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BESO3D.cs
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BESO3D.cs
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using System;
using System.Collections.Generic;
using System.Linq;
using System.Diagnostics;
using System.Text;
using System.Threading.Tasks;
using System.IO;
namespace BESO
{
public class BESO3D
{
public int solver = 2;
public bool parallel = true;
#region Resolution
public int nelx;
public int nely;
public int nelz;
#endregion
#region FE varialbes
private int nEl;
private double[] U;
private int[] ik;
private int[] jk;
private double[] sk;
#endregion
#region BESO Parameters
/// <summary>
/// Filter radius
/// </summary>
public double rmin;
/// <summary>
/// Volume fraction
/// </summary>
public double vf;
/// <summary>
/// Evolution rate
/// </summary>
public double ert;
/// <summary>
/// The maximum iteration
/// </summary>
public int maxIter;
#endregion
#region BESO variables
/// <summary>
/// Design variables
/// </summary>
public double[] Xe;
public double[] dc;
public double[] dc_old;
private int[,] cMat;
/// <summary>
/// Elemental stiffness matrix
/// </summary>
private double[] Ke0;
private double[] Ke;
/// <summary>
/// The iterative history of the global compliance
/// </summary>
private List<double> HistoryC = new List<double>();
public int[] free_dofs;
public double Compliance = 0.0;
public double vol = 1.0;
public double delta = 1.0;
public int iter = 0;
public bool convergence = false;
public string info = null;
public StringBuilder initInfo;
public StringBuilder optInfo;
#endregion
#region Flt variables
public int[] ih;
public int[] jh;
public int[] kh;
public double[] vh;
public double[] sh;
#endregion
private Stopwatch stopwatch;
public bool OutputK = false;
#region Constructors
public BESO3D() { }
public BESO3D(double rmin, double vf, double ert = 0.03, int maxIter = 100)
{
if (rmin <= 0.0)
throw new Exception("Rmin must be large than 0.");
if (!(vf > 0.0 && vf < 1.0))
throw new Exception("Vt must be large than 0 and be less than 1.");
this.vf = vf;
this.ert = ert;
this.maxIter = maxIter;
this.rmin = rmin;
stopwatch = new Stopwatch();
optInfo = new StringBuilder("====================== Optimization ======================" + '\n');
}
public BESO3D(BESO3D beso)
{
vf = beso.vf;
ert = beso.ert;
maxIter = beso.maxIter;
rmin = beso.rmin;
nelx = beso.nelx;
nely = beso.nely;
Xe = (double[])beso.Xe.Clone();
dc = (double[])beso.dc.Clone();
dc_old = (double[])beso.dc_old.Clone();
Ke0 = (double[])beso.Ke0.Clone();
ih = (int[])beso.ih.Clone();
jh = (int[])beso.jh.Clone();
vh = (double[])beso.vh.Clone();
sh = (double[])beso.sh.Clone();
ik = (int[])beso.ik.Clone();
jk = (int[])beso.jk.Clone();
stopwatch = new Stopwatch();
optInfo = new StringBuilder("====================== Optimization ======================" + '\n');
