# Publications

##### Journal Publications

- Sigal Gottlieb, Zachary J. Grant, Jingwei Hu, Ruiwen Shu, “High order positivity preserving and asymptotic preserving multi-derivative methods.”
- Victor DeCaria, Sigal Gottlieb, Zachary J. Grant, William J. Layton, “A general linear method approach to the design and optimization of efficient, accurate, and easily implemented time-stepping methods in CFD.” https://arxiv.org/abs/2010.06360.
- Scott E. Field, Sigal Gottlieb, Zachary J. Grant, Leah F. Isherwood, Gaurav Khanna, “A GPU-accelerated mixed-precision WENO method for extremal black hole and gravitational wave physics computations.” https://arxiv.org/abs/2010.04760.
- Adi Ditkowski, Sigal Gottlieb, Zachary J. Grant, “Two-derivative error inhibiting schemes with post-processing.” SIAM Journal on Numerical Analysis (2020), Volume 58 Issue 6, pp. 3197–3225. Also on ArXiv https://arxiv.org/abs/1912.04159.
- Adi Ditkowski, Sigal Gottlieb, Zachary J. Grant, “Explicit and implicit error inhibiting schemes with post-processing.” Computers & Fluids (2020), Volume 208, 104534. https://doi.org/10.1016/j.compfluid.2020.104534. Also on Arxiv. arxiv.org/abs/1910.02937
- Yanlai Chen, Sigal Gottlieb, Lijie Ji, Yvon Maday, Zhenli Xu, “L1-ROC and R2-ROC: L1- and R2-based Reduced Over-Collocation methods for parametrized nonlinear partial differential equations.” https://arxiv.org/abs/1906.07349
- L. Isherwood, Z. Grant, S. Gottlieb, “Strong Stability Preserving Integrating Factor Two-Step Runge–Kutta Methods.” Journal of Scientific Computing (2019), Volume 81, Issue 3, pp 1446–1471. https://arxiv.org/abs/1904.07194
- Z. Grant, S. Gottlieb, D.C. Seal, “A Strong Stability Preserving Analysis for Explicit Multistage Two-Derivative Time-Stepping Schemes Based on Taylor Series Conditions.”
*Communications on Applied Mathematics and Computation*(2019) 1: pp.21-59. Also in https://arxiv.org/abs/1804.10526 - L. Isherwood, S. Gottlieb, Z. Grant, “Downwinding for Preserving Strong Stability in Explicit Integrating Factor Runge–Kutta Methods.”
*Pure and Applied Mathematics Quarterly*(2018) 14(1): pp.3-25. https://arxiv.org/abs/1810.04800 - L. Isherwood, S. Gottlieb, Z. Grant, “Strong Stability Preserving Integrating Factor Runge–Kutta Methods.”
*SIAM Journal on Numerical Analysis*(2018) 56(6): pp. 3276-3307. https://arxiv.org/abs/1708.02595 - S. Conde, S. Gottlieb, Z. Grant, J.N. Shadid, “Implicit and Implicit-Explicit Strong Stability Preserving Runge–Kutta Methods with High Linear Order.”
*Journal of Scientific Computing*(2017) 73(2): pp. 667-690. https://arxiv.org/abs/1702.04621 - A. Ditkowski and S. Gottlieb, “Error Inhibiting Block One-step Schemes for Ordinary Differential Equations.”
*Journal of Scientific Computing*(2017) 73(2): pp. 691- 711. https://arxiv.org/abs/1701.08568 - C. Bresten, S. Gottlieb, Z. Grant, D. Higgs, D.I. Ketcheson, and A. Nemeth, “Explicit strong stability preserving multistep Runge-Kutta methods.”
*Mathematics of Computation*(2017) 86: pp. 747-769. https://arxiv.org/abs/1307.8058 - A.J. Christlieb, S. Gottlieb, Z. Grant, and D. C. Seal, “Explicit Strong Stability Preserving Multistage Two-Derivative Time-Stepping Schemes.”
*Journal of Scientific Computing*(2016) 68(3): pp.914-942. https://arxiv.org/abs/1504.07599 - Y. Chen, S. Gottlieb, A. Heryudono and A. Narayan, “A Reduced Radial Basis Function Method for Partial Differential Equations on irregular domains”.
*Journal of Scientific Computing*(2016) 66(1):67-90. https://arxiv.org/abs/1410.1890 - Dong B., Gottlieb S., Hristova Y., Jiang Y., Wang H, “The Effect of the Sensitivity Parameter in Weighted Essentially Non-oscillatory Methods.” In: Brenner S. (eds) Topics in Numerical Partial Differential Equations and Scientific Computing. The IMA Volumes in Mathematics and its Applications, vol 160. Springer, New York, NY. (2016)
- S. Gottlieb, “Strong Stability Preserving Time Discretizations: A Review” in Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014. Editors R. Kirby, M. Berzins,and J. S. Hesthaven, Volume 106 of Lecture Notes in Computational Science and Engineering, pp. 17-30. Springer International (2015).
- S. Gottlieb, Z. Grant, and D. Higgs, “Optimal Explicit Strong Stability Preserving Runge–Kutta Methods with High Linear Order and optimal Nonlinear Order.”
*Mathematics of Computation*(2015) 84: 2743-2761. https://arxiv.org/abs/1403.6519 - K. Cheng, W. Feng, S. Gottlieb, and C. Wang. “A Fourier Pseudospectral Method for the ”Good” Boussinesq Equation with Second Order Temporal Accuracy”.
