void Strand2dFCBlockMesh::initialize(const int& level0,
const int& meshOrder0,
const int& nSurfElem0,
const int& nSurfNodeG,
const int& nBndNode0,
const int& nStrandNodeG,
const int& nCompBd0,
int** surfElemG,
const Array1D<int>& bndNodeG,
const Array2D<double>& surfXG,
const Array1D<double>& strandXG,
const Array1D<int>& surfElemTagG,
const Array1D<int>& bndNodeTagG,
const Array2D<double>& bndNodeNormalG)
{
// copy dimensions for this block
level = level0;
meshOrder = meshOrder0;
nSurfElem = nSurfElem0;
nBndNode = nBndNode0;
nCompBd = nCompBd0;
// allocate space for the mesh data, and copy the known data
surfElem.allocate(nSurfElem,meshOrder+1);
surfElemTag.allocate(nSurfElem);
bndNode.allocate(nBndNode);
bndNodeTag.allocate(nBndNode);
bndNodeNormal.allocate(nBndNode,2);
for (int n=0; n<nSurfElem; n++) surfElemTag(n) = surfElemTagG(n);
for (int n=0; n<nBndNode; n++){
bndNodeTag(n) = bndNodeTagG(n);
bndNodeNormal(n,0) = bndNodeNormalG(n,0);
bndNodeNormal(n,1) = bndNodeNormalG(n,1);
}
// form surface elements of the desired order, count surface nodes
int n1,n2;
Array1D<int> flag(nSurfNodeG);
flag.set(-1);
nSurfNode = 0;
for (int n=0; n<nSurfElem; n++){ //add element end points first
n1 = surfElemG[n][1];
n2 = surfElemG[n][2];
if (flag(n1) == -1) flag(n1) = nSurfNode++;
if (flag(n2) == -1) flag(n2) = nSurfNode++;
surfElem(n,0) = flag(n1);
surfElem(n,1) = flag(n2);
}
for (int n=0; n<nSurfElem; n++) //add interior dofs next
for (int j=2; j<meshOrder+1; j++) surfElem(n,j) = nSurfNode++;
// point the bndNode array to the new node numbers
for (int n=0; n<nBndNode; n++) bndNode(n) = flag(bndNodeG(n));
// find surface mesh coordinates based on mappings from the mesh file
Array1D<double> ss(meshOrder+1);
int spacing=0; // assume equal spacing for now
solutionPoints1D(meshOrder, //find s-locations based on desired spacing
spacing,
&ss(0));
surfX.allocate(nSurfNode,2);
surfX.set(0.);
bool test=false;
int orderM;
double lm;
Array1D<double> sM;
Array2D<double> lcM;
flag.deallocate();
flag.allocate(nSurfNode);
flag.set(-1);
for (int n=0; n<nSurfElem; n++){
orderM = surfElemG[n][0];
// s-locations using numbering consistent with the mesh
sM.allocate(orderM+1);
solutionPoints1D(orderM,
spacing,
&sM(0));
// lagrange polynomials at the sM locations
lcM.allocate(orderM+1,orderM+1);
lagrangePoly1D(test,
orderM,
&sM(0),
&lcM(0,0));
// evaluate the x-coordinates at the local solution points
for (int i=0; i<meshOrder+1; i++) //ith local point
if (flag(surfElem(n,i)) == -1){//haven't computed this location yet
for (int m=0; m<orderM+1; m++){ //mth Lagrange poly. used in mapping
lm = 0.;
for (int k=0; k<orderM+1; k++) lm += pow(ss(i),k)*lcM(m,k);
