xal.tools.math.r3

Class PoissonGrid

java.lang.Object

xal.tools.math.r3.Grid

xal.tools.math.r3.PoissonGrid

All Implemented Interfaces:

java.io.Serializable

public class PoissonGrid
extends Grid
implements java.io.Serializable

Solves Poisson's equation for a potential function defined on a grid in R3. The grid object then solved the discretized version of Div Grad Val = - Src where Val is potential value on the grid and Src is a source function. NOTES: - The vector field derived from the potential function is calculated by taking the gradient of the interpolated potential. - Potential values at grid points may be set manuallly. - Potential values at grid points can be determined by solving Poisson's equation. The values of the source term must be set at each grid point, along with the type of field point (open, dirichlet, neumann).

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Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
static int	PT_DIRICHLET Grid point is a boundary point with Dirichlet boundary conditions
static int	PT_NEUMANN1 Grid point with Neumann boundary conditions, gradient in the first direction
static int	PT_NEUMANN2 Grid point with Neumann boundary conditions, gradient in the second direction
static int	PT_NEUMANN3 Grid point with Neumann boundary conditions, gradient in the third direction
static int	PT_OPEN Grid point is in an open region
static int	PT_UNDEFINED Grid point type is undefined

Constructor Summary

Constructors

Constructor and Description
PoissonGrid(int n1, int n2, int n3) Allocate a new PotentialGrid

Method Summary

Modifier and Type	Method and Description
protected xal.tools.math.r3.Grid.GridCell[][][]	allocateCells(int n1, int n2, int n3) Override base class allocator in order to allocate modified grid cell objects.
protected xal.tools.math.r3.Grid.GridPt[][][]	allocatePts(int n1, int n2, int n3) Override base class allocator in order to allocate modified grid point objects.
R3	fieldCartesian(R3 pt) Compute and return the field in cartesian coordinates at point pt as generated by the potential values on the grid.
R3	fieldCylindrical(R3 pt) Compute and return the field in cylindrical coordinates at point pt as generated by the potential values on the grid.
R3	fieldSpherical(R3 pt) Compute and return the field in spherical coordinates at point pt as generated by the potential values on the grid.
protected xal.tools.math.r3.PoissonGrid.Point	getPt(int i, int j, int k) Return grid point object located with index (i,j,k)
double	potential(R3 pt) Compute and return interpolated potential at a point pt within grid definition.
protected double[]	relaxWeightsCartesian() Compute the weighting coefficients of this grid for a Gauss-Seidel relaxation solution technique for Poisson's equation.
protected double[]	relaxWeightsCylindrical(double r) Compute the weighting coefficients of this grid for a Gauss-Seidel relaxation solution technique for Poisson's equation.
void	setPtPotential(int i, int j, int k, double dblPot) Set the potential value at grid point given by index
void	setPtSource(int i, int j, int k, double dblSrc) Set the source value at grid point given by index
void	setPtType(int i, int j, int k, int enmType) Set the type of the grid point given by index
double	solveCartesian(int intIterMax, double dblErrMax) Solve for the potential on the grid using a gauss-seidel relaxation technique.
double	solveCylindrical(int intIterMax, double dblErrMax) Solve for the potential on the grid using a gauss-seidel relaxation technique.

Methods inherited from class xal.tools.math.r3.Grid

compCellContaining, compCellIndex, compPtCoords, compPtCoords, getGridCell, getGridCell, getGridDomain, getGridOrigin, getGridPt, getGridPt, getGridResolution, getGridSize, getPtValue, interpolateGradient, interpolateValue, main, membershipGrid, print, setGridDomain, setPtValue

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

PT_UNDEFINED

public static final int PT_UNDEFINED

Grid point type is undefined

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Constant Field Values

PT_OPEN

public static final int PT_OPEN

Grid point is in an open region

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Constant Field Values

PT_DIRICHLET

public static final int PT_DIRICHLET

Grid point is a boundary point with Dirichlet boundary conditions

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Constant Field Values

PT_NEUMANN1

public static final int PT_NEUMANN1

Grid point with Neumann boundary conditions, gradient in the first direction

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Constant Field Values

PT_NEUMANN2

public static final int PT_NEUMANN2

Grid point with Neumann boundary conditions, gradient in the second direction

See Also:

Constant Field Values

PT_NEUMANN3

public static final int PT_NEUMANN3

Grid point with Neumann boundary conditions, gradient in the third direction

See Also:

Constant Field Values

Constructor Detail

PoissonGrid

public PoissonGrid(int n1,
                   int n2,
                   int n3)
            throws GridException

Allocate a new PotentialGrid

Parameters:

n1 - number of grid points in first dimension

n2 - number of grid points in second dimension

n3 - number of grid points in third dimension

Throws:

GridException - invalid size vector encountered

Method Detail

setPtPotential

public void setPtPotential(int i,
                           int j,
                           int k,
                           double dblPot)

Set the potential value at grid point given by index

Parameters:

i - x dimension index of grid point

j - y dimension index of grid point

k - z dimension index of grid point

dblPot - value of the potential at grid point (i,j,k)

setPtType

public void setPtType(int i,
                      int j,
                      int k,
                      int enmType)

Set the type of the grid point given by index

Parameters:

i - x dimension index of grid point

j - y dimension index of grid point

k - z dimension index of grid point

enmType - type enumeration of grid point (i,j,k)

setPtSource

public void setPtSource(int i,
                        int j,
                        int k,
                        double dblSrc)

Set the source value at grid point given by index

Parameters:

i - x dimension index of grid point

j - y dimension index of grid point

k - z dimension index of grid point

dblSrc - value of the driving source at grid point (i,j,k)

solveCartesian

public double solveCartesian(int intIterMax,
                             double dblErrMax)
                      throws GridException

Solve for the potential on the grid using a gauss-seidel relaxation technique.