}
#endregion
public void Initialize(int nelx, int nely, int nelz, bool parallel=false, int solver = 2)
{
this.parallel = parallel;
nEl = nelx * nely * nelz;
initInfo = new StringBuilder("====================== Launch BESO ======================" + '\n');
this.nelx = nelx;
this.nely = nely;
this.nelz = nelz;
dc = new double[nEl];
dc_old = new double[nEl];
Xe = new double[nEl];
Array.Fill(Xe, 1);
stopwatch.Start();
GetKe();
PreFE3D(nelx, nely, nelz);
stopwatch.Stop();
initInfo.Append("PreFE: " + stopwatch.Elapsed.TotalMilliseconds + '\n');
stopwatch.Restart();
PreFlt();
stopwatch.Stop();
initInfo.Append("PreFlt: " + stopwatch.Elapsed.TotalMilliseconds + '\n');
}
public void Optimize()
{
if (delta > 0.001 && iter < maxIter)
{
optInfo.Append("====================== Iter: " + iter.ToString() + " ======================" + '\n');
iter += 1;
vol = Math.Max(vf, vol * (1.0 - ert));
// Record the previous sensitivity numbers
if (iter > 1) dc_old = (double[])dc.Clone();
#region FEA
stopwatch.Restart();
FE();
stopwatch.Stop();
#endregion
#region Prepare report
optInfo.Append("FEA:" + stopwatch.Elapsed.TotalMilliseconds + '\n');
#endregion
#region Get DC
stopwatch.Restart();
GetDc();
HistoryC.Add(Compliance);
stopwatch.Stop();
#endregion
#region Prepare report
optInfo.Append("Getting Sensitivity:" + stopwatch.Elapsed.TotalMilliseconds + '\n');
#endregion
#region Flt
stopwatch.Restart();
Wrapper.Flt(nEl, dc, sh);
// Record the sensitiveies in each step
if (iter > 1)
for (int i = 0; i < nEl; i++)
dc[i] = (dc[i] + dc_old[i]) * 0.5;
stopwatch.Stop();
#endregion
#region Prepare report
optInfo.Append("Flt:" + stopwatch.Elapsed.TotalMilliseconds + '\n');
#endregion
#region ADD & DEL
stopwatch.Restart();
ADD_DEL(vol);
stopwatch.Stop();
#endregion
#region Prepare report
optInfo.Append("ADD & DEL:" + stopwatch.Elapsed.TotalMilliseconds + '\n');
#endregion
#region Checking Convergence
stopwatch.Restart();
// Check convergence
if (iter > 10)
{
var newV = 0.0;
var lastV = 0.0;
for (int i = 1; i < 6; i++)
{
newV += HistoryC[HistoryC.Count - i];
lastV += HistoryC[HistoryC.Count - 5 - i];
}
delta = Math.Abs((newV - lastV) / lastV);
}
#endregion
#region Prepare report
optInfo.Append("Checking Convergence:" + stopwatch.Elapsed.TotalMilliseconds + '\n');
optInfo.Append("Volume: " + vol.ToString() + '\n');
optInfo.Append("Compliance: " + Compliance.ToString() + '\n');
optInfo.Append("Change: " + delta.ToString() + '\n');
#endregion
info = "Iter: " + iter.ToString() + ", Volume: " + Math.Round(vol,3).ToString()
+ ", Compliance: " + Math.Round(Compliance, 3).ToString() + ", Change: " + Math.Round(delta, 3).ToString();
}
else
{
convergence = true;
}
}
private void PreFlt()
{
int rminf = (int)Math.Floor(rmin);
ih = new int[(int)(nEl * Math.Pow((2 * rminf - 1), 3))];
jh = new int[ih.Length];
vh = new double[ih.Length];
