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physicsSolverSDampGPUs.cl
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physicsSolverSDampGPUs.cl
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void TtKT(const double *T, const double *K,
double *tmp, double *res)
{
for (uint i = 0; i < 3; i++)
{
for (uint j = 0; j < 3; j++)
{
tmp[i*3+j] = T[i]*K[j] + T[3+i]*K[3+j] + T[6+i]*K[6+j];
}
}
for (uint i = 0; i < 3; i++)
{
for (uint j = 0; j < 3; j++)
{
res[i*3+j] = tmp[i*3]*T[j] + tmp[i*3+1]*T[3+j] + tmp[i*3+2]*T[6+j];
}
}
}
/* Assemble matrix K (stiffness) and M (mass) at the initial.
- nodes: (nGNodes, 3) the global coords of all the nodes.
- elmNodeIds: (nElm, 3) the node ids' of each element.
- Ku: (nGNodes*3, nSmp) the product result after assembling.
*/
__kernel void assemble_K_M_P(const long nSmp, const double pressure,
const __global double *pVals, const __global double *nodes,
const __global long *elmNodeIds, const __global double *thickness,
const __global double *elmThicknessE,
const __global double *u, __global double *Ku,
__global double *LM, __global double *P)
{
uint iElm = get_global_id(0);
const __global long *nodeIds = elmNodeIds + iElm * 3;
__global double *sM;
__global double *sKu;
__global double *sP;
const double density = pVals[0];
// pE[0]: v
// pE[1]: 0.5*(1-v)
// pE[2]: 0.5*k*(1-v)
// pE[3]: (1-v^2)
const __global double *pE = pVals + 1;
double elmThick[3];
double T[9];
double lNodes[6];
double lB[6];
double llK[9] = {0};
double glK[9];
// tmp vars
double tmpVec[3];
double tmpBP[4]; // product of two rows of B
double tmpMat[9];
double area = 0.0;
double lm = 0.0;
// tmp vars
double tmpVal = 0.0;
double tmpNorm = 0.0;
// Transform coordernates to referenced coord.
// 1. Get coordinate transformation matrix T.
// T : x 0 1 2
// y 3 4 5
// z 6 7 8
// x
tmpVec[0] = nodes[nodeIds[2]*3] - nodes[nodeIds[1]*3];
tmpVec[1] = nodes[nodeIds[2]*3+1] - nodes[nodeIds[1]*3+1];
tmpVec[2] = nodes[nodeIds[2]*3+2] - nodes[nodeIds[1]*3+2];
tmpNorm = sqrt(pow(tmpVec[0],2) + pow(tmpVec[1],2) + pow(tmpVec[2],2));
T[0] = tmpVec[0] / tmpNorm;
T[1] = tmpVec[1] / tmpNorm;
T[2] = tmpVec[2] / tmpNorm;
// y
tmpVec[0] = nodes[nodeIds[0]*3] - nodes[nodeIds[2]*3];
tmpVec[1] = nodes[nodeIds[0]*3+1] - nodes[nodeIds[2]*3+1];
tmpVec[2] = nodes[nodeIds[0]*3+2] - nodes[nodeIds[2]*3+2];
tmpVal = T[0]*tmpVec[0] + T[1]*tmpVec[1] + T[2]*tmpVec[2];
tmpVec[0] -= tmpVal*T[0];
tmpVec[1] -= tmpVal*T[1];
tmpVec[2] -= tmpVal*T[2];
tmpNorm = sqrt(pow(tmpVec[0],2) + pow(tmpVec[1],2) + pow(tmpVec[2],2));
T[3] = tmpVec[0] / tmpNorm;
T[4] = tmpVec[1] / tmpNorm;
T[5] = tmpVec[2] / tmpNorm;
// z, the cross product of x and y
T[6] = T[1]*T[5] - T[2]*T[4];
T[7] = T[2]*T[3] - T[0]*T[5];
T[8] = T[0]*T[4] - T[1]*T[3];
// 2. Transform triangle in 3D to local 2D coord.
// node 0 : 0 1 0 1
// node 1 : 0 1 2 3
// node 2 : 0 1 4 5
lNodes[0] = nodes[nodeIds[0]*3]*T[0] + nodes[nodeIds[0]*3+1]*T[1] + nodes[nodeIds[0]*3+2]*T[2];
lNodes[1] = nodes[nodeIds[0]*3]*T[3] + nodes[nodeIds[0]*3+1]*T[4] + nodes[nodeIds[0]*3+2]*T[5];
lNodes[2] = nodes[nodeIds[1]*3]*T[0] + nodes[nodeIds[1]*3+1]*T[1] + nodes[nodeIds[1]*3+2]*T[2];
lNodes[3] = nodes[nodeIds[1]*3]*T[3] + nodes[nodeIds[1]*3+1]*T[4] + nodes[nodeIds[1]*3+2]*T[5];
lNodes[4] = nodes[nodeIds[2]*3]*T[0] + nodes[nodeIds[2]*3+1]*T[1] + nodes[nodeIds[2]*3+2]*T[2];
lNodes[5] = nodes[nodeIds[2]*3]*T[3] + nodes[nodeIds[2]*3+1]*T[4] + nodes[nodeIds[2]*3+2]*T[5];
// 3. Calculate area by |x1 y1 1| lNodes[0] lNodes[1] 1
// 0.5*|x2 y2 1| lNodes[2] lNodes[3] 1
// |x3 y3 1| lNodes[4] lNodes[5] 1
area = 0.5*(lNodes[0]*(lNodes[3]-lNodes[5]) - lNodes[2]*(lNodes[1]-lNodes[5]) + lNodes[4]*(lNodes[1]-lNodes[3]));
// 4. Compute local B (strain matrix).
