public static mikity.LinearAlgebra.vector initWeight(int N)
{
mikity.LinearAlgebra.vector res = new mikity.LinearAlgebra.vector(N);
if (N == 3)
{
res = new mikity.LinearAlgebra.vector(new double[3] {
5d / 18d, 8d / 18d, 5d / 18d
});
}
return(res);
}
public static mikity.LinearAlgebra.vector initCoord(int N)
{
mikity.LinearAlgebra.vector res = new mikity.LinearAlgebra.vector(N);
if (N == 3)
{
res = new mikity.LinearAlgebra.vector(new double[3] {
(-Math.Sqrt(3d / 5d) + 1d) / 2d, 1d / 2d, (Math.Sqrt(3d / 5d) + 1d) / 2d
});
}
return(res);
}
unsafe public static void y_equals_xA(vector x, matrix A, vector y)
{
fixed(double *_ptr1 = &x.rawData[0], _ptr2 = &A.rawData[0, 0], _ptr3 = &y.rawData[0])
{
double *ptr1 = _ptr1;
double *ptr2 = _ptr2;
double *ptr3 = _ptr3;
for (int j = 0; j < A.nCol; j++)
{
ptr2 = _ptr2 + j;
ptr1 = _ptr1;
double v = 0;
for (int i = 0; i < A.nRow; i++)
{
v += *ptr2 * *ptr1;
ptr1++;
ptr2 += A.nCol;
}
*ptr3 = v;
ptr3++;
}
}
}
public double bilinear(vector v1, vector v2)
{
return(matrix.bilinear(this, v1, v2));
}
public isoparametricElement(params int[] _el)
: base(_el)
{
if (this.nNodes == 2)
{
__N = 1;
}
else if (this.nNodes == 4)
{
__N = 2;
}
else if (this.nNodes == 8)
{
__N = 3;
}
else
{
throw new mikity.Exceptions.NumberOfNodesIncompatibleException("Isoparametric element only accept 2,4,8 nodes.");
}
nNodes = this.nNodes;
nIntPoints = mikity.MathUtil.__pow_INT_INT(nIntMed, __N);
nVisPoints = mikity.MathUtil.__pow_INT_INT(nVisMed, __N);
intPoints = new integralPoint[nIntPoints];
this.nodes = new matrix(this.nNodes, this.__dim);
for (int i = 0; i < intPoints.Length; i++)
{
intPoints[i] = new integralPoint(__N, this.nodes, this.__dim);
}
//形状関数生成用数列
psi = mikity.MathUtil.generate(__N, 2);
phi = -2 * psi + 1;
psi2 = mikity.MathUtil.generate(__N, nIntMed);
psi3 = mikity.MathUtil.generate(__N, nVisMed);
//積分点要素内座標生成
for (int i = 0; i < nIntPoints; i++)
{
double[] t = new double[__N];
for (int j = 0; j < __N; j++)
{
t[j] = __u[psi2[i, j]];
}
intPoints[i].setLocalCoordinates(t);
}
//積分点積分用重み生成
for (int i = 0; i < nIntPoints; i++)
{
double w = 1.0d;
for (int j = 0; j < __N; j++)
{
w *= __w[psi2[i, j]];
}
intPoints[i].setIntegralWeights(w);
}
//重み算出用補助数列生成
for (int i = 0; i < nIntPoints; i++)
{
mikity.LinearAlgebra.matrix T = new mikity.LinearAlgebra.matrix(nNodes, __N);
for (int j = 0; j < nNodes; j++)
{
for (int k = 0; k < __N; k++)
{
T[j, k] = intPoints[i].localCoordinates(k) * phi[j, k] + psi[j, k];
}
}
intPoints[i].setHelperNumber(T);
}
//積分点位置ベクトル算出用重み生成
for (int i = 0; i < nIntPoints; i++)
{
mikity.LinearAlgebra.vector tt = new mikity.LinearAlgebra.vector(nNodes);
