to- 2009 		A49 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), pp. 367-387 (20 pages).
[ PDF  | Journal ]
[248p] A48 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), pp. 2947-2951 (4 pages).
[ PDF  | Journal ]
A47 M. Holst, J. Ovall, and R. Szypowski, An Efficient, Reliable and Robust Error Estimator for Elliptic Problems in R3. Appl. Numer. Math. 61 (2011), pp. 675-695 (21 pages).
[ PDF  | Journal  | Report ]
A46 L. Chen and M. Holst, Efficient Mesh Optimization Schemes Based on Optimal Delaunay Triangulations. Comp. Meth. in Appl. Mech. and Engr. 200 (2010), pp. 967-984 (18 pages).
[ PDF  | Journal ]
A45 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), pp. 781-795 (15 pages).
[ PDF  | Journal ]
A44 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), pp. e1000972:1-16 (16 pages).
[ PDF  | Journal ]
A43 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), pp. 6679-7794 (16 pages).
[ PDF  | Journal ]
A42 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), pp. 179-214 (35 pages).
[ PDF  | Journal  | arXiv:math.NA/1009.6034 ]
A41 M. Holst, E. Lunasin, and G. Tsogtgerel, Analysis of a General Family of Regularized Navier-Stokes and MHD Models. J. Nonlinear Science 20 (2010), pp. 523-567 (44 pages).
[ PDF  | Journal  | arXiv:math.AP/0901.4412 ]
A40 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), 145007 (28 pages).
[ PDF  | Journal  | arXiv:gr-qc/0801.1823 ]
A39 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), pp. 937-948 (12 pages).
[ PDF  | Journal ]
A38 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., 122 (2009), pp. 1005-1013 (9 pages).
[ PDF  | Journal ]
A37 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, 164 (2008), pp. 304-313 (10 pages).
[ PDF  | Journal ]
2008
-to- 2006 		A36 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, 100 (2008), pp. 161101.1-161101.4 (4 pages).
[ PDF  | Journal  | arXiv:gr-qc/0802.1031 ]
[300p] A35 M. Holst, G. Nagy, and G. Tsogtgerel, Rough Solutions of the Einstein Constraints on closed manifolds without near-CMC conditions. Comm. Math. Phys., 288 (2009), pp. 547-613 (67 pages).
[ PDF  | Journal  | arXiv:gr-qc/0712.0798 ]
A34 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., 95 (2008), pp. 4659-4667 (9 pages).
[ PDF  | Journal ]
A33 S. Lu, A. Michailova, J. Saucerman, Y. Cheng Z. Yu, T. Kaiser, W. Li, R. Bank, M. Holst, J.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, 28 (2009), pp. 46-57 (12 pages).
[ PDF  | Journal ]
A32 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., 3 (2008), pp. 973-1009 (37 pages).
[ PDF  | Journal ]
A31 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, 26 (2008), pp. 1370-1380 (11 pages).
[ PDF  | Journal ]
A30 Z. Yu, M. Holst, and J.A. McCammon, High-Fidelity Geometric Modelling for Biomedical Applications. Finite Elements in Analysis and Design, 44 (2008), pp. 715-723 (9 pages).
[ PDF  | Journal ]
A29 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, 112 (2008), pp. 270-275 (6 pages).
[ PDF  | Journal ]
A28 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., 127 (2007), pp. 135102.1-135102.16 (16 pages).
[ PDF  | Journal ]
A27 Y. Zhou, M. Holst, and J.A. McCammon, Nonlinear elastic modeling of macromolecular conformational change induced by electrostatic forces. J. Math. Anal. Appl., 340 (2008), pp. 135-164 (30 pages).
[ PDF  | Journal  | arXiv:math.AP/1001.1371 ]
A26 L. Chen, M. Holst, and J. Xu, The Finite Element Approximation of the Nonlinear Poisson-Boltzmann equation. SIAM J. Numer. Anal., 45 (2007), pp. 2298-2320 (23 pages).
[ PDF  | Journal  | arXiv:math.NA/1001.1350 ]
A25 L. Chen, M. Holst, and J. Xu, Convergence and Optimality of Adaptive Mixed Finite Element Methods. Math. Comp., 78 (2009), pp. 33-53 (21 pages).
[ PDF  | Journal  | arXiv:math.NA/1001.1353 ]
A24 W. Li, N. Baker, K. Baldridge, J.A. 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, 2 (2006), pp. 6-17 (12 pages).
[ PDF  | Journal ]
A23 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., 92 (2007), pp. 3397-3406 (10 pages).
[ PDF  | Journal ]
A22 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 (11 pages).
[ PDF  | Journal ]
A21 B. Aksoylu and M. Holst, Optimality of multilevel preconditioners for local mesh refinement in three dimensions. SIAM J. Numer. Anal., 44 (2006), pp. 1005-1025 (21 pages).
[ PDF  | Journal  | arXiv:math.NA/1001.1369 ]
2005
-to- 2003 		A20 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., 88 (2005), pp. 1659-1665 (7 pages).
