Felix Kwok

Refereed journal publications

Potential-based reduced Newton algorithm for nonlinear multiphase flow in porous media. F. Kwok and H. Tchelepi, J. Comput. Phys., 227:706–727, 2007.
Convergence of implicit monotone schemes with applications in multiphase flow in porous media. F. Kwok and H. Tchelepi, SIAM J. Numer. Anal., 46:2662–2687, 2008.
Optimized additive Schwarz with Harmonic Extension as a discretization of continuous parallel Schwarz methods. F. Kwok, SIAM J. Numer. Anal., 49:1289–1316, 2011.
Chladni Figures and the Tacoma Bridge: Motivating PDE Eigenvalue Problems via Vibrating Plates. M. J. Gander and F. Kwok, SIAM Rev., 54(3):573–596, 2012.
Best Robin parameters for optimized Schwarz methods at cross points. M. J. Gander and F. Kwok, SIAM J. Sci. Comput., 34(4):A1849–A1879, 2012.
B-Methods for the Numerical Solution of Evolution Problems with Blow-up Solutions, Part I: Variation of the Constant. M. Beck, M. J. Gander and F. Kwok, SIAM J. Sci. Comput., 37(6):A2998–3029, 2015.
Nonlinear preconditioning: How to use a nonlinear Schwarz method to precondition Newton's Method. V. Dolean, M. J. Gander, W. Kheriji, F. Kwok and R. Masson, SIAM J. Sci. Comput., 38: A3357–3380, 2016.
Dirichlet-Neumann and Neumann-Neumann Waveform Relaxation Algorithms for Parabolic Problems. M. J. Gander, F. Kwok and B. C. Mandal, Electron. T. Numer. Ana., 45: 424–456, 2016.
Discrete Analysis of Domain Decomposition Approaches for Mesh Generation via the Equidistribution Principle. R. D. Haynes and F. Kwok, Math. Comp., 86(303):233–273, 2017.
Multigrid Interpretations of the Parareal Algorithm Leading to an Overlapping Variant and MGRIT. M.J. Gander, F. Kwok and H. Zhang, Comput. Visualization Sci., 19:59–74, 2018.
Schwarz Waveform Relaxation with Adaptive Pipelining. F. Kwok and B. Ong, SIAM J. Sci. Comput., 41(1):A339–A364, 2019.
Sequential-Implicit Newton Method for Multiphysics Simulation. Z.-Y. Wong, F. Kwok, R. N. Horne and H. A. Tchelepi, J. Comput. Phys., 391:155–178, 2019.
PARAOPT: A parareal algorithm for optimality systems. M. J. Gander, F. Kwok and J. Salomon, SIAM J. Sci. Comput., 42(5):A2773–A2802, 2020.
Dirichlet-Neumann Waveform Relaxation Methods for Parabolic and Hyperbolic Problems in Multiple Subdomains. M. J. Gander, F. Kwok and B. C. Mandal, BIT, 61:173–207, 2021.
On the choice of Robin Parameters for the Optimized Schwarz method for domains with non-conforming heterogeneities. Y. Gu and F. Kwok, J. Sci. Comput., 89(1):5, 2021.
B-Methods for the Numerical Simulation of Evolution Problems with Blow-up Solutions, Part II: Splitting Methods. M. Beck, M.J. Gander and F. Kwok, Comput. Math. Appl.,152:143–154, 2023.