*Numerical Methods for Partial Differential Equations*(2015) 31 (1): 202-22. https://arxiv.org/abs/1401.6327 - Y. Chen, S. Gottlieb, and Y. Maday, “Parametric Analytical Preconditioning and its Applications to the Reduced Collocation Methods”.
*Comptes Rendus Mathematique*(2014) 352(7-8):661-666. https://arxiv.org/abs/1403.7273 - Y. Chen and S. Gottlieb, “Reduced Collocation Methods: Reduced Basis Methods in the Collocation Framework.”
*Journal of Scientific Computing*(2013) 55(3): pp. 718–737. - S. Gottlieb, F. Tone, C. Wang, X. Wang, and D. Wirosoetisno, “Long time stability of a classical efficient scheme for two dimensional Navier-Stokes equations.”
*SIAM Journal on Numerical Analysis*(2012) 50: pp. 126-150 - S. Gottlieb and C. Wang, “Stability and convergence analysis of fully discrete Fourier collocation spectral method for 3-D viscous Burgers’
^{e}quation.” J*ournal of Sci-ntific Computing*( 2012) 5 3(1),:pp. 102-128. - D.I. Ketcheson, S. Gottlieb, and C. B. Macdonald, “Strong stability preserving two- step Runge-Kutta methods.”
*SIAM Journal on Numerical Analysis*(2012) 49: pp. 2618-2639. - S. Gottlieb, J.-H. Jung, and S. Kim, “Iterative adaptive RBF methods for detection of edges in two dimensional functions.”
*Applied Numerical Mathematics*(2011) 61(1): pp. 77-91. - S. Gottlieb, J.-H. Jung, and S. Kim, “A review of David Gottlieb’s work on the resolution of the Gibbs phenomenon”
*Communications in Computational Physics*(2011), 9:pp. 497-519. - J.-H. Jung, S. Gottlieb, S. O. Kim, C. L. Bresten and D. Higgs, “Recovery of High Order Accuracy in Radial Basis Function Approximations of Discontinuous Problems.”
*Journal of Scientific Computing*(2010) 45(1-3), pp. 359–381. - S. Gottlieb, D. Ketcheson, and C.-W. Shu “High Order Strong Stability Preserving Time Discretizations.”
*Journal of Scientific Computing*, vol 38, No. 3 (2009), pp. 251–289. - J.-H. Jung and S. Gottlieb, “On the Numerical Implementation of spectral Galerkin Penalty Methods.”
*Communications in Computational Physics*vol. 5, No. 2-4, (2009) pp. 600-619. - D. Ketcheson, C. Macdonald, and S. Gottlieb, “Optimal implicit strong stability preserving Runge-Kutta methods.” Applied Numerical Mathematics, vol. 59, No. 2, (2009) pp. 373-392.
- C. Macdonald, S. Gottlieb, and S. J. Ruuth, “A numerical study of diagonally split Runge–Kutta methods for PDEs with discontinuities.” Journal of Scientific Computing vol, 36, No. 1 (2008) , pp. 89-112.
- R. Archibald, A. Gelb, S. Gottlieb and J. Ryan, “One-sided post-processing for the Discontinuous Galerkin Method Using ENO-type stencil choice and the Edge Detection Method.” Journal of Scientific Computing vol. 28 (2006), pp.167- 190.
- S. Gottlieb, D. Gottlieb and C.-W. Shu, “Recovering High Order Accuracy in WENO Computations of Steady State Hyperbolic Systems” Journal of Scientific Computing vol. 28 (2006), pp.307-318.
- S. Gottlieb and S. J. Ruuth, “Optimal strong stability preserving time-stepping schemes with fast downwind spatial discretizations.” Journal of Scientific Computing vol. 27 (2006), pp. 289-304.
- S. Gottlieb, J. S. Mullen and S. J. Ruuth, “A fifth order flux-implicit WENO method.”Journal of Scientific Computing vol. 27 (2006), pp. 271-288.
- S. Gottlieb, “On High Order Strong Stability Preserving Runge-Kutta and Multi Step Time Discretizations.” Journal of Scientific Computing vol. 25 (2005), pp. 105-128.
- D. Gottlieb and S. Gottlieb, “Spectral Methods for Compressible Reactive Flows”Comptes Rendus Mecanique 333 (2005), pp. 3-16.
- S. Gottlieb and L.-A. J. Gottlieb, “ Strong Stability Preserving Properties of Runge– Kutta Time Discretization Methods for Linear Constant Coefficient Operators”Journal of Scientific Computing 18 (1) (2003), pp. 89-109.
- S. Gottlieb, C.W. Shu and E. Tadmor, “Strong Stability Preserving High Order Time Discretization Methods.” SIAM review vol. 43 no. 1 (2001), pp. 89-112
- P.F. Fischer and S. Gottlieb, “Solving A x = b using a modified conjugate gradient method based on the roots of A.” Journal of Scientific Computing vol. 15 no. 4 (2000), pp.441-456.
- S. Gottlieb and C.W. Shu, “Total Variation Diminishing Runge-Kutta Schemes.”Mathematics of Computation vol. 67 (1998), pp.73-85.
- P. F. Fischer and S. Gottlieb “A Modified Conjugate Gradient Method for the Solution of Ax = b.”Journal of Scientific Computing vol. 13 no. 2 (1998), pp.173-183.
- C.R. Johnson, I.M. Spitkovsky and S. Gottlieb “Inequalities Involving the Numerical Radius.” Linear and Multilinear Algebra vol. 37 (1994), pp.13-24.

