jabble.stencils
Class SecondDerivativeStencils

java.lang.Object
  jabble.stencils.SecondDerivativeStencils

public class SecondDerivativeStencils
extends java.lang.Object

Stencil library for second derivates on Fields in any dimensions.

Method Summary

static double	d2FieldBulk(Field field, int dirIndex) Calculates (F(x+1) - 2*F(x) + F(x-1)) / dx2.
static double	d2FieldLowerBoundary(Field field, int dirIndex) Calculates (2*F(x) - 5*F(x+1) + 4*F(x+2) - F(x+3)) / dx2.
static double	d2FieldMixedBulk(Field field, int dirIndex1, int dirIndex2) Calculates mixed second derivative using a nine-point stencil (F(x+1, y+1) - F(x+1, y-1) - F(x-1, y+1) + F(x-1, y-1) / dx*dy.
static double	d2FieldUpperBoundary(Field field, int dirIndex) Calculates (2*F(x) - 5*F(x-1) + 4*F(x-2) - F(x-3)) / dx2.

Methods inherited from class java.lang.Object

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

Method Detail

d2FieldBulk

public static double d2FieldBulk(Field field,
                                 int dirIndex)

Calculates (F(x+1) - 2*F(x) + F(x-1)) / dx2.

Parameters:

field - The Field on which to calculate the derivative

dirIndex - The direction on which to calculate the derivative

Returns:

The derivate of the Field at the point defined by StencilUtils.getPoint()

d2FieldMixedBulk

public static double d2FieldMixedBulk(Field field,
                                      int dirIndex1,
                                      int dirIndex2)

Calculates mixed second derivative using a nine-point stencil (F(x+1, y+1) - F(x+1, y-1) - F(x-1, y+1) + F(x-1, y-1) / dx*dy.

Parameters:

field - The Field on which to calculate the derivative

dirIndex1 - The first direction on which to calculate the derivative

dirIndex2 - The second direction on which to calculate the derivative

Returns:

The derivative of the Field at the point defined by StencilUtils.getPoint()

d2FieldUpperBoundary

public static double d2FieldUpperBoundary(Field field,
                                          int dirIndex)

Calculates (2*F(x) - 5*F(x-1) + 4*F(x-2) - F(x-3)) / dx2.

Parameters:

field - The Field on which to calculate the derivative

dirIndex - The direction on which to calculate the derivative

Returns:

The derivate of the Field at the point defined by StencilUtils.getPoint()

d2FieldLowerBoundary

public static double d2FieldLowerBoundary(Field field,
                                          int dirIndex)

Calculates (2*F(x) - 5*F(x+1) + 4*F(x+2) - F(x+3)) / dx2.

Parameters:

field - The Field on which to calculate the derivative

dirIndex - The direction on which to calculate the derivative

Returns:

The derivate of the Field at the point defined by StencilUtils.getPoint()