Akers-Nicholls short course on HOPS numerical methods

graphic-47Dave Nicholls and Ben Akers are giving a four hour short course on HOPS Methods for boundary value problems with particular attention to their use in water wave problems. HOPS (higher order perturbation of surfaces) are effective numerical methods for PDEs on piecewise homogeneous domains.  In the first lecture, on Tuesday 15 July, Dave presented a method for solving for the Dirichlet-Neumann operator for a domain which is periodic in the x-direction, infinite in the y-direction but bounded above by a surface y=g(x).  Lecture II focussed on the computation of travelling wave solutions, particularly periodic waves and nonlinear waves bifurcating near the Wilton ripples.  Lecture III covered the role of analyticity in the expansion techniques, and convergence proofs.  Lecture IV covered methods for spectral stability: boundary perturbation for spectral stability, analyticity of the spectrum, resonant interaction theory, and modulational instablities. See the HOPS website for .pdf files and matlab files associated with the lectures.  Videos of the four lectures are available here (I), here (II), here (III), and here (IV).

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