[ PDF  | Journal ]
[111p] A19 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, 70 (2004), pp. 084017.1-084017.17 (17 pages).
[ PDF  | Journal  | arXiv:gr-qc/0407011 ]
A18 D. Estep, M. Holst, and M. Larson, Generalized Green's Functions and the Effective Domain of Influence. SIAM J. Sci. Comput., 26 (2005), pp. 1314-1339 (26 pages).
[ PDF  | Journal ]
A17 B. Aksoylu, S. Bond, and M. Holst, An Odyssey into Local Refinement and Multilevel Preconditioning III: Implementation and Numerical Experiments. SIAM J. Sci. Comput., 25 (2003), pp. 478-498 (20 pages).
[ PDF  | Journal  | arXiv:math.NA/arXiv:1001.1370 ]
A16 R. Bank and M. Holst, A New Paradigm for Parallel Adaptive Meshing Algorithms. SIAM Review, 45 (2003), pp. 291-323 (33 pages).
[ PDF  | Journal ]
A15 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 (8 pages).
[ PDF  | Journal ]
2002
-to- 2000 		A14 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 (16 pages).
[ PDF  | Journal ]
[181p] A13 M. Holst, Adaptive numerical treatment of elliptic systems on manifolds. Advances in Computational Mathematics, 15 (2001), pp. 139-191 (53 pages).
[ PDF  | Journal  | arXiv:math.NA/1001.1367 ]
A12 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 (5 pages).
[ PDF  | Journal ]
A11 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 (12 pages).
[ PDF  | Journal ]
A10 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 (10 pages).
[ PDF  | Journal ]
A9 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 (24 pages).
[ PDF  | Journal ]
A8 R. Bank and M. Holst, A New Paradigm for Parallel Adaptive Meshing Algorithms. SIAM J. Sci. Comput., 22 (2000), pp. 1411-1443 (33 pages).
[ PDF  | Journal ]
A7 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 (28 pages).
[ PDF  | Journal ]
1999
-to- 1993 		A6 M. Holst and S. Vandewalle, Schwarz methods: to symmetrize or not to symmetrize. SIAM J. Numer. Anal., 34 (1997), pp. 699-722 (24 pages).
[ PDF  | Journal  | arXiv:math.NA/arXiv:1001.1362 ]
[86p] A5 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 (28 pages).
[ PDF  | Journal ]
A4 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 (9 pages).
[ info  | Journal ]
A3 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 (15 pages).
[ info  | Journal ]
A2 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 (1 pages).
[ info  |  Journal ]
A1 M. Holst and F. Saied, Multigrid solution of the Poisson-Boltzmann equation. J. Comput. Chem., 14 (1993), pp. 105-113 (9 pages).
[ PDF  | Journal ]


Books and Book Chapters
Info No. Authors, Title. Other Information.
[1541p] B2 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, 686 pages, 2012.
[ PDF Preview  | Journal ]
B1 I. Stakgold and M. Holst, Green's Functions and Boundary Value Problems. John Wiley & Sons, New York, NY, Third Edition, 855 pages, February 2011.
[ PDF Preview  | Wiley ]


Refereed Conference Proceedings
Info No. Authors, Title. Other Information.
[147p] C14 Y. Zhang, K. Key, J. Ovall, and M. Holst, Parallel goal-oriented adaptive finite element modeling for 3D electromagnetic exploration. SEG Technical Program Proceedings (2015), pp. 806-811 (6 pages).
[ PDF  | Journal ]
C13 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. (9 pages)
[ PDF  | Journal  | arXiv:math.NA/1107.2160 ]
C12 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. (8 pages)
[ PDF  | Journal  | arXiv:math.NA/1107.2143 ]
C11 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 (12 pages).
[ PDF  | Journal ]
C10 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 (16 pages).
[ PDF  | Journal  | arXiv:math.NA/arXiv:1001.1364 ]
C9 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 (29 pages).
[ PDF  | Journal ]
C8 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. (6 pages)
[ PDF  | Journal ]
C7 D. Zorin, M. Holst, and P. Schroeder, Subdivision-Based Surface Representations. TeamCAD 97 Workshop, Atlanta, GA, 1997, pp. 35-38 (4 pages).
[ PDF  | Journal ]
C6 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. (14 pages)
[ PDF  | Journal  | arXiv:math.AP/arXiv:1001.1357 ]
C5 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. (3 pages)
[ PDF  |  Journal ]
C4 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. (8 pages)
[ PDF  | Journal ]
C3 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. (16 pages)
[ PDF  |  Journal ]
C2 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. (11 pages)
[ PDF  |  Journal ]
C1 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. (5 pages)
[ PDF  |  Journal ]


Popular Works
Info No. Authors, Title. Other Information.
P3 M. Holst and T.Y. Hou, Obiturary Story on Herbert Bishop Keller. SIAM News, 41 (July 2008), p. 2.