surfX(surfElem(n,i),0) += lm*surfXG(surfElemG[n][m+1],0);
surfX(surfElem(n,i),1) += lm*surfXG(surfElemG[n][m+1],1);
}
flag(surfElem(n,i)) = 0;
}
sM.deallocate();
lcM.deallocate();
}
// generate pointing vectors
// first find surface mapping based on global mesh
Array2D<double> xS(nSurfElem,meshOrder+1),yS(nSurfElem,meshOrder+1);
xS.set(0.);
yS.set(0.);
int ni,nm;
Array2D<double> lsM;
for (int n=0; n<nSurfElem; n++){
orderM = surfElemG[n][0];
// s-locations using numbering consistent with the mesh
sM.allocate(orderM+1);
solutionPoints1D(orderM,
spacing,
&sM(0));
// lagrange polynomials at the sM locations
lcM.allocate(orderM+1,orderM+1);
lagrangePoly1D(test,
orderM,
&sM(0),
&lcM(0,0));
// ls(i,j) = (dl_j/ds)_i (a row is all Lagrange polynomials (derivatives)
// evaluated at a single mesh point i)
lsM.allocate(meshOrder+1,orderM+1);
lsM.set(0.);
int km;
for (int i=0; i<meshOrder+1; i++) // ith mesh point
for (int j=0; j<orderM+1; j++) // jth Lagrange polynomial
for (int k=0; k<orderM+1; k++){
km = max(0,k-1);
lsM(i,j) +=((double)k)*pow(ss(i),km)*lcM(j,k);
}
for (int n=0; n<nSurfElem; n++)
for (int i=0; i<meshOrder+1; i++) //ith point in the element
for (int m=0; m<orderM+1; m++){ //mth Lagrange poly. in mapping
xS(n,i) += lsM(i,m)*surfXG(surfElemG[n][m+1],0);
yS(n,i) += lsM(i,m)*surfXG(surfElemG[n][m+1],1);
}
sM.deallocate();
lcM.deallocate();
}
// initialize all pointing vectors
// using the surface mapping (averaged among neighboring elements)
pointingVec.allocate(nSurfNode,2);
pointingVec.set(0.);
int m;
double nx,ny,ds,rms;
for (int n=0; n<nSurfElem; n++)
for (int i=0; i<meshOrder+1; i++){
m = surfElem(n,i);
nx =-yS(n,i);
ny = xS(n,i);
ds = 1./sqrt(nx*nx+ny*ny);
nx *= ds;
ny *= ds;
////////////////////////////////////////////////////////////////////////
//~ change the 2 comment lines below with code lines to have normal
//~ pointing vectors instead of verticle pointing vectors
//~ pointingVec(m,0) += nx;
//~ pointingVec(m,1) += ny;
pointingVec(m,0) = 0.; //shaun change
pointingVec(m,1) = 1.;
}
for (int n=0; n<nSurfNode; n++){
ds = 1./sqrt(pointingVec(n,0)*pointingVec(n,0)+
pointingVec(n,1)*pointingVec(n,1));
pointingVec(n,0) *= ds;
pointingVec(n,1) *= ds;
}
// smooth the strands interior to elements iteratively
int* psp1;
int** psp2;
psp1 = new int[meshOrder+1];
psp2 = new int*[meshOrder+1];
if (meshOrder == 1){
psp1[0] = 1;
psp1[1] = 1;
psp2[0] = new int[psp1[0]];
psp2[0][0] = 1;
psp2[1] = new int[psp1[1]];
psp2[1][0] = 0;
}
else if (meshOrder == 2){
psp1[0] = 1;
psp1[1] = 1;
psp1[2] = 2;
psp2[0] = new int[psp1[0]];
psp2[0][0] = 2;
psp2[1] = new int[psp1[1]];
psp2[1][0] = 2;
psp2[2] = new int[psp1[2]];
psp2[2][0] = 0;
psp2[2][1] = 1;
}
else if (meshOrder == 3){
