mathcomp.gridgeom
Class Transformation

java.lang.Object
  mathcomp.gridgeom.Transformation

public class Transformation
extends java.lang.Object

Author:

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Field Summary

static Node[]	gaussPoints
static double[]	gaussPoints1D The gauss points for a five point 1D gauss formula on [-1,1].
static double[]	gaussWeights Gauss weights for a four point 2D gauss formula on the standart triangle.
static double[]	gaussWeights1D The gauss weights for a five point 1D gauss formula on [-1,1].

Constructor Summary

Transformation()

Method Summary

static void	fillGradVector(Triangle t, Vector[] toFillVector) For every triangle preprocessed method to calculate the gradVector.
static Vector[]	getGradVector(Triangle t, Vector[] toFillVector)
static Node	getRealFromRef(Triangle t, Node v_onRef) Returns the coordinates of v_onRef in x coordinates.
static Node	getRealFromRefEdge(Edge e, double d_onRef) Returns the coordinates of d_onRef in [-1,1] mapped on the Edge e.
static Node	getRefFromReal(Triangle t, Node v_onReal) Returns the coordinates of v_onReal in eta coordinates.
static double[]	mapGradientRealToRef(Triangle t, double xg, double yg)
static double[]	mapGradientRefToReal(Triangle t, double xg, double yg)

Methods inherited from class java.lang.Object

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

Field Detail

gaussWeights1D

public static final double[] gaussWeights1D

The gauss weights for a five point 1D gauss formula on [-1,1].

gaussPoints1D

public static final double[] gaussPoints1D

The gauss points for a five point 1D gauss formula on [-1,1].

gaussWeights

public static final double[] gaussWeights

Gauss weights for a four point 2D gauss formula on the standart triangle.

gaussPoints

public static final Node[] gaussPoints

Constructor Detail

Transformation

public Transformation()

Method Detail

getRealFromRefEdge

public static Node getRealFromRefEdge(Edge e,
                                      double d_onRef)

Returns the coordinates of d_onRef in [-1,1] mapped on the Edge e.

Parameters:

e - the "real"-Edge

d_onRef - coordinates in eta

Returns:

d in x coordinates

getRealFromRef

public static Node getRealFromRef(Triangle t,
                                  Node v_onRef)

Returns the coordinates of v_onRef in x coordinates.

Parameters:

t - the "real"-triangle

v_onRef - coordinates in eta

Returns:

v in x coordinates

getRefFromReal

public static Node getRefFromReal(Triangle t,
                                  Node v_onReal)

Returns the coordinates of v_onReal in eta coordinates.

Parameters:

t - the "real"-triangle

v_onReal - coordinates in x

Returns:

v in eta coordinates

fillGradVector

public static void fillGradVector(Triangle t,
                                  Vector[] toFillVector)

For every triangle preprocessed method to calculate the gradVector. That means that we calculate the constant gradient to every basis function in a Vector array. The array indices stand for the derivation variable - ie. gradVector[0].get(u) returns the derivation by x (or x_1) of the basis function indentified by the Node u. Abstract we calculate [d(b_i o phi)/d(x_j)]i=1..3,j=1..2 where b_i are the basis functions on the real triangle, phi is the transformation map and the x_1 are the real coordinate directions.

Parameters:

t - the current triangle

toFillVector - the vector array

getGradVector

public static Vector[] getGradVector(Triangle t,
                                     Vector[] toFillVector)

mapGradientRealToRef

public static double[] mapGradientRealToRef(Triangle t,
                                            double xg,
                                            double yg)

mapGradientRefToReal

public static double[] mapGradientRefToReal(Triangle t,
                                            double xg,
                                            double yg)