Refereed conference proceedings and book chapters

Optimal interface conditions for an arbitrary decomposition into subdomains. M. J. Gander and F. Kwok, Domain Decomposition Methods in Science and Engineering XIX, Lecture Notes in Computational Science and Engineering 78, pp. 101–108, Springer-Verlag 2010.
Is Additive Schwarz with Harmonic Extension just Lions' method in disguise? F. Kwok, Domain Decomposition Methods in Science and Engineering XIX, Lecture Notes in Computational Science and Engineering 78, pp. 439–446, Springer-Verlag 2010.
On the applicability of Lions' energy estimates in the analysis of discrete optimized Schwarz methods with cross points. M. J. Gander and F. Kwok, Domain Decomposition Methods in Science and Engineering XX, Lecture Notes in Computational Science and Engineering 91, pp. 475–483, Springer-Verlag 2013.
Neumann–Neumann waveform relaxation for the time-dependent heat equation. F. Kwok, Domain Decomposition Methods in Science and Engineering XXI, Lecture Notes in Computational Science and Engineering 98, pp. 189–198, Springer-Verlag 2014.
A parallel Crank–Nicolson predictor-corrector method for many subdomains. F. Kwok, Domain Decomposition Methods in Science and Engineering XXI, Lecture Notes in Computational Science and Engineering 98, pp. 799–808, Springer-Verlag 2014.
Constrained Optimization: From Lagrangian Mechanics to Optimal Control and PDE Constraints. M. J. Gander, F. Kwok and G. Wanner, in Optimization with PDE Constraint, R. Hoppe (Ed.), Lecture Notes in Computational Science and Engineering 101, pp. 151–202, Springer 2014.
Schwarz Methods for the Time-Parallel Solution of Parabolic Control Problems. M. J. Gander and F. Kwok, Domain Decomposition Methods in Science and Engineering XXII, Lecture Notes in Computational Science and Engineering 104, pp. 207–216, Springer-Verlag 2016.
Pipeline Schwarz Waveform Relaxation. B. Ong, S. High and F. Kwok, Domain Decomposition Methods in Science and Engineering XXII, Lecture Notes in Computational Science and Engineering 104, pp. 363–370, Springer-Verlag 2016.
Dirichlet-Neumann and Neumann-Neumann Waveform Relaxation for the Wave Equation. M. J. Gander, F. Kwok and B. C. Mandal, Domain Decomposition Methods in Science and Engineering XXII, Lecture Notes in Computational Science and Engineering 104, pp. 501–509, Springer-Verlag 2016.
On the Time-domain Decomposition of Parabolic Optimal Control Problems. F. Kwok, Domain Decomposition Methods in Science and Engineering XXIII, Lecture Notes in Computational Science and Engineering 116, pp. 55–67, Springer-Verlag 2017.
Convergence of substructuring methods for elliptic optimal control problems. M. J. Gander, F. Kwok and B. C. Mandal, Domain Decomposition Methods in Science and Engineering XXIV, Lecture Notes in Computational Science and Engineering 125, pp. 291–300, Springer-Verlag 2018.
Numerical Methods for Spectral Theory. F. Kwok, in Spectral Theory and Applications, A. Girouard (Ed.), Contemporary Mathematics 720, pp. 101–151, American Mathematical Society 2018.
Optimized Schwarz-based Nonlinear Preconditioning for Elliptic PDEs. Y. Gu and F. Kwok, Domain Decomposition Methods in Science and Engineering XXV, Lecture notes in Computational Science and Engineering 138, pp. 260–267, Springer 2020.
Nonlinear optimized Schwarz preconditioner for elliptic optimal control problems. G. Ciaramella, F. Kwok and G. Müller, Domain Decomposition Methods in Science and Engineering XXVI, Lecture notes in Computational Science and Engineering 145, pp. 391–398, Springer 2022.
Optimized Schwarz method in time for transport control. D.-Q. Bui, B. Delourme, L. Halpern and F. Kwok, in Domain Decomposition Methods in Science and Engineering XXVII, Lecture notes in Computational Science and Engineering 149, pp. 93 –100, Springer 2024.
Multigrid interpretation of a three-level Parareal algorithm. S. Friedhoff, M.J. Gander and F. Kwok, in Domain Decomposition Methods in Science and Engineering XXVII, Lecture notes in Computational Science and Engineering 149, pp. 173 –180, Springer 2024.
A Parallel in Time Algorithm Based on ParaExp for Optimal Control Problems. F. Kwok and D. N. Tognon, accepted for publication in the Proceedings of the 63rd IEEE Conference on Decision and Control (CDC), Milan, Italy, 2024.

Books and Theses

Scalable Linear and Nonlinear Algorithms for Multiphase Flow in Porous Media. F. Kwok, Ph.D. thesis, Stanford University, December 2007.
Scientific Computing: an Introduction Using Maple and MATLAB. W. Gander, M. J. Gander and F. Kwok. Texts in Computational Science and Engineering 11, Springer 2014.
Numerical Analysis of Partial Differential Equations Using Maple and MATLAB. M. J. Gander and F. Kwok. Fundamentals of Algorithms 12, SIAM 2018.
Domain Decomposition Methods in Science and Engineering XXVI, Lecture Notes in Computational Science and Engineering, Vol 145, S.C. Brenner, E. Chung, A. Klawonn, F. Kwok, J. Xu and J. Zou (Eds.), Springer 2022.

Conference posters and miscellany

Ordering-based approaches for improving solver efficiency in reservoir simulation. F. Kwok, Colloque Numérique Suisse, Université de Fribourg, April 2008.
Optimized Schwarz method for problems with cross points. M. J. Gander and F. Kwok, Swiss Numerics Colloquium, ETH Zurich, April 2010.
A domain decomposition method that converges in two iterations for any subdomain decomposition and PDE. M. J. Gander and F. Kwok, High Performance Computing and Emerging Architectures, IMA, University of Minnesota, January 2011.
Prix Nobel de chimie, quasi-cristaux, périodicité et pavages. Pierre de la Harpe and Felix Kwok, Images des Mathématiques, CNRS, 2011. (Online article for general public, available at http://images.math.cnrs.fr/Prix-Nobel-de-chimie-quasi.html)
Analysis of a Crank-Nicolson predictor-corrector method. F. Kwok, Swiss Numerics Day, Universität Bern, April 2012.
Discrete convergence analysis for Optimized Schwarz methods using energy estimates. M. J. Gander, F. Kwok and K. Santugini, 22nd International Conference on Domain Decomposition Methods, Lugano, Switzerland, September 2013.