sh = new double[nEl];
int sum = 0;
for (int k1 = 1; k1 <= nelz; k1++)
{
for (int j1 = 1; j1 <= nely; j1++)
{
for (int i1 = 1; i1 <= nelx; i1++)
{
var e1 = (k1 - 1) * nelx * nely + (j1 - 1) * nelx + i1;
for (int k2 = Math.Max(k1 - rminf + 1, 1); k2 <= Math.Min(k1 + rminf - 1, nelz); k2++)
{
for (int j2 = Math.Max(j1 - rminf + 1, 1); j2 <= Math.Min(j1 + rminf - 1, nely); j2++)
{
for (int i2 = Math.Max(i1 - rminf + 1, 1); i2 <= Math.Min(i1 + rminf - 1, nelx); i2++)
{
var e2 = (k2 - 1) * nelx * nely + (j2 - 1) * nelx + i2;
ih[sum] = e1 - 1;
jh[sum] = e2 - 1;
vh[sum] = Math.Max(0.0, rmin - Math.Sqrt((i1 - i2) * (i1 - i2) + (j1 - j2) * (j1 - j2) + (k1 - k2) * (k1 - k2)));
sum++;
}
}
}
}
}
}
Wrapper.GetRowSum(sum, nEl, ih, jh, vh, sh);
}
private void ADD_DEL(double volfra)
{
double lowest = dc.Min();
double highest = dc.Max();
double th = 0.0;
double vol = volfra * nEl;
while (((highest - lowest) / highest) > 1e-5)
{
th = (highest + lowest) * 0.5;
double sum = 0.0;
for (int i = 0; i < nEl; i++)
{
Xe[i] = dc[i] > th ? 1.0 : 1e-3;
sum += Xe[i];
}
if (sum - vol > 0.0) lowest = th;
else highest = th;
}
}
private void GetDc()
{
Compliance = 0.0;
if (parallel)
{
double[] C = new double[nEl];
Parallel.For(0, nEl, i =>
{
double[] Ue = new double[24]
{
U[cMat[i, 0]], U[cMat[i, 1]], U[cMat[i, 2]],
U[cMat[i, 3]], U[cMat[i, 4]], U[cMat[i, 5]],
U[cMat[i, 6]], U[cMat[i, 7]], U[cMat[i, 8]],
U[cMat[i, 9]], U[cMat[i, 10]], U[cMat[i, 11]],
U[cMat[i, 12]], U[cMat[i, 13]], U[cMat[i, 14]],
U[cMat[i, 15]], U[cMat[i, 16]], U[cMat[i, 17]],
U[cMat[i, 18]], U[cMat[i, 19]], U[cMat[i, 20]],
U[cMat[i, 21]], U[cMat[i, 22]], U[cMat[i, 23]]
};
double v = Wrapper.TransposeMultiply(24, 24, Ke0, Ue);
var p1 = Xe[i] == 1 ? 1.0 : 1e-9;
var p2 = Xe[i] == 1 ? 1.0 : 1e-6;
C[i] = 0.5 * p1 * v;
dc[i] = 0.5 * p2 * v;
});
Compliance = C.Sum();
}
else
{
for (int i = 0; i < nEl; i++)
{
double[] Ue = new double[24]
{
U[cMat[i, 0]], U[cMat[i, 1]], U[cMat[i, 2]],
U[cMat[i, 3]], U[cMat[i, 4]], U[cMat[i, 5]],
U[cMat[i, 6]], U[cMat[i, 7]], U[cMat[i, 8]],
U[cMat[i, 9]], U[cMat[i, 10]], U[cMat[i, 11]],
U[cMat[i, 12]], U[cMat[i, 13]], U[cMat[i, 14]],
U[cMat[i, 15]], U[cMat[i, 16]], U[cMat[i, 17]],
U[cMat[i, 18]], U[cMat[i, 19]], U[cMat[i, 20]],
U[cMat[i, 21]], U[cMat[i, 22]], U[cMat[i, 23]]
};
double v = Wrapper.TransposeMultiply(24, 24, Ke0, Ue);
var p1 = Xe[i] == 1 ? 1.0 : 1e-9;
var p2 = Xe[i] == 1 ? 1.0 : 1e-6;
Compliance += 0.5 * p1 * v;
dc[i] = 0.5 * p2 * v;
}
}
}
#region Finite element analysis
private void PreFE3D(int nelx, int nely, int nelz)
{
int[,,] nodeNrs = new int[nelz + 1, nely + 1, nelx + 1];
int nEl = nelx * nely * nelz;
int[] cVec = new int[nEl];
cMat = new int[nEl, 24];
int[] edofs = new int[24]
{
-3, -2, -1,
0, 1, 2,
3 * (nelx + 1), 3 * (nelx + 1) + 1, 3 * (nelx + 1) + 2,
3 * (nelx + 1) - 3, 3 * (nelx + 1) - 2, 3 * (nelx + 1) - 1,
