Abstract We study the unique solvability of discretized Helmholtz problem with Robin boundary conditions using a conforming Galerkin finite element method. Well-posedness discrete equations is typically investigated by applying compact perturbation argument to continuous so that `sufficiently rich' discretization results in small' and well-posedness inherited via Fredholm’s alternative. The qua...

This chapter is devoted to the investigation of the Dirichlet problem for the Helmholtz equation in a bounded domain. In Section 1, we briefly explain why and how boundary valued problems for the Helmholtz equation are solved. Using the properties ofDα, Tα, Fα as well as the projections defined by the singular Cauchy operator the Dirichlet problem for classical α−hyperholomophic functions are s...

This paper presents an approach using the method of separation of variables applied to 2D Helmholtz equations in the Cartesian coordinate. The solution is then computed by a series solutions resulted from solving a sequence of 1D problems, in which the 1D solutions are computed using pollution free difference schemes. Moreover, non-polluted numerical integration formulae are constructed to hand...

A radiated immunity test method using fields in a three-dimensional Helmholtz-coil set is described. The incident field to equipment under test (EUT) is generated by an orthogonally structured three sets of Helmholtz coil. Using this structure, the resultant field can be generated with arbitrary amplitude and direction. Therefore, the three dimensional immunity characteristics of an EUT can be ...

We describe development of a fast multipole method accelerated iterative solution of boundary element equations for large problems involving hundreds of thousands elements for the Laplace and Helmholtz equations in 3D. The BEM requires several approximate computations (numerical quadrature, approximations of the boundary shapes using elements) and the convergence criterion for iterative computa...

The Helmholtz equation governing wave propagation and scattering phenomena is difficult to solve numerically. Its discretization with piecewise linear finite elements results in typically large linear systems of equations. The inherently parallel domain decomposition methods constitute hence a promising class of preconditioners. An essential element of these methods is a good coarse space. Here...

This paper investigates the pollution effect, and explores the feasibility of a local spectral method, the discrete singular convolution (DSC) algorithm for solving the Helmholtz equation with high wavenumbers. Fourier analysis is employed to study the dispersive error of the DSC algorithm. Our analysis of dispersive errors indicates that the DSC algorithm yields a dispersion vanishing scheme. ...

We describe a linear network that models correlations between real-valued visible variables using one or more real-valued hidden variables-a factor analysis model. This model can be seen as a linear version of the Helmholtz machine, and its parameters can be learned using the wake-sleep method, in which learning of the primary generative model is assisted by a recognition model, whose role is t...