1,056,090 research outputs found
Moving grid method without interpolations
In their method, to solve a one—dimensional moving boundary problem, Crank and Gupta suggest a grid system which moves with the Interface. The method requires some interpolations to be carried out which they perform by using a cubic spline or an ordinary polynomial. In the present paper these interpolations are avoided by employing a Taylor's expansion in space and time dimensions. A practical diffusion problem is solved and the results are compared with those obtained from other methods
An Arbitrary Curvilinear Coordinate Method for Particle-In-Cell Modeling
A new approach to the kinetic simulation of plasmas in complex geometries,
based on the Particle-in- Cell (PIC) simulation method, is explored. In the two
dimensional (2d) electrostatic version of our method, called the Arbitrary
Curvilinear Coordinate PIC (ACC-PIC) method, all essential PIC operations are
carried out in 2d on a uniform grid on the unit square logical domain, and
mapped to a nonuniform boundary-fitted grid on the physical domain. As the
resulting logical grid equations of motion are not separable, we have developed
an extension of the semi-implicit Modified Leapfrog (ML) integration technique
to preserve the symplectic nature of the logical grid particle mover. A
generalized, curvilinear coordinate formulation of Poisson's equations to solve
for the electrostatic fields on the uniform logical grid is also developed. By
our formulation, we compute the plasma charge density on the logical grid based
on the particles' positions on the logical domain. That is, the plasma
particles are weighted to the uniform logical grid and the self-consistent mean
electrostatic fields obtained from the solution of the logical grid Poisson
equation are interpolated to the particle positions on the logical grid. This
process eliminates the complexity associated with the weighting and
interpolation processes on the nonuniform physical grid and allows us to run
the PIC method on arbitrary boundary-fitted meshes.Comment: Submitted to Computational Science & Discovery December 201
Adaptive Wavelet Collocation Method for Simulation of Time Dependent Maxwell's Equations
This paper investigates an adaptive wavelet collocation time domain method
for the numerical solution of Maxwell's equations. In this method a
computational grid is dynamically adapted at each time step by using the
wavelet decomposition of the field at that time instant. In the regions where
the fields are highly localized, the method assigns more grid points; and in
the regions where the fields are sparse, there will be less grid points. On the
adapted grid, update schemes with high spatial order and explicit time stepping
are formulated. The method has high compression rate, which substantially
reduces the computational cost allowing efficient use of computational
resources. This adaptive wavelet collocation method is especially suitable for
simulation of guided-wave optical devices
The 3-dimensional Fourier grid Hamiltonian method
A method to compute the bound state eigenvalues and eigenfunctions of a
Schr\"{o}dinger equation or a spinless Salpeter equation with central
interaction is presented. This method is the generalization to the
three-dimensional case of the Fourier grid Hamiltonian method for
one-dimensional Schr\"{o}dinger equation. It requires only the evaluation of
the potential at equally spaced grid points and yields the radial part of the
eigenfunctions at the same grid points. It can be easily extended to the case
of coupled channel equations and to the case of non-local interactions.Comment: 13 pages, 1 figure. RevTeX file. To appear in J. Comput. Phy
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