3 * (nelx + 1) * (nely + 1) - 3, 3 * (nelx + 1) * (nely + 1) - 2, 3 * (nelx + 1) * (nely + 1) - 1,
3 * (nelx + 1) * (nely + 1), 3 * (nelx + 1) * (nely + 1) + 1, 3 * (nelx + 1) * (nely + 1) + 2,
3 * (nelx + 1) * (nely + 2), 3 * (nelx + 1) * (nely + 2) + 1, 3 * (nelx + 1) * (nely + 2) + 2,
3 * (nelx + 1) * (nely + 2) - 3, 3 * (nelx + 1) * (nely + 2) - 2, 3 * (nelx + 1) * (nely + 2) - 1,
};
if (parallel)
{
Parallel.For(0, nelx, x =>
{
for (int z = 0; z < nelz + 1; z++)
for (int y = 0; y < nely + 1; y++)
nodeNrs[z, y, x] = z * (nelx + 1) * (nely + 1) + y * (nelx + 1) + x;
});
Parallel.For(0, nelx, x =>
{
for (int z = 0; z < nelz; z++)
for (int y = 0; y < nely; y++)
cVec[z * nelx * nely + y * nelx + x] = 3 * (nodeNrs[z, y, x] + 1) + 1;
});
Parallel.For(0, nEl, i =>
{
for (int j = 0; j < 24; j++)
cMat[i, j] = cVec[i] + edofs[j] - 1;
});
var sI = new int[300];
var sII = new int[300];
int num = 0;
int num2 = 0;
for (int i = 0; i < 24; i++)
{
for (int j = i; j < 24; j++)
{
sI[num] = j;
sII[num] = num2;
num++;
}
num2++;
}
ik = new int[300 * nEl];
jk = new int[300 * nEl];
Parallel.For(0, nEl, i =>
{
for (int j = 0; j < 300; j++)
{
var a = cMat[i, sI[j]];
var b = cMat[i, sII[j]];
if (a >= b)
{
ik[i * 300 + j] = a;
jk[i * 300 + j] = b;
}
else
{
ik[i * 300 + j] = b;
jk[i * 300 + j] = a;
}
}
});
}
else
{
for (int z = 0; z < nelz + 1; z++)
for (int y = 0; y < nely + 1; y++)
for (int x = 0; x < nelx + 1; x++)
nodeNrs[z, y, x] = z * (nelx + 1) * (nely + 1) + y * (nelx + 1) + x;
for (int z = 0; z < nelz; z++)
for (int y = 0; y < nely; y++)
for (int x = 0; x < nelx; x++)
cVec[z * nelx * nely + y * nelx + x] = 3 * (nodeNrs[z, y, x] + 1) + 1;
for (int i = 0; i < nEl; i++)
for (int j = 0; j < 24; j++)
cMat[i, j] = cVec[i] + edofs[j] - 1;
var sI = new int[300];
var sII = new int[300];
int num = 0;
int num2 = 0;
for (int i = 0; i < 24; i++)
{
for (int j = i; j < 24; j++)
{
sI[num] = j;
sII[num] = num2;
num++;
}
num2++;
}
ik = new int[300 * nEl];
jk = new int[300 * nEl];
for (int j = 0; j < nEl; j++)
{
for (int i = 0; i < 300; i++)
{
var a = cMat[j, sI[i]];
var b = cMat[j, sII[i]];
if (a >= b)
{
ik[j * 300 + i] = a;
jk[j * 300 + i] = b;
}
else
{
ik[j * 300 + i] = b;
jk[j * 300 + i] = a;
}
}
}
}
}
private void FE()
{
// Assemble stiffness matrix with all DOFs
sk = new double[300 * nEl];
if (parallel)
{
Parallel.For(0, nEl, i =>
{
var ex = Xe[i] == 1 ? 1.0 : 1e-9;
for (int j = 0; j < 300; j++)
{
sk[300 * i + j] = ex * Ke[j];
}
});
}
else
{
for (int i = 0; i < nEl; i++)
{
var ex = Xe[i] == 1 ? 1.0 : 1e-9;
for (int j = 0; j < 300; j++)
{
sk[300 * i + j] = ex * Ke[j];
}
}
}
int num_allDofs = 3 * (nelx + 1) * (nely + 1) * (nelz + 1);
var F = new double[num_allDofs];
U = new double[num_allDofs];
// Define force vector
int forceID = (int)Math.Floor((nelz + 1) * 0.5) * (nelx + 1) * (nely + 1) + (int)Math.Floor((nelx + 1) * 0.5) + 1;
