Jon Wilkening's publications

• C. L. Epstein and J. Wilkening, Some analytic results for Kimura diffusion operators, Acta Mathematica Vietnamica, 45 (2020) 171-181. preprint link to journal
• C. L. Epstein and J. Wilkening, Eigenfunctions and the Dirichlet problem for the classical Kimura diffusion operator, SIAM J. Applied Math, 77/1 (2017) 51-81. preprint link to journal
• J. Wilkening and A. Cerfon, A spectral transform method for singular Sturm-Liouville problems with applications to energy diffusion in plasma physics, SIAM J. Appl. Math., 75/2 (2015) 350-392. preprint link to journal
• J. Wilkening, A. Cerfon, and M. Landreman, Accurate spectral numerical schemes for kinetic equations with energy diffusion, J. Comput. Phys, 294 (2015) 58-77. preprint link to journal
• J. Birrell, J. Wilkening and J. Rafelski, Boltzmann equation solver adapted to emergent chemical non-equilibrium, J. Comput. Phys., 281 (2015) 896-916. preprint, link to journal
• F. A. Grunbaum, L. Velazquez and J. Wilkening, Occupation time for classical and quantum walks, From Operator Theory to Orthogonal Polynomials, Combinatorics and Number Theory, Editors: Fritz Gesztesy and Andrei Martinez-Finkelshtein. Birkhauser (2021). preprint link to book
• J. Bourgain, F. A. Grunbaum, L. Velazquez and J. Wilkening, Quantum recurrence of a subspace and operator-valued Schur functions, Comm. Math. Phys., 329 (2014) 1031-1067. preprint, link to journal

• J. Wilkening and X. Zhao, Spatially quasi-periodic water waves of finite depth, Proc R Soc A 479 (2023) 20230019:1-28, link to journal
• J. Wilkening and X. Zhao, Spatially quasi-periodic bifurcations from periodic traveling water waves and a method for detecting bifurcations using signed singular values, J Comput Phys 478 (2023) 111954:1-34, link to journal
• DM Ambrose, R Camassa, JL Marzuola, RM McLaughlin, Q Robinson and J. Wilkening, Numerical algorithms for water waves with background flow over obstacles and topography, Adv Comput Math 48 (2022) 46:1-62. link to journal
• J. Wilkening, Traveling-standing water waves, Fluids, 6 (2021) 187:1-35. link to journal
• J. Wilkening and X. Zhao, Spatially quasi-periodic water waves of infinite depth, J. Nonlinear Sci., 31 (2021) 52:1-43. link to journal
• J. Wilkening and X. Zhao, Quasi-periodic travelling gravity-capillary waves, J. Fluid Mech., 915 (2021) A7:1-35. link to journal
• J. Wilkening, Harmonic stability of standing water waves, Quarterly of Applied Math, 78/2 (2020) 219-260. preprint link to journal
• C.H. Aurther, R. Granero-Belinchon, S. Shkoller and J. Wilkening, Rigorous asymptotic models of water waves, Water Waves, 1 (2019) 71-130. preprint link to journal
• O. Trichtchenko, B. Deconinck and J. Wilkening, The instability of Wilton ripples, Wave Motion, 66 (2016) pp. 147-155. preprint, link to journal
• J. Wilkening, Relative-periodic elastic collisions of water waves, Contemp. Math., 635, (2015) 109-129. preprint link to book
• C. H. Rycroft and J. Wilkening, Computation of three-dimensional standing water waves, J. Comput. Phys., 255 (2013) 612-638. preprint, link to journal
• J. Wilkening and J. Yu, Overdetermined shooting methods for computing standing water waves with spectral accuracy, Comput. Sci. Disc. 5 (2012) 014017. water2.pdf
• M. O. Williams, E. Shlizerman, J. Wilkening and J. N. Kutz, The low dimensionality of time-periodic standing waves in water of finite and infinite depth, SIAM J. Appl. Dyn. Syst., 11/3 (2012), 1033-1061. water_pod.pdf
• Jon Wilkening, Breakdown of self-similarity at the crests of large amplitude standing water waves, Phys. Rev. Lett, 107 (2011) 184501. water1.pdf