for (int j = 0; j < nNodes; j++)
{
tt[j] = 1.0d;
for (int k = 0; k < __N; k++)
{
tt[j] *= (intPoints[i].Tij[j, k]);
}
}
intPoints[i].setNodeWeights(tt);
}
//積分点基底ベクトル算出用重み生成
for (int i = 0; i < nIntPoints; i++)
{
mikity.LinearAlgebra.matrix ttt = new mikity.LinearAlgebra.matrix(nNodes, __N);
for (int j = 0; j < nNodes; j++)
{
for (int k = 0; k < __N; k++)
{
ttt[j, k] = intPoints[i].wp[j] / (intPoints[i].Tij[j, k]) * phi[j, k];
}
}
intPoints[i].setBaseWeights(ttt);
}
this.makeBoundary();
}
//一辺に並ぶ積分点の数
public simplexElement(int[] _el)
: base(_el)
{
__N = _el.Length - 1;
if (__N < 1)
{
throw new mikity.Exceptions.NumberOfNodesIncompatibleException("Simplex element only accept 2,3,4 nodes.");
}
if (__N > 3)
{
throw new mikity.Exceptions.NumberOfNodesIncompatibleException("Simplex element only accept 2,3,4 nodes.");
}
nIntPoints = 1;
nVisPoints = 1;
intPoints = new integralPoint[nIntPoints];
this.nodes = new matrix(this.nNodes, this.__dim);
for (int i = 0; i < intPoints.Length; i++)
{
intPoints[i] = new integralPoint(__N, this.nodes, this.__dim);
}
//積分点要素内座標生成
for (int i = 0; i < nIntPoints; i++)
{
double[] t = new double[__N];
double F = __N + 1;
for (int j = 0; j < __N; j++)
{
t[j] = (double)j / F;
}
intPoints[i].setLocalCoordinates(t);
}
//積分点積分用重み生成
for (int i = 0; i < nIntPoints; i++)
{
double w = 1.0d;
for (int j = 1; j <= __N; j++)
{
w /= (double)j;
}
intPoints[i].setIntegralWeights(w);
}
//積分点位置ベクトル算出用重み生成
for (int i = 0; i < nIntPoints; i++)
{
mikity.LinearAlgebra.vector tt = new mikity.LinearAlgebra.vector(nNodes);
if (__N == 1)
{
tt[0] = intPoints[i].localCoordinates(0);
tt[1] = -intPoints[i].localCoordinates(0) + 1;
}
if (__N == 2)
{
tt[0] = intPoints[i].localCoordinates(0);
tt[1] = -intPoints[i].localCoordinates(0) + intPoints[i].localCoordinates(1);
tt[2] = -intPoints[i].localCoordinates(1) + 1;
}
if (__N == 3)
{
tt[0] = intPoints[i].localCoordinates(0);
tt[1] = -intPoints[i].localCoordinates(0) + intPoints[i].localCoordinates(1);
tt[1] = -intPoints[i].localCoordinates(1) + intPoints[i].localCoordinates(2);
tt[2] = -intPoints[i].localCoordinates(2) + 1;
}
intPoints[i].setNodeWeights(tt);
}
//積分点基底ベクトル算出用重み生成
for (int i = 0; i < nIntPoints; i++)
{
mikity.LinearAlgebra.matrix ttt = new mikity.LinearAlgebra.matrix(nNodes, __N);
if (__N == 1)
{
ttt[0, 0] = 1;
ttt[1, 0] = -1;
}
if (__N == 2)
{
ttt[0, 0] = 1;
ttt[1, 0] = -1;
ttt[1, 1] = 1;
ttt[2, 1] = -1;
}
if (__N == 3)
{
ttt[0, 0] = 1;
ttt[1, 0] = -1;
ttt[1, 1] = 1;
ttt[2, 1] = -1;
ttt[2, 2] = 1;
ttt[3, 2] = -1;
}
intPoints[i].setBaseWeights(ttt);
}
this.makeBoundary();
}