[ HTML ]
P2 M. Holst, Kansas hosts macromolecular modeling workshop. SIAM News, 28 (March 1995), p. 11.
[ HTML ]
P1 M. Holst, Symposium honors Herbert B. Keller. SIAM News, 28 (December 1995), p. 3.
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Theses, Technical Reports, and Other Research Projects
Info No. Authors, Title. Other Information.
T27 B. Faktor and M. Holst, A Note on Determining Projections for Non-Homogeneous Incompressible Fluids. Preprint (20 pages).
[ PDF  | arXiv:math.AP/2102.04654 ]
T26 M. Holst, A. Mihalik, and R. Szypowski, Convergence and Optimality of Adaptive Mixed Methods on Surfaces. Submitted for publication (22 pages).
[ PDF  | arXiv:math.NA/1404.1956 ]
T25 J. Erway and M. Holst, Barrier Methods for Critical Exponent Problems in Geometric Analysis and Mathematical Physics. Technical Note, 2011.
[ PDF  | arXiv:math.NA/1107.0360 ]
T24 R. Bank, M. Holst, R. Szypowski, and Y. Zhu, Finite Element Error Estimates for Critical Growth Semilinear Problems without Angle Conditions. Technical Note, 2011.
[ PDF  | arXiv:math.NA/1108.3661 ]
T23 M. Holst, G. Tsogtgerel, and Y. Zhu, Local Convergence of Adaptive Methods for Nonlinear Partial Differential Equations. Technical Note, 2008.
[ PDF  | arXiv:math.NA/1001.1382 ]
T22 M. Holst and C. Meier, An Alternative Between Non-Unique and Negative Yamabe Solutions to the Conformal Formulation of the Einstein Constraint Equations. Technical Note, 2013.
[ PDF  | arXiv:gr-qc/1306.1210 ]
T21 M. Holst, J. Kommemi, and G. Nagy, Rough Solutions of the Einstein Constraint Equations with Nonconstant Mean Curvature. Technical Note, 2007.
[ PDF  | arXiv:gr-qc/0708.3410 ]
T20 B. Aksoylu, D. Bernstein, S. Bond, and M. Holst, Generating Initial Data in General Relativity using Adaptive Finite Element Methods. Technical Note, 2008.
[ PDF ] | arXiv:gr-qc/0801.3142 ]
T19 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.
[ PDF ]
T18 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.
[ PDF ]
T17 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.
[ PDF ]
T16 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.
[ PDF ]
T15 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.
[ PDF ]
T14 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.
[ info ]
T13 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.
[ PDF ]
T12 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.
[ PDF ]
T11 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.
[ PDF ]
T10 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.
[ PDF ]
T9 M. Holst, Algebraic Schwarz Theory. Technical Report CRPC-94-12, Applied Mathematics and CRPC, California Institute of Technology, 1994.
[ PDF ]
T8 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.
[ PDF ]
T7 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.
[ PDF ]
T6 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.
[ PDF ]
T5 M. Holst, Notes on the KIVA-II software and chemically reactive fluid mechanics. Technical Report UCRL-ID-112019, Lawrence Livermore National Laboratory, 1993.
[ PDF ]
(Ph.D.) T4 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.)
[ PDF ]
T3 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.
[ PDF ]
T2 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.
[ info ]
(M.S.) T1 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.
[ PDF ]


Lecture Notes and Book Projects
Info No. Authors, Title. Other Information.
N9 I. Stakgold and M. Holst, Boundary Value Problems: Theory and Applications. John Wiley & Sons, New York, NY, 496 pages, 2016. [This is an abridged version of B1 with some chapters removed to bring the topics and the page count more inline with a 2-3 quarter course. The production of this abridged version was delayed due to the long illness and sad passing of I. Stakgold in 2018, but it is still planned for publication by Wiley.]
[ PDF Preview ]
N8 M. Holst, Notes on Mathematical and Numerical General Relativity. Lecture notes (UCSD Math 259C), 2009.
[ PDF ]
N7 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.
[ PDF ]
N6 M. Holst, Nonlinear Functional Analysis: Applications in PDE and Numerical Analysis. Lecture notes (UCSD Math 241B), 2007.
[ PDF ]
N5 M. Holst, Differential Geometry: Applications in Shell Theory and General Relativity. Lecture notes (UCSD Math 237AB), 2007.
[ PDF ]
N4 M. Holst, Approximation Theory: Nonlinear Approximation and Numerical Analysis. Lecture notes (UCSD Math 273C), 2005.
[ PDF ]
N3 M. Holst, Linear Functional Analysis: Applications in PDE and Numerical Analysis. Lecture notes (UCSD Math 273AB), 2000.
[ PDF ]
N2 M. Holst, Matrix Theory: Linear Operators on Finite-Dimensional Vector Spaces. Lecture notes (Caltech AMa 104), 1997.
[ PDF ]
N1 M. Holst, Elliptic Equations: Theory and Finite Element Approximation. Lecture notes (Caltech AMa 204A), 1995.
[ PDF ]