A new characterization of harmonic functions is obtained. It based on quadrature identities involving mean values over annular domains and concentric spheres lying within these or their boundaries. The analogous result with a logarithmic weight in the volume means conjectured. similar derived for real-valued solutions modified Helmholtz equation (panharmonic functions), whereas (metaharmonic fu...

Providing an illustration of sound propagation in the Hormoz Strait ,this paper is about acoustic wave propagation in shallow water for a harmonic point source with low frequency, less than 1000 and solution of a homogenous Helmholtz equation using parabolic equation. C++ programming is used to solve Helmholtz equation [9] and MATLAB software is used to illustrate figures and animate them [6], ...

Transcranial ultrasound therapy is increasingly used for the non-invasive treatment of brain disorders. However, conventional numerical wave solvers are currently too computationally expensive to be online during treatments predict acoustic field passing through skull (e.g., account subject-specific dose and targeting variations). As a step towards real-time predictions, in current work, fast i...

We consider three problems for the Helmholtz equation in interior and exterior domains in R, (d = 2, 3): the exterior Dirichlet-to-Neumann and Neumann-to-Dirichlet problems for outgoing solutions, and the interior impedance problem. We derive sharp estimates for solutions to these problems that, in combination, give bounds on the inverses of the combined-field boundary integral operators for ex...

The problem addressed herein is the efficient management of the Grid/Cluster intense computation involved, when the preconditioned Bi-CGSTAB Krylov method is employed for the iterative solution of the large and sparse linear system arising from the discretization of the Modified Helmholtz-Dirichlet problem by the Hermite Collocation method. Taking advantage of the Collocation matrix’s red-black...