The optical eld in a weakly guiding homogeneous waveguide satis es scalar Helmholtz equations in both the core and cladding, and transmission conditions on the boundary. The transverse wavenumbers of the two scalar Helmholtz equations for the core and cladding are di erent and both of them depend on the propagation constants in the longitudinal direction of the waveguide. Two di erent systems o...

A kind of non-overlapping domain decomposition preconditioner was proposed to solve the systems generated by the plane wave least-squares (PWLS) method for discretization of Helmholtz equation and Maxwell equations respectively in [13] and [14]. In this paper we introduce overlapping variants of this kind of preconditioner and give some comparison among these domain decomposition preconditioner...

The numerical solution of the Helmholtz equation subject to nonlocal radiation boundary conditions is studied. The speciic problem is the propagation of hydroacoustic waves in a two-dimensional curvilinear duct. The problem is discretized with a second-order accurate nite-diierence method, resulting in a linear system of equations. To solve the system of equations, a preconditioned Krylov subsp...

Abstract. In this study, we consider new finite difference schemes for solving the Helmholtz equation. Novel difference schemes which do not introduce truncation error are presented, consequently the exact solution for the Helmholtz equation can be computed numerically. The most important features of the new schemes are that while the resulting linear system has the same simple structure as tho...

The weak-form of Helmholtz differential equation, in conjunction with vector test-functions (which are gradients of the fundamental solutions to the Helmholtz differential equation in free space) is utilized as the basis in order to directly derive non-hyper-singular boundary integral equations for the velocity potential, as well as its gradients. Thereby, the presently proposed boundary integr...

We present Helmholtz or Helmholtz like equations for the approximation of the timeharmonic wave propagation in gases with small viscosity, which are completed with local boundary conditions on rigid walls. We derived approximative models based on the method of multiple scales for the pressure and the velocity separately, both up to order 2. Approximations to the pressure are described by the He...

An algebraic multigrid AMG with aggregation technique to coarsen is applied to construct a better preconditioner for solving Helmholtz equations in this paper. The solution process consists of constructing the preconditioner by AMG and solving the preconditioned Helmholtz problems by Krylov subspace methods. In the setup process of AMG, we employ the double pairwise aggregation DPA scheme first...

The Navier-Stokes equations describe a large class of fluid flows but are difficult to solve analytically because of their nonlinearity. We present in this paper a parallel solver for the 3-D Navier-Stokes equations of incompressible unsteady flows with constant coefficients, discretized by the finite difference method. We apply the prediction-projection method which transforms the Navier-Stoke...

A new multigrid algorithm is constructed for the solution of linear systems of equations which arise from the discretization of elliptic PDEs. It is defined in terms of the difference scheme on the fine grid only, and no rediscretization of the PDE is required. Numerical experiments show that this algorithm gives high convergence rates for several classes ofproblems: symmetric, nonsymmetdc and ...