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...

Exact chirped elliptic wave solutions are obtained within the framework of coupled cubic nonlinear Helmholtz equations in presence non-Kerr nonlinearity like self steepening and frequency shift. It is shown that, for a particular combination shift parameters, associated nontrivial phase gives rise to chirp reversal across solitary profile. But different terms leads chirping but no reversal. The...

We give a brief overview of some new results in Helmholtz soliton theory. Firstly, fundamental considerations are made in terms of new contexts for Helmholtz solitons that arise directly from Maxwell’s equations. We then detail applications of Helmholtz solitons in material interface geometries: generalising Snell’s law to nonlinear beams and reporting new qualitative phenomena. Novel families ...

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 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...

Mean value properties of solutions to the m-dimensional Helmholtz and modified equations are considered. An elementary derivation these is given. It involves Euler–Poisson–Darboux equation. Despite similar form for both equations, their consequences distinguish essentially. The restricted mean property harmonic functions amended so that a function satisfying this in bounded domain special class...

The free vibration analysis ofhomogeneous isotropic micropolar thermoelastic cylindrical curved plate in circumferential direction has been investigated in the context of generalized themoelasticity III, recently developed by Green and Naghdi. The model has been simplified using Helmholtz decomposition technique and the resulting equations have been solved using separation of variable method. M...

Numerical integration of the compressible nonhydrostatic equations using semi-implicit techniques is complicated by the need to solve a Helmholtz equation at each time step. The authors present an accurate and efficient technique for solving the Helmholtz equation using a conjugate-residual (CR) algorithm that is accelerated by ADI preconditioners. These preconditioned CR solvers possess four d...