In this paper we present a new highly efficient calculation method for the far field amplitude pattern that arises from scattering problems governed by the d-dimensional Helmholtz equation and, by extension, Schrödinger’s equation. The new technique is based upon a reformulation of the classical real-valued Green’s function integral for the far field amplitude to an equivalent integral over a c...

A fast and efficient three-dimensional generalized rectangular wide-angle beam propagation method (GR-WABPM) based on a recently proposed modified Padé (1,1) approximant is presented. In our method, at each propagation step, the beam propagation equation is recast in terms of a Helmholtz equation with a source term, which is solved quickly and accurately by a recently introduced complex Jacobi ...

which describes stationary reaction-diffusion phenomena but is often also called Helmholtz equation in certain communities. For example in meteorology, the early seminal papers [48, 56] led an entire community to call equations of the form (2) Helmholtz equations, see for example [14]. Even standard texts in applied mathematics now sometimes use the term Helmholtz equation for both (1) and (2),...

Numerical solutions of the Helmholtz equation and the one-way Helmholtz equation are compared in the weak range dependence limit, where the overall range distance is increased while the range dependence is weakened. It is observed that the difference between the solutions of these two equations persists in this limit. The one-way Helmholtz equation involves a square root operator and it can be ...

We develop a reconstruction algorithm to determine penetrable obstacles inside a domain in the plane from acoustic measurements made on the boundary. This algorithm uses complex geometrical optics solutions to the Helmholtz equation with polynomial-type phase functions.

   In this paper, numerical results obtained and explained from an exact formula in relation to sound pressure load due to the presence of liquid inside the finite-length non-rigid carbon nanotubes (CNTs), which is coupled with the dynamic equations of motion for the CNT. To demonstrate the accuracy of this work, the obtained formula has been compared to what has been used by other research...

we have developed a three level implicit method for solution of the helmholtz equation. using the cubic spline in space and nite dierence in time directions. the approach has been modied to drive numerov type nite dierence 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...

The thermal relaxation of a dense gas described by the modified Enskog equation is studied for closed system in contact with heat bath. As case Boltzmann equation, Helmholtz free energy $ \mathcal{F} that decreases monotonically time found under conventional kinetic boundary condition satisfies Darrozes–Guiraud inequality. extension to Enskog–Vlasov also presented.