##### Book Publications

- Jan S. Hesthaven, Sigal Gottlieb, David Gottlieb,
**Spectral Methods for Time Dependent Problems**. Cambridge Monographs on Applied and Computational Mathematics (No. 21)*Cambridge University Press*(2006). ISBN 0521792118 - Sigal Gottlieb, David Ketcheson and Chi-Wang Shu,
**Strong Stability Preserving Runge– Kutta and Multistep Time Discretizations.***World Scientific Press.*January 2011. ISBN 978-981-4289-26-9

##### Conference Proceedings

- D. Gottlieb and S. Gottlieb, “Spectral Methods for Discontinuous Problems.” Proceedings 20th biennial Conference on Numerical Analysis, D.F. Griffiths and G. A. Watson, editors. University of Dundee Numerical Analysis Report NA/217 (2003).
- S. Gottlieb and J. S. Mullen, “ An Implicit WENO Scheme for Steady-State Com- putation of Scalar Hyperbolic Equations” in Computational Fluid and Solid Mechanics 2003 (ed. K.J. Bathe) , (2003) Proceedings Second MIT Con- ference on Computational Fluid and Solid Mechanics June 17–20, 2003 Pages 1946-1950.
- U. Qidwai and S. Gottlieb, “An efficient hole-filling algorithm for c-scan enhance- ment.” Review of the progress in Quantitative Nondestructive Evaluation (RQNDE), Maine, 2001.

##### Other Publications

- Y. Chen, G. Davis, S. Gottlieb, A. Hausknecht, A. Heryudono, and S.Kim. “Trans- formation of a mathematics department’s teaching and research through a focus on computational science.” JOCSE, 4(1):24–29, 2013.
- D. Gottlieb and S. Gottlieb “Spectral methods”. Scholarpedia, (2009) 4(9):7504.
- S. Gottlieb and D. Gottlieb, Review of “Spectral Methods for Incompressible Visocous Flow” by Roger Payret, SIAM Review vol. 45 (2003), pp.147-148
- D. Gottlieb and S. Gottlieb, Review of “High-Order Methods for Incompressible Fluid Flow” by M.O. Deville, P.F. Fischer and E.H. Mund., Mathematics of Computa- tion vol. 73 (2003), pp. 1039-1040