focus areas:

nonlinear, higher order and eigenvalue problems

S. Pollock, L. G. Rebholz and D. Vargun, An efficient nonlinear solver and convergence analysis for a viscoplastic flow model, submitted, 2021. preprint: arxiv.math.NA/2108.08945

S. Pollock and L. R. Scott, An algorithm for the grade-two rheological model, submitted, 2021.

S. Pollock and L. R. Scott, Transport equations with inflow boundary conditions, submitted, 2021.

S. Pollock and L. R. Scott, Extrapolating the Arnoldi algorithm to improve eigenvector convergence, accepted, International Journal of Numerical Analysis and Modeling, 2021.
preprint: arXiv:math.NA/2103.08635.

S. Pollock and L.R. Scott, Using small eigenproblems to accelerate power method iterations, Research Report UC/CS TR-2021-10, Dept. Comp. Sci., Univ. Chicago, 2021.

N. Nigam and S. Pollock, A simple extrapolation method for clustered eigenvalues, published online, Numerical Algorithms, 2021. preprint: arXiv:math.NA/2006.10164.
Journal article @ SpringerNature. DOI: 10.1007/s11075-021-01108-7

S. Pollock, L. G. Rebholz and M. Xiao, Acceleration of nonlinear solvers for natural convection problems, accepted, Journal of Numerical Mathematics, 2020.
DOI: 10.1515/jnma-2020-0067. preprint: arXiv:math.NA/2004.06471

S. Pollock and H. Schwartz, Benchmarking results for the Newton-Anderson method, Results in Applied Mathematics, 8, 11 pages, 2020. Open access. DOI: 10.1016/j.rinam.2020.100095.

S. Pollock and L. G. Rebholz, Anderson acceleration for contractive and noncontractive operators, in press, IMA Journal of Numerical Analysis, 2021.
DOI: 10.1093/imanum/draa095. preprint: arXiv:math.NA/1909.04638.

C. Evans, S. Pollock, L. G. Rebholz and M. Xiao, A proof that Anderson acceleration improves the convergence rate in linearly converging fixed point methods (but not in those converging quadratically), SIAM J. Numer. Anal., 58(1), p. 788-810, 2020.
DOI: 10.1137/19M1245384.   preprint: arXiv:math.NA/1810.08455.

S. Pollock, L. G. Rebholz and M. Xiao, Anderson-accelerated convergence of Picard iterations for
incompressible Navier-Stokes equations, SIAM J. Numer. Anal., 57(2), p. 615–637, 2019.
DOI: 10.1137/18M1206151.   preprint: arXiv:math.NA/1810.08494.   pdf (Copyright © by SIAM)

S. Pollock and Y. Zhu, A matrix analysis approach to discrete comparison principles for nonmonotone PDE, Numer. Algor., 83(3), p. 1007-1027, 2020.
DOI:10.1007/s11075-019-00713-x . preprint: arXiv:math.NA/1711.07506. publisher’s full-text (view only).

S. Pollock and Y. Zhu, Discrete comparison principles for quasilinear elliptic PDE, Appl. Numer. Math., 156, p. 106-124, 2020. DOI: 10.1016/j.apnum.2020.04.013.  preprint:  arXiv:math.NA/1708.02301.

S. Pollock and Y. Zhu, Uniqueness of discrete solutions of nonmonotone PDEs without a globally fine mesh condition, Numer. Math., 139 (4), p. 845-865, 2018.
DOI: 10.1007/s00211-018-0956-4.   preprint: arXiv:math.NA/1704.04319.

S. Pollock, Stabilized and inexact adaptive methods for capturing internal layers in quasilinear PDE, J. Comput. Appl. Math., 308, p 243-262, 2016.
DOI: 10.1016/   preprint: arXiv:math.NA/1507.06965.

S. Brenner, M. Oh, S. Pollock, K. Porwal, M. Schedensack, N. Sharma, A C^0 interior penalty method for elliptic distributed optimal control problems in three dimensions with pointwise state constraints, in Topics in Numerical Partial Differential Equations and Scientific Computing, p 1-22, S. Brenner, ed, IMA Volumes in Mathematics and Its Applications, 160, 2016

S. Pollock, An improved method for solving quasilinear convection diffusion problems, SIAM J. Sci. Comput., 38-2, p A1121-A1145, 2016.
DOI: 10.1137/15M1007823.   preprint: arXiv:math.NA/1502.02629.

S. Pollock, A regularized Newton-like method for nonlinear PDE, Numer. Func. Anal. Opt., 36(11), p 1493-1511, 2015.
DOI: 10.1080/01630563.2015.1069328.   preprint: arXiv:math.NA/1412.6487.

multiscale methods and goal-oriented adaptivity

E. Chung, S. Pollock, S. M. Pun, Online basis construction for goal-oriented adaptivity in the Generalized Multiscale Finite Element Method,
J. Comput. Phys., 393, p. 59-73, 2019.
DOI: 10.1016/ preprint: arXiv:math.NA/1812.02290

E. T. Chung, S. Pollock, S. M. Pun, Goal-oriented adaptivity of mixed GMsFEM for flows in heterogeneous media, Comput. Methods Appl. Mech. Eng., 323, p 151-173, 2017.
DOI: 10.1016/j.cma.2017.05.019

E.T. Chung, W.T. Leung, S. Pollock, Goal-oriented adaptivity for GMsFEM, J. Comput. Appl. Math., 296, p 625-637, 2016.
DOI: 10.1016/   preprint: arXiv:math.NA/1509.05643.

M. Holst, S. Pollock, and Y. Zhu, Convergence of goal-oriented adaptive finite element methods for semilinear problems, Comp. Vis. Sci., 17(1), p 43-63, 2015.
DOI: 10.1007/s00791-015-0243-1.   preprint: arXiv:math.NA/1203.1381.

M. Holst and S. Pollock, Convergence of goal-oriented adaptive finite element methods for nonsymmetric problems, Numer. Meth. Part. D.E., 32(2), p 479-509, 2016.
DOI: 10.1002/num.22002.   preprint: arXiv:math.NA/1108.3660.

inverse kinematics

E. A. Coutsias, K. W. Lexa, M. J. Wester, S. N. Pollock, M. P. Jacobson, Exhaustive conformational sampling of complex fused ring macrocycles using inverse kinematics, J. Chem. Theory Comput., 12 (9), p 4674-4687, 2016.
DOI: 10.1021/acs.jctc.6b00250

W.M. Brown, S. Martin, S.N. Pollock, E.A. Coutsias, J.P. Watson, Algorithmic dimensionality reduction for molecular structure analysis, J. Chem. Phys. 129(6): 064118, 2008.
DOI: 10.1063/1.2968610.

S.N. Pollock, E.A. Coutsias, M.J. Wester and T.I. Oprea, Scaffold topologies I: exhaustive enumeration up to eight rings, J. Chem. Inf. Model, 48(7), p. 1304-1310, 2008.
DOI: 10.1021/ci7003412.

M.J. Wester, S.N. Pollock, E.A. Coutsias, T.K. Allu, S. Muresan and T.I. Oprea, Scaffold topologies II: analysis of chemical databases, J. Chem Inf. Model., 48(7), p. 1311-1324, 2008.
DOI: 10.1021/ci700342h.