Parameters:

intIterMax - maximum number of iterations

dblErrMax - maximum residual error

Returns:

the residual error in the solution

Throws:

GridException - procedure did not converge to prescribed residual error

solveCylindrical

public double solveCylindrical(int intIterMax,
                               double dblErrMax)
                        throws GridException

Solve for the potential on the grid using a gauss-seidel relaxation technique.

Parameters:

intIterMax - maximum number of iterations

dblErrMax - maximum residual error

Returns:

the residual error in the solution

Throws:

GridException - procedure did not converge to prescribed residual error

potential

public double potential(R3 pt)
                 throws GridException

Compute and return interpolated potential at a point pt within grid definition. The potential is calculated by linear interpolation of the potential values at each vertex of the cell containing point pt. NOTES: - The grid may be in any coordinate system - The potential V must be determined for all points on the grid.

Parameters:

pt - coordinates of field point within grid

Returns:

interpolated potential at pt

Throws:

GridException - point pt is outside grid domain

fieldCartesian

public R3 fieldCartesian(R3 pt)
                  throws GridException

Compute and return the field in cartesian coordinates at point pt as generated by the potential values on the grid. NOTES: - The coordinates of the grid are assumed to be (x1,x2,x3)=(x,y,z) - The potential V must be determined for all points on the grid. - The generated field is given by F=-grad V where V is the potential on the grid.

Parameters:

pt - field point to compute field

Returns:

vector field at point pt in cartesian (Fx,Fy,Fz)

Throws:

GridException - field undefined or pt is outside grid

fieldCylindrical

public R3 fieldCylindrical(R3 pt)
                    throws GridException

Compute and return the field in cylindrical coordinates at point pt as generated by the potential values on the grid. NOTES: - The grid coordinates are assumed to be (x1,x2,x3)=(r,theta,z) - The potential V must be determined for all points on the grid. - The generated field is given by F=-grad V where V is the potential on the grid.

Parameters:

pt - field point to compute field

Returns:

vector field at point pt in cylindrical (Fr,Ftheta,Fz)

Throws:

GridException - field undefined or pt is outside grid

fieldSpherical

public R3 fieldSpherical(R3 pt)
                  throws GridException

Compute and return the field in spherical coordinates at point pt as generated by the potential values on the grid. NOTES: - The grid coordinates are assumed to be (x1,x2,x3)=(R,theta,phi) - The potential V must be determined for all points on the grid. - The generated field is given by F=-grad V where V is the potential on the grid.

Parameters:

pt - field point to compute field

Returns:

vector field at point pt in spherical (FR,Ftheta,Fphi)

Throws:

GridException - field undefined or pt is outside grid

getPt

protected xal.tools.math.r3.PoissonGrid.Point getPt(int i,
                                                    int j,
                                                    int k)

Return grid point object located with index (i,j,k)

allocatePts

protected xal.tools.math.r3.Grid.GridPt[][][] allocatePts(int n1,
                                                          int n2,
                                                          int n3)
                                                   throws GridException

Override base class allocator in order to allocate modified grid point objects. Allocates the array of grid points for the grid.

Overrides:

allocatePts in class Grid

Parameters:

n1 - size of the first dimension

n2 - size of the second dimension

n3 - size of the third dimension

Returns:

array of grid point objects

Throws:

GridException - unable to allocate array

allocateCells

protected xal.tools.math.r3.Grid.GridCell[][][] allocateCells(int n1,
                                                              int n2,
                                                              int n3)
                                                       throws GridException

Override base class allocator in order to allocate modified grid cell objects. Allocates the array of grid cells for the grid

Overrides:

allocateCells in class Grid

Parameters:

n1 - size of the first dimension

n2 - size of the second dimension

n3 - size of the third dimension

Returns:

array of grid cell objects

Throws:

GridException - unable to allocate array

relaxWeightsCartesian

protected double[] relaxWeightsCartesian()

Compute the weighting coefficients of this grid for a Gauss-Seidel relaxation solution technique for Poisson's equation. The coefficients are determined for a cartesian coordinate system where the grid dimensions are assumed (x1,x2,x3)=(x,y,z).

Returns:

vector (ws,w1,w2,w3) of weights in the 1st, 2nd, 3rd dimensions and source term weight

relaxWeightsCylindrical

protected double[] relaxWeightsCylindrical(double r)

Compute the weighting coefficients of this grid for a Gauss-Seidel relaxation solution technique for Poisson's equation. The coefficients are determined for a cylindrical coordinate system where the grid dimensions are assumed (x1,x2,x3)=(r,theta,z).

Parameters:

r - the radius at which the weights are determined

Returns:

vector (ws,w1,w1p,w2,w3)