F[forceID * 3 - 1] = -1.0;
//var test = new List<int>(6) { 0, 56, 112, 168, 224, 280 };
//for (int i = 0; i < test.Count; i++)
//{
// F[test[i] * 3 + 1] = -1;
//}
// Define fixed dofs
int num_fixedDofs = 3 * (nelx + 1) * (nelz + 1);
//int num_fixedDofs = 42 * 3;
int num_freeDofs = num_allDofs - num_fixedDofs;
var fixed_dofs = new int[num_fixedDofs];
//var testSup = new List<int>(42) { 7, 15, 23, 31, 39, 47, 55, 63, 71, 79, 87, 95, 103, 111, 119, 127, 135, 143, 151, 159, 167, 175, 183, 191, 199, 207, 215, 223, 231, 239, 247, 255, 263, 271, 279, 287, 295, 303, 311, 319, 327, 335 };
//int sum = 0;
//for (int i = 0; i < testSup.Count; i++)
//{
// fixed_dofs[sum] = 3 * testSup[i];
// sum++;
// fixed_dofs[sum] = 3 * testSup[i] + 1;
// sum++;
// fixed_dofs[sum] = 3 * testSup[i] + 2;
// sum++;
//}
// my order
for (int z = 0; z < nelz + 1; z++)
{
for (int x = 0; x < nelx + 1; x++)
{
int id = nely * (nelx + 1) + z * (nelx + 1) * (nely + 1) + x;
fixed_dofs[3 * (z * (nelx + 1) + x)] = 3 * id;
fixed_dofs[3 * (z * (nelx + 1) + x) + 1] = 3 * id + 1;
fixed_dofs[3 * (z * (nelx + 1) + x) + 2] = 3 * id + 2;
}
}
var all_dofs = new int[num_allDofs];
for (int i = 0; i < num_allDofs; i++)
all_dofs[i] = i;
// Obtain free dofs
free_dofs = all_dofs.Except(fixed_dofs).ToArray();
var U_freedof = new double[num_freeDofs];
Wrapper.Assembly_Solve(solver, parallel, num_freeDofs, num_allDofs, ik.Length, free_dofs, ik, jk, sk, F, U_freedof);
for (int i = 0; i < num_freeDofs; i++)
{
U[free_dofs[i]] = U_freedof[i];
}
}
private void GetKe()
{
var E = 1.0;
var nu = 0.3;
var w = 1 / (1 + nu) / (2 * nu - 1) / 144;
var p1 = new double[300]{-32, -6, -6, 8, 6, 6, 10, 6, 3, -4, -6, -3, -4, -3, -6, 10,
3, 6, 8, 3, 3, 4, -3, -3, -32, -6, -6, -4, -3, 6, 10, 3, 6, 8, 6, -3, -4, -6, -3, 4, -3, 3, 8, 3,
3, 10, 6, -32, -6, -3, -4, -3, -3, 4, -3, -6, -4, 6, 6, 8, 6, 3, 10, 3, 3, 8, 3, 6, 10, -32, 6, 6,
-4, 6, 3, 10, -6, -3, 10, -3, -6, -4, 3, 6, 4, 3, 3, 8, -3, -3, -32, -6, -6, 8, 6, -6, 10, 3, 3, 4,
-3, 3, -4, -6, -3, 10, 6, -3, 8, 3, -32, 3, -6, -4, 3, -3, 4, -6, 3, 10, -6, 6, 8, -3, 6, 10, -3,
3, 8, -32, -6, 6, 8, 6, -6, 8, 3, -3, 4, -3, 3, -4, -3, 6, 10, 3, -6, -32, 6, -6, -4, 3, 3, 8, -3,
3, 10, -6, -3, -4, 6, -3, 4, 3, -32, 6, 3, -4, -3, -3, 8, -3, -6, 10, -6, -6, 8, -6, -3, 10, -32,
6, -6, 4, 3, -3, 8, -3, 3, 10, -3, 6, -4, 3, -6, -32, 6, -3, 10, -6, -3, 8, -3, 3, 4, 3, 3, -4, 6,
-32, 3, -6, 10, 3, -3, 8, 6, -3, 10, 6, -6, 8, -32, -6, 6, 8, 6, -6, 10, 6, -3, -4, -6, 3, -32, 6,
-6, -4, 3, 6, 10, -3, 6, 8, -6, -32, 6, 3, -4, 3, 3, 4, 3, 6, -4, -32, 6, -6, -4, 6, -3, 10, -6, 3,
-32, 6, -6, 8, -6, -6, 10, -3, -32, -3, 6, -4, -3, 3, 4, -32, -6, -6, 8, 6, 6, -32, -6, -6, -4,
-3, -32, -6, -3, -4, -32, 6, 6, -32, -6, -32};
var p2 = new double[300]{48, 0, 0, 0, -24, -24, -12, 0, -12, 0,
