Variational solution of Poisson's equation using plane waves in adaptive coordinates

Variational solution of Poisson's equation using plane waves in adaptive coordinates.

A procedure for solving Poisson's equation using plane waves in adaptive coordinates (u) is described. The method, based on Gygi's work, writes a trial potential ξ as the product of a preselected Coulomb weight μ times a plane-wave expansion depending on u. Then, the Coulomb potential generated by a given density ρ is obtained by variationally optimizing ξ, so that the error in the Coulomb ener...

Fast and accurate multigrid solution of Poissons equation using diagonally oriented grids

We solve Poisson’s equation using new multigrid algorithms that converge rapidly. The novel feature of the 2D and 3D algorithms are the use of extra diagonal grids in the multigrid hierarchy for a much richer and effective communication between the levels of the multigrid. Numerical experiments solving Poisson’s equation in the unit square and unit cube show simple versions of the proposed algo...

Numerical solution of Klein-Gordon equation by using the Adomian's decomposition and variational iterative methods

Optimization of Solution Regularized Long-wave Equation by Using Modified Variational Iteration Method

In this paper, a regularized long-wave equation (RLWE) is solved by using the Adomian's decomposition method (ADM) , modified Adomian's decomposition method (MADM), variational iteration method (VIM), modified variational iteration method (MVIM) and homotopy analysis method (HAM). The approximate solution of this equation is calculated in the form of series which its components are computed by ...

The Solution of Laminar Incompressible Flow Equation with Free Surfaces in Curvilinear Coordinates

In this paper a novel numerical approach is presented for solving the transient incompressible fluid flow problems with free surfaces in generalized two-dimensional curvilinear coordinate systems. Solution algorithm is a combination of implicit real-time steps and explicit pseudo-time steps. Governing fluid flow equations are discretized using a collocated finite-volume mesh. Convective terms a...