Consider the Poisson equation −∆u = f in a planar exterior domain of a bounded domain O. Assume that f = 0 in the outside of a disc with sufficiently large diameter. The solution u is assumed to be bounded at infinity. Discretizing the problem, we employ the finite element method (FEM, in short) inside the disc, and the charge simulation method (CSM, in short) outside the disc. A result of math...

Helmholtz stereopsis has been introduced recently as a surface reconstruction technique that does not assume a model of surface reflectance. In the reported formulation, correspondence was established using a rank constraint, necessitating at least three viewpoints and three pairs of images. Here, it is revealed that the fundamental Helmholtz stereopsis constraint defines a nonlinear partial di...

Helmholtz resonators are commonly used for tuning of acoustic systems such as industrial processes, vehicle exhaust, engine intake manifold systems and more. Past efforts resulted in limited tuning capability and significant mechanical complexity. The work presented here considers a system that modifies the acoustic response of a system continuously, online, allowing optimum performance over a ...

We report, to the best of our knowledge, the first exact analytical algebraic solitons of a generalized cubic-quintic Helmholtz equation. This class of governing equation plays a key role in photonics modelling, allowing a full description of the propagation and interaction of broad scalar beams. New conservation laws are presented, and the recovery of paraxial results is discussed in detail. T...

A three-dimensional Cartesian parabolic-equation model with a higher-order approximation to the square-root Helmholtz operator is presented for simulating underwater sound propagation in ocean waveguides. The higher-order approximation includes cross terms with the free-space square-root Helmholtz operator and the medium phase speed anomaly. It can be implemented with a split-step Fourier algor...

1 Rosettastein Consulting UG, Freising, Germany, 2 Wissenschaftszentrum Weihenstephan für Ernährung, Landnutzung und Umwelt, TUM-Technische Universität München, Freising, Germany, 3 Institute for Medical and Pharmaceutical Proficiency Assessment, Mainz, Germany, 4 Department of Pharmaceutical Sciences, Karl-Franzens-University Graz, Graz, Austria, 5 Molecular EXposomics, German Research Center ...

We have constructed a sequence of solutions of the Helmholtz equation forming an orthogonal sequence on a given surface. Coefficients of these functions depend on an explicit algebraic formulae from the coefficient of the surface. Moreover, for exterior Helmholtz equation we have constructed an explicit normal derivative of the Dirichlet Green function. In the same way the Dirichlet-to-Neumann ...

We have developed a three level implicit method for solution of the Helmholtz equation. Using the cubic spline in space and finite difference in time directions. The approach has been modied to drive Numerov type nite difference method. The method yield the tri-diagonal linear system of algebraic equations which can be solved by using a tri-diagonal solver. Stability and error estimation of the...

Susanne Tan ([email protected]) André Scherag ([email protected]) Onno Eilard Janssen ([email protected]) Susanne Hahn ([email protected]) Harald Lahner ([email protected]) Tiina Dietz ([email protected]) Susann Friedel ([email protected]) Harald Grallert ([email protected]) Carla IG Vogel ([email protected]) Rainer Kim...

A general symmetric Trefftz Discontinuous Galerkin method is built for solving the Helmholtz equation with piecewise constant coefficients. The construction of the corresponding local solutions to the Helmholtz equation is based on a boundary element method. A series of numerical experiments displays an excellent stability of the method relatively to the penalty parameters, and more importantly...