• S. Qadeer and J. Wilkening, Computing the Dirichlet-Neumann operator on a cylinder, SIAM J. Numer. Anal., 57/3 (2019) 1183-1204. preprint link to journal
• J. Wilkening and V. Vasan, Comparison of five methods of computing the Dirichlet-Neumann operator for the water wave problem, Contemp. Math., 635, (2015), 175-210. preprint link to book
• L. C. Lee, S. J. S. Morris and J. Wilkening, Stress concentrations, diffusionally-accommodated grain boundary sliding and the viscoelasticity of polycrystals, Proc. Royal Soc. A, 467 (2011), pp. 1624-1644. gb-sliding.pdf
• J. Wilkening, L. Borucki, J. A. Sethian, Analysis of stress-driven grain boundary diffusion, part I, SIAM J. Appl. Math. 64/6 (2004), pp. 1839-1863. gb-diff1.pdf
• J. Wilkening, L. Borucki, J. A. Sethian, Analysis of stress-driven grain boundary diffusion, part II: degeneracy, SIAM J. Appl. Math. 64/6 (2004), pp. 1864-1886. gb-diff2.pdf
• J. A. Sethian, J. Wilkening, A numerical model of stress driven grain boundary diffusion, J. Comput. Phys., 193/1 (2004), pp. 275-305. gb-num.pdf
• J. Wilkening, Mathematical Analysis and Numerical Simulation of Electromigration, PhD thesis, University of California, Berkeley, May 2002. wilkening-thesis.pdf

• M. J. Zahr, P.-O. Persson and J. Wilkening, A fully discrete adjoint method for optimization of flow problems on deforming domains with time-periodicity constraints, Computers and Fluids, 139 (2016) 130-147. arXiv:1512.00616 preprint, link to journal
• Sanjay Govindjee, Trevor Potter and Jon Wilkening, Dynamic stability of spinning viscoelastic cylinders at finite deformation, Int. J. Solids Struct. 51 (2014) 3589-3603. preprint, link to journal
• Sanjay Govindjee, Trevor Potter and Jon Wilkening, Cyclic steady states of treaded rolling bodies, Int. J. Numer. Meth. Engng. 99 (2014) 203-220. preprint, link to journal
• M. O. Williams, J. Wilkening, E. Shlizerman and J. N. Kutz, Continuation of periodic solutions in the waveguide array mode-locked laser, Physica D, 240/22 (2011), pp. 1791-1804. laser.pdf
• David M. Ambrose and Jon Wilkening, Computation of symmetric, time-periodic solutions of the vortex sheet with surface tension, Proc. Natl. Acad. Sci., 107/8 (2010), pp. 3361-3366. vtxs1.pdf
• David M. Ambrose and Jon Wilkening, Dependence of time-periodic vortex sheets with surface tension on mean vortex sheet strength, Procedia IUTAM 11 (2014) 15-22. vtxs2.pdf
• D.M. Ambrose and J. Wilkening. Computation of time-periodic solutions of nonlinear systems of partial differential equations. Proceedings of Hyperbolic Problems: Theory, Numerics, and Applications. Beijing, China, 2010. Higher Education Press, pp. 273-280, (2012). vtxs3.pdf
• David M. Ambrose and Jon Wilkening, Computation of time-periodic solutions of the Benjamin-Ono equation, J. Nonlinear Sci., 20/3 (2010), pp. 277-308. benj1.pdf
• David M. Ambrose and Jon Wilkening, Global paths of time-periodic solutions of the Benjamin-Ono equation connecting pairs of traveling waves, Comm. App. Math. and Comp. Sci., 4/1 (2009), pp. 177-215. benj2.pdf
• Jon Wilkening, An infinite branching hierarchy of time-periodic solutions of the Benjamin-Ono equation, arXiv:0811.4209. benj3.pdf

• E. Kim and J. Wilkening, Convergence of a mass-lumped finite element method for the Landau-Lifshitz equation, Quarterly of Appl. Math., 76/2 (2018) pp. 383-405. preprint link to journal

• A. Lieb, C. H. Rycroft and J. Wilkening, Optimizing intermittent water supply in urban pipe distribution networks, SIAM J. Appl. Math., 76/4, (2016), pp. 1492-1514. preprint link to journal
• Jon Wilkening, Practical error estimates for Reynolds' lubrication approximation and its higher order corrections, SIAM J. Math. Anal., 41/2 (2009), pp. 588-630. rle.pdf
• Jon Wilkening, Inf-sup estimates for the Stokes problem in a periodic channel, arXiv:0706.4082. infsup.pdf
• Jon Wilkening, A. E. Hosoi, Shape optimization of a sheet swimming over a thin liquid layer, J. Fluid Mech., 601 (2008), pp. 25-61. snail.pdf

• X. Tu, M. Morzfeld, J. Wilkening and A. Chorin, Parameter estimation by implicit sampling, Comm. App. Math. and Comp. Sci., 10/2 (2015), pp. 205-225. preprint link to journal

• Michael Westdickenberg and Jon Wilkening, Variational particle scheme for the porous medium equation and for the system of isentropic Euler equations, ESAIM-Math. Model. Num., 44 (2010), pp. 133-166. VarScheme.pdf

• Jon Wilkening and Jia Yu, A local construction of the Smith normal form of a matrix polynomial, J. Symbolic Comput., 46 (2011), pp. 1-22. smith.pdf
• J. Wilkening, An algorithm for computing Jordan chains and inverting analytic matrix functions, Linear Algebra Appl., 427/1 (2007), pp. 6-25. Achain.pdf