43 citations · 292 across the 26 of their papers we have counts for
27 papers
Spatially quasi-periodic water waves of finite depth
Jon Wilkening, Xinyu Zhao
We present a numerical study of spatially quasi-periodic gravity-capillary waves of finite depth in both the initial value problem and traveling wave settings. We adopt a quasi-per…
Spatially quasi-periodic bifurcations from periodic traveling water waves and a method for detecting bifurcations using signed singular values
Jon Wilkening, Xinyu Zhao
We present a method of detecting bifurcations by locating zeros of a signed version of the smallest singular value of the Jacobian. This enables the use of quadratically convergent…
Numerical Algorithms for Water Waves with Background Flow over Obstacles and Topography
David M. Ambrose, Roberto Camassa, Jeremy L. Marzuola +3
We present two accurate and efficient algorithms for solving the incompressible, irrotational Euler equations with a free surface in two dimensions with background flow over a peri…
Quasi-periodic traveling gravity-capillary waves
Jon Wilkening, Xinyu Zhao
We present a numerical study of spatially quasi-periodic traveling waves on the surface of an ideal fluid of infinite depth. This is a generalization of the classic Wilton ripple p…
Spatially quasi-periodic water waves of infinite depth
Jon Wilkening, Xinyu Zhao
We formulate the two-dimensional gravity-capillary water wave equations in a spatially quasi-periodic setting and present a numerical study of solutions of the initial value proble…
Harmonic Stability of Standing Water Waves
Jon Wilkening
A numerical method is developed to study the stability of standing water waves and other time-periodic solutions of the free-surface Euler equations using Floquet theory. A Fourier…
Computing the Dirichlet-Neumann Operator on a Cylinder
Saad Qadeer, Jon Wilkening
The computation of the Dirichlet-Neumann operator for the Laplace equation is the primary challenge for the numerical simulation of the ideal fluid equations. The techniques used c…
Rigorous Asymptotic Models of Water Waves
C. H. Arthur Cheng, Rafael Granero-Belinchon, Steve Shkoller +1
We develop a rigorous asymptotic derivation for two mathematical models of water waves that capture the full nonlinearity of the Euler equations up to quadratic and cubic interacti…
Convergence of a mass-lumped finite element method for the Landau-Lifshitz equation
Eugenia Kim, Jon Wilkening
The dynamics of the magnetic distribution in a ferromagnetic material is governed by the Landau-Lifshitz equation, which is a nonlinear geometric dispersive equation with a nonconv…
The instability of Wilton ripples
Olga Trichtchenko, Bernard Deconinck, Jon Wilkening
Wilton ripples are a type of periodic traveling wave solution of the full water wave problem incorporating the effects of surface tension. They are characterized by a resonance phe…
A Fully Discrete Adjoint Method for Optimization of Flow Problems on Deforming Domains with Time-Periodicity Constraints
Matthew J. Zahr, Per-Olof Persson, Jon Wilkening
A variety of shooting methods for computing fully discrete time-periodic solutions of partial differential equations, including Newton-Krylov and optimization-based methods, are di…
Optimizing intermittent water supply in urban pipe distribution networks
Anna M. Lieb, Chris H. Rycroft, Jon Wilkening
In many urban areas of the developing world, piped water is supplied only intermittently, as valves direct water to different parts of the water distribution system at different ti…
Eigenfunctions and the Dirichlet problem for the Classical Kimura Diffusion Operator
Charles L. Epstein, Jon Wilkening
We study the classical Kimura diffusion operator defined on the n-simplex, We give novel constructions for th…
Comparison of five methods of computing the Dirichlet-Neumann operator for the water wave problem
Jon Wilkening, Vishal Vasan
We compare the effectiveness of solving Dirichlet-Neumann problems via the Craig-Sulem (CS) expansion, the Ablowitz-Fokas-Musslimani (AFM) implicit formulation, the dual AFM formul…
Relative-Periodic Elastic Collisions of Water Waves
Jon Wilkening
We compute time-periodic and relative-periodic solutions of the free-surface Euler equations that take the form of overtaking collisions of unidirectional solitary waves of differe…
Boltzmann Equation Solver Adapted to Emergent Chemical Non-equilibrium
Jeremiah Birrell, Jon Wilkening, Johann Rafelski
We present a novel method to solve the spatially homogeneous and isotropic relativistic Boltzmann equation. We employ a basis set of orthogonal polynomials dynamically adapted to a…
Accurate Spectral Numerical Schemes for Kinetic Equations with Energy Diffusion
Jon Wilkening, Antoine Cerfon, Matt Landreman
We examine the merits of using a family of polynomials that are orthogonal with respect to a non-classical weight function to discretize the speed variable in continuum kinetic cal…
A Spectral Transform Method for Singular Sturm-Liouville Problems with Applications to Energy Diffusion in Plasma Physics
Jon Wilkening, Antoine Cerfon
We develop a spectrally accurate numerical method to compute solutions of a model partial differential equation used in plasma physics to describe diffusion in velocity space due t…
Overdetermined Shooting Methods for Computing Standing Water Waves with Spectral Accuracy
Jon Wilkening, Jia Yu
A high-performance shooting algorithm is developed to compute time-periodic solutions of the free-surface Euler equations with spectral accuracy in double and quadruple precision.…
Breakdown of self-similarity at the crests of large amplitude standing water waves
Jon Wilkening
We study the limiting behavior of large-amplitude standing waves on deep water using high-resolution numerical simulations in double and quadruple precision. While periodic traveli…
An infinite branching hierarchy of time-periodic solutions of the Benjamin-Ono equation
Jon Wilkening
We present a new representation of solutions of the Benjamin-Ono equation that are periodic in space and time. Up to an additive constant and a Galilean transformation, each of the…
Global paths of time-periodic solutions of the Benjamin-Ono equation connecting pairs of traveling waves
David M. Ambrose, Jon Wilkening
We classify all bifurcations from traveling waves to non-trivial time-periodic solutions of the Benjamin-Ono equation that are predicted by linearization. We use a spectrally accur…
A local construction of the Smith normal form of a matrix polynomial
Jon Wilkening, Jia Yu
We present an algorithm for computing a Smith form with multipliers of a regular matrix polynomial over a field. This algorithm differs from previous ones in that it computes a loc…
Variational Particle Schemes for the Porous Medium Equation and for the System of Isentropic Euler Equations
Michael Westdickenberg, Jon Wilkening
Both the porous medium equation and the system of isentropic Euler equations can be considered as steepest descents on suitable manifolds of probability measures in the framework o…