psp1[0] = 1;
psp1[1] = 1;
psp1[2] = 2;
psp1[3] = 2;
psp2[0] = new int[psp1[0]];
psp2[0][0] = 2;
psp2[1] = new int[psp1[1]];
psp2[1][0] = 3;
psp2[2] = new int[psp1[2]];
psp2[2][0] = 0;
psp2[2][1] = 3;
psp2[3] = new int[psp1[3]];
psp2[3][0] = 2;
psp2[3][1] = 1;
}
else if (meshOrder == 4){
psp1[0] = 1;
psp1[1] = 1;
psp1[2] = 2;
psp1[3] = 2;
psp1[4] = 2;
psp2[0] = new int[psp1[0]];
psp2[0][0] = 2;
psp2[1] = new int[psp1[1]];
psp2[1][0] = 4;
psp2[2] = new int[psp1[2]];
psp2[2][0] = 0;
psp2[2][1] = 3;
psp2[3] = new int[psp1[3]];
psp2[3][0] = 2;
psp2[3][1] = 4;
psp2[4] = new int[psp1[4]];
psp2[4][0] = 3;
psp2[4][1] = 1;
}
else{
cout << "\nPlease choose meshOrder=3 or less." << endl;
exit(0);
}
if (meshOrder > 1)
for (int n=0; n<nSurfElem; n++)
for (int iter=0; iter<1000; iter++){
rms = 0.;
for (int i=2; i<meshOrder+1; i++){
ni = surfElem(n,i);
nx = 0.;
ny = 0.;
for (int m=0; m<psp1[i]; m++){
nm = surfElem(n,psp2[i][m]);
nx += pointingVec(nm,0);
ny += pointingVec(nm,1);
}
ds = 1./sqrt(nx*nx+ny*ny);
nx *= ds;
ny *= ds;
rms += (nx-pointingVec(ni,0))*(nx-pointingVec(ni,0))+
(ny-pointingVec(ni,1))*(ny-pointingVec(ni,1));
pointingVec(ni,0) = nx;
pointingVec(ni,1) = ny;
}
rms = sqrt(rms/(double)(meshOrder-1));
if (rms < 1.e-13) break;
}
/*
for (int n=0; n<nSurfNode; n++){
pointingVec(n,0) = 0.;
pointingVec(n,1) = 1.;
}
*/
// determine strand node distribution
int ks=nStrandNodeG-1,js=pow(2,level);
if (ks%js != 0){
cout << "\n***Number of strand nodes not a good multigrid number.***"
<< endl;
exit(0);
}
nStrandNode =(nStrandNodeG-1)/pow(2,level);
nStrandNode++;
strandX.allocate(nStrandNode);
int i=0;
for (int j=0; j<nStrandNode; j++){
strandX(j) = strandXG(i);
i += pow(2,level);
}
// generate clipping index
clip.allocate(nSurfNode);
clip.set(nStrandNode-1);
// report mesh statistics
if (level == 0){
cout.setf(ios::scientific);
cout << "\nMesh statistics: " << endl
<< "Number of surface elements: " << nSurfElem << endl
<< "Number of surface nodes: " << nSurfNode << endl
<< "Number of boundary nodes: " << nBndNode << endl
<< "Number of boundary comp.: " << nCompBd << endl
<< "Number of strand nodes: " << nStrandNode << endl;
cout << "\nstrand distribution:";
for (int n=0; n<nStrandNode; n++) cout << "\n" << n << "\t" << strandX(n);
cout << "\nwall spacing: " << strandX(1)
<< "\ntip spacing: " << strandX(nStrandNode-1)-strandX(nStrandNode-2)
<< "\n" << endl;
}
// clean up
if (psp1){
delete [] psp1;
psp1 = NULL;
}
if (psp2){
for (int i=0; i<meshOrder+1; i++)
if (psp2[i]){
delete [] psp2[i];
psp2[i] = NULL;
}
delete [] psp2;
psp2 = NULL;
}
xS.deallocate();
yS.deallocate();
lcM.deallocate();
lsM.deallocate();
sM.deallocate();
ss.deallocate();
flag.deallocate();
}
