O P A R - Open Architecture Particle in Cell Simulation - Version 3.0
Plasma simulations with dust particles
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Public Member Functions | Protected Attributes
Poisson Class Reference

Solves Poisson equation using a multigrid method for 2D and 3D simulations. The Poisson equation is given by $\Delta u(x) + f(x) = 0$ where $u(x)$ is the unknown scalar field (plasma potential). The outer boundary condition is set to zero, this means on the very outer grid points of the simulation box $u=0$ is set. The grid points on the surface of the dust particle(s) is set as a inner boundary condition according to the surface potential of the dust particle(s), calculated from the dust charge, see Potential. This inner boundary condition is time-dependent and can be different in the next timestep, because the charge of the dust particle(s) can change. To follow the spherical surface, reduced grid spacings are used here, which are calculated und stored in the beginning of a simulation, see ClosedGeometry. Periodic boundary conditions are not implemented. For 1D simulations a tridiagonal matrix solver is implemented. More...

#include <poisson.h>

List of all members.

Public Member Functions

 Poisson (Geometry *geom_)
 The default constructor reads the attributes from global variables.
void solve (grid< double > &u, grid< double > &f, double potd[20])
 Solves the poisson equation $\Delta u(x) + f(x) = 0$.

Protected Attributes

double dx
 Grid spacing in x direction.
double dy
 Grid spacing in y direction.
double dz
 Grid spacing in z direction.
int nu1
 Do nu1 Gauss steps then repeat multigrid refinement gama times then do nu2 Gauss steps.
int nu2
int Rg
 Dust particle radius.
int nd
 Number of dust particles in the simulation.
int ig
 Number of gird points at the dust particle(s)
double epsilon
 The error to reach.
std::valarray< double > potd
 Surface potential of the dust particle(s)
Geometry * geom
 Pointer to the reference geometry.
Wall * pWall
 Pointer to the reference wall.
Potential * pPotential
 Pointer to the reference potential.

Detailed Description

Solves Poisson equation using a multigrid method for 2D and 3D simulations. The Poisson equation is given by $\Delta u(x) + f(x) = 0$ where $u(x)$ is the unknown scalar field (plasma potential). The outer boundary condition is set to zero, this means on the very outer grid points of the simulation box $u=0$ is set. The grid points on the surface of the dust particle(s) is set as a inner boundary condition according to the surface potential of the dust particle(s), calculated from the dust charge, see Potential. This inner boundary condition is time-dependent and can be different in the next timestep, because the charge of the dust particle(s) can change. To follow the spherical surface, reduced grid spacings are used here, which are calculated und stored in the beginning of a simulation, see ClosedGeometry. Periodic boundary conditions are not implemented. For 1D simulations a tridiagonal matrix solver is implemented.

The documentation for this class was generated from the following files:
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