Yearly Archives: 2017

Harmonic density interpolation methods for high-order evaluation of Laplace layer potentials in 2D and 3D

We present a simple but effective harmonic density interpolation method for the numerical evaluation of singular and nearly singular Laplace boundary integral operators and layer poten- tials in two and three spatial dimensions. The method relies on the use of Green’s third identity and local Taylor-like interpolations of density functions […]

Equation Level Matching: An Extension of the Method of Matched Asymptotic Expansion for Problems of Wave Propagation

We introduce an alternative to the method of matched asymptotic expansions. In the “traditional” implementation, approximate solutions, valid in different (but overlapping) regions, are matched by using “intermediate” variables. Here we propose to match at the level of the equations involved, via a “uniform expansion” whose equations enfold those of […]

Non-specular reflection of walking droplets

Since their discovery by Yves Couder and Emmanuel Fort, droplets walking on a vibrating liquid bath have attracted considerable attention because they unexpectedly exhibit certain features reminiscent of quantum particles. While the behaviour of walking droplets in unbounded geometries has to a large extent been rationalized theoretically, no such rationale […]