[PDF] Top 20 High Order Finite Difference Method for Helmholtz Equation in Polar Coordinates

... a high-order fast algorithm for solving the two-dimensional Helmholtz equation with Dirichlet and Neumann boundary conditions in polar ...compact finite difference ap- ... See full document

... Abstract: Helmholtz equation is widely applied in the scientific and engineering ...dimensional Helmholtz equation, the computational efficiency of the algorithm is especially ...in ... See full document

... The Helmholtz equation governs wave propagation and scattering phenomena arising in acoustic problems in many areas, ...the Helmholtz equation, such as, the finite volume method, ... See full document

... developing high-order compact finite difference ...the high accuracy compact difference method has attracted more and more atten- tion; see ...advection–diffusion equation, it has been seen ... See full document

... FS equation, see for example Hartree (1937), Asaithambii (1997), Asaithambi (1998, 2004b, 2005), Abbasbandy (2007), Alizadeh et ...shooting method (see Cebeci and Bradshaw (1977); Cebeci and Keller (1971) ... See full document

... higher order schemes; however, one may note that a higher order compact scheme will require a higher order Taylor extension (see Section ...the Helmholtz equation have been developed ... See full document

... new high order finite difference algorithm for solving a class of time fractional sub-diffusion equation with variable coefficient was ...sixth order and temporal 2 − α ... See full document

... the method of Hockney into three dimensions, the Poisson’s equation in cylindrical coordinates system with the Dirichlet’s boundary conditions in a portion of a cylinder for r ≠ 0 is solved ... See full document

... second-order finite differ- ence approximation scheme and solve the resulting large algebraic system of linear equations systematically using block tridiagonal system [14] and extend the Hockney’s ... See full document

... –1. There have been different kinds of numerical methods on the solution for various Schrödinger equations [5–10]. For example, Bao and Cai [11] established uniform error estimates of finite differ- ence methods for the NLS ... See full document

... highest order of finite difference scheme. This method represents by sum up all the derivatives of the function at any grid points, and then the equation transforms to a system of ... See full document

... Quadrature method (DQM). DQM is an extension of FDM for the highest order of finite difference scheme ...this method linearly sum up all the derivatives of a function at any location of ... See full document

... standard finite difference approxima- ...discretization method to both the boundary conditions and the differential ...erential equation has a singularity at the ...mimetic method produces a ... See full document

... Burgers’ equation into two sub-equations and solve them by fi- nite difference ...splitting method for solving the radiative transfer ...splitting method (SSM) is an effective numerical method ... See full document

... wave equation is an important problem. The Helmholtz equation is the ver- sion of acoustic wave equation in the frequency ...the Helmholtz equation have been under ac- tive ... See full document

... the high- order scheme for this kind of boundary condition was derived in ...the Helmholtz equation after reduction from the large cavity electromagnetic scattering, the inhomogeneous Robin ... See full document

... stochastic Helmholtz equation, we should consider two issues: one is randomness, and the other is a high ...stochastic Helmholtz equation is a stochastic partial differential ... See full document

... In order to capture the boundary effects more accurately, the use of non-uniform grid with grid clustering at the boundary proved to be a viable ...the finite difference form of the governing ... See full document

... Helmholtz equation appears from general conservation laws of physics and can be interpreted as wave ...equations. Helmholtz equation is widely applied in the scientific and engineering design ... See full document

... where E is unit operator. The difference Equation (3.6) contains unknown nonzero parameter ω and therefore it may be considered as a nonlinear equation with respect to the parameter ω and The series ... See full document