Journal Publications

Manas Vishal, Scott E. Field, Katherine Rink, Sigal Gottlieb, Gaurav Khanna, "Towards exponentially-convergent simulations of extreme-mass-ratio inspirals: A time-domain solver for the scalar Teukolsky equation with singular source terms" Phys. Rev. D 110, 104009 – Published 5 November 2024
On ArXiv https://arxiv.org/abs/2307.01349
URL: https://link.aps.org/doi/10.1103/PhysRevD.110.104009

DOI: 10.1103/PhysRevD.110.104009

Scott E. Field, Sigal Gottlieb, Gaurav Khanna, Ed McClain, "Discontinuous Galerkin method for linear wave equations involving derivatives of the Dirac delta distribution" Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2020+1 Selected Papers from the ICOSAHOM Conference, Vienna, Austria, July 12-16, 2021. Springer 2023.
Also on ArXiv https://arxiv.org/abs/2211.14390

Sigal Gottlieb, Zachary J. Grant, Jingwei Hu, Ruiwen Shu, "High order unconditionally strong stability preserving multi-derivative implicit and IMEX Runge--Kutta methods with asymptotic preserving properties." SIAM Journal on Numerical Analysis (2022), Volume 60(1) pp. 423-449.
https://doi.org/10.1137/21M1403175
Also on ArXiv https://arxiv.org/abs/2102.11939

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." Journal of Computational Physics  (2022), Volume 455, pp. 110927.
https://doi.org/10.1016/j.jcp.2021.110927
Also on ArXiv  https://arxiv.org/abs/2010.06360. 

Yanlai Chen, Sigal Gottlieb, Lijie Ji, Yvon Maday, Zhenli Xu, “An EIM-degradation free reduced basis method via over collocation and residual hyper reduction-based error estimation." Journal of Computational Physics (2021) Volume 444: 110545,
https://doi.org/10.1016/j.jcp.2021.110545
Also on ArXiv https://arxiv.org/abs/2101.05902.  

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."  Communications on Applied Mathematics and Computation (2021)
https://doi.org/10.1007/s42967-021-00129-2.  
Also on ArXiv 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

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. Also on ArXiv  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' equation.” Journal 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.