24, 0, 0, 0, 24, -12, -12, 0, -12, 0, 0, -12, 12, 12, 48, 0, 24, 0, 0, 0, -12, -12, -24, 0, -24,
0, 0, 24, 12, -12, 12, 0, -12, 0, -12, -12, 0, 48, 24, 0, 0, 12, 12, -12, 0, 24, 0, -24, -24, 0,
0, -12, -12, 0, 0, -12, -12, 0, -12, 48, 0, 0, 0, -24, 0, -12, 0, 12, -12, 12, 0, 0, 0, -24,
-12, -12, -12, -12, 0, 0, 48, 0, 24, 0, -24, 0, -12, -12, -12, -12, 12, 0, 0, 24, 12, -12, 0,
0, -12, 0, 48, 0, 24, 0, -12, 12, -12, 0, -12, -12, 24, -24, 0, 12, 0, -12, 0, 0, -12, 48, 0, 0,
0, -24, 24, -12, 0, 0, -12, 12, -12, 0, 0, -24, -12, -12, 0, 48, 0, 24, 0, 0, 0, -12, 0, -12,
-12, 0, 0, 0, -24, 12, -12, -12, 48, -24, 0, 0, 0, 0, -12, 12, 0, -12, 24, 24, 0, 0, 12, -12,
48, 0, 0, -12, -12, 12, -12, 0, 0, -12, 12, 0, 0, 0, 24, 48, 0, 12, -12, 0, 0, -12, 0, -12, -12,
-12, 0, 0, -24, 48, -12, 0, -12, 0, 0, -12, 0, 12, -12, -24, 24, 0, 48, 0, 0, 0, -24, 24, -12,
0, 12, 0, 24, 0, 48, 0, 24, 0, 0, 0, -12, 12, -24, 0, 24, 48, -24, 0, 0, -12, -12, -12, 0, -24,
0, 48, 0, 0, 0, -24, 0, -12, 0, -12, 48, 0, 24, 0, 24, 0, -12, 12, 48, 0, -24, 0, 12, -12, -12,
48, 0, 0, 0, -24, -24, 48, 0, 24, 0, 0, 48, 24, 0, 0, 48, 0, 0, 48, 0, 48};
Ke = new double[300];
Ke0 = new double[24 * 24];
if (parallel)
{
Parallel.For(0, 300, i =>
{
Ke[i] = E * w * (p1[i] + nu * p2[i]);
});
int num = 0;
for (int i = 0; i < 24; i++)
{
for (int j = 0; j < 24; j++)
{
if (i <= j)
{
Ke0[i * 24 + j] = Ke[num];
num++;
}
}
}
Parallel.For(0, 24, i =>
{
for (int j = 0; j < 24; j++)
if (i > j)
Ke0[i * 24 + j] = Ke0[j * 24 + i];
});
}
else
{
for (int i = 0; i < 300; i++)
Ke[i] = E * w * (p1[i] + nu * p2[i]);
int num = 0;
for (int i = 0; i < 24; i++)
{
for (int j = 0; j < 24; j++)
{
if (i <= j)
{
Ke0[i * 24 + j] = Ke[num];
num++;
}
}
}
for (int i = 0; i < 24; i++)
for (int j = 0; j < 24; j++)
if (i > j)
Ke0[i * 24 + j] = Ke0[j * 24 + i];
}
}
#endregion
#region Debug Methods
public StringBuilder ModelInfo()
{
StringBuilder report = new StringBuilder("=================== Model Info ===================" + '\n');
report.Append("Nodes: " + ((nelx + 1) * (nely + 1) * (nelz + 1)).ToString() + '\n');
report.Append("Elements: " + (nelx * nely * nelz).ToString() + '\n');
report.Append("Parallel mode: " + parallel.ToString() + '\n');
report.Append('\n');
report.Append("=================== Parameters Info ===================" + '\n');
report.Append("xCount: " + nelx.ToString() + '\n');
report.Append("yCount: " + nely.ToString() + '\n');
report.Append("zCount: " + nelz.ToString() + '\n');
return report;
}
public void WriteValue(string path, double[] a)
{
StreamWriter sw = new StreamWriter(path);
for (int i = 0; i < a.Length; i++)
{
sw.WriteLine(a[i].ToString());
}
sw.Flush();
sw.Close();
sw.Dispose();
}
public void WriteValue(string path, int[] a)
{
StreamWriter sw = new StreamWriter(path);
for (int i = 0; i < a.Length; i++)
{
sw.WriteLine(a[i].ToString());
}
sw.Flush();
sw.Close();
sw.Dispose();
}
#endregion
}
}