lB[0] = lNodes[3] - lNodes[5]; // y23: y2 - y3
lB[1] = lNodes[4] - lNodes[2]; // x32: x3 - x2
lB[2] = lNodes[5] - lNodes[1]; // y31: y3 - y1
lB[3] = lNodes[0] - lNodes[4]; // x13: x1 - x3
lB[4] = lNodes[1] - lNodes[3]; // y12: y1 - y2
lB[5] = lNodes[2] - lNodes[0]; // x21: x2 - x1
for (uint iSmp = 0; iSmp < nSmp; iSmp++)
{
sKu = Ku + iSmp;
sM = LM + iSmp;
sP = P + iSmp;
elmThick[0] = thickness[nodeIds[0]*nSmp+iSmp];
elmThick[1] = thickness[nodeIds[1]*nSmp+iSmp];
elmThick[2] = thickness[nodeIds[2]*nSmp+iSmp];
// Loop through the nodes and "assemble" K
// 5. Compute local K (stiffness) matrix.
tmpVal = elmThicknessE[iElm*nSmp+iSmp]/(4.0*area*pE[3]);
for (uint i = 0; i < 3; i++)
{
for (uint j = i; j < 3; j++)
{
tmpBP[0] = lB[i*2]*lB[j*2];
tmpBP[1] = lB[i*2]*lB[j*2+1];
tmpBP[2] = lB[i*2+1]*lB[j*2];
tmpBP[3] = lB[i*2+1]*lB[j*2+1];
llK[0] = tmpBP[0] + tmpBP[3]*pE[1];
llK[1] = tmpBP[1]*pE[0] + tmpBP[2]*pE[1];
llK[3] = tmpBP[2]*pE[0] + tmpBP[1]*pE[1];
llK[4] = tmpBP[3] + tmpBP[0]*pE[1];
llK[8] = (tmpBP[0] + tmpBP[3])*pE[2];
// 6. Transform to global coord, gK = TtKT.
TtKT(T, llK, tmpMat, glK);
// 7. Calculate Ku, then assemble to vector 'Ku'.
sKu[nodeIds[i]*3*nSmp] += (glK[0]*u[nodeIds[j]*3] + glK[1]*u[nodeIds[j]*3+1] + glK[2]*u[nodeIds[j]*3+2])*tmpVal;
sKu[(nodeIds[i]*3+1)*nSmp] += (glK[3]*u[nodeIds[j]*3] + glK[4]*u[nodeIds[j]*3+1] + glK[5]*u[nodeIds[j]*3+2])*tmpVal;
sKu[(nodeIds[i]*3+2)*nSmp] += (glK[6]*u[nodeIds[j]*3] + glK[7]*u[nodeIds[j]*3+1] + glK[8]*u[nodeIds[j]*3+2])*tmpVal;
// use symetrical char. to save computation
if (j > i)
{
sKu[nodeIds[j]*3*nSmp] += (glK[0]*u[nodeIds[i]*3] + glK[3]*u[nodeIds[i]*3+1] + glK[6]*u[nodeIds[i]*3+2])*tmpVal;
sKu[(nodeIds[j]*3+1)*nSmp] += (glK[1]*u[nodeIds[i]*3] + glK[4]*u[nodeIds[i]*3+1] + glK[7]*u[nodeIds[i]*3+2])*tmpVal;
sKu[(nodeIds[j]*3+2)*nSmp] += (glK[2]*u[nodeIds[i]*3] + glK[5]*u[nodeIds[i]*3+1] + glK[8]*u[nodeIds[i]*3+2])*tmpVal;
}
}
// 'Assemble' the force vector.
sP[nodeIds[i]*3*nSmp] += T[6] * pressure * area / 3.0;
sP[(nodeIds[i]*3+1)*nSmp] += T[7] * pressure * area / 3.0;
sP[(nodeIds[i]*3+2)*nSmp] += T[8] * pressure * area / 3.0;
}
// Calculate M_ab^e
// ab = 00
lm = density * area * (elmThick[0]/4.0 + elmThick[1]/8.0 + elmThick[2]/8.0) / 3.0;
sM[(nodeIds[0]*3)*nSmp] += lm;
sM[(nodeIds[0]*3+1)*nSmp] += lm;
sM[(nodeIds[0]*3+2)*nSmp] += lm;
// ab = 01
lm = density * area * (elmThick[0]/8.0 + elmThick[1]/8.0) / 3.0;
sM[(nodeIds[0]*3)*nSmp] += lm;
sM[(nodeIds[0]*3+1)*nSmp] += lm;
sM[(nodeIds[0]*3+2)*nSmp] += lm;
// ab = 10 with symetrical
sM[(nodeIds[1]*3)*nSmp] += lm;
sM[(nodeIds[1]*3+1)*nSmp] += lm;
sM[(nodeIds[1]*3+2)*nSmp] += lm;
// ab = 02
lm = density * area * (elmThick[0]/8.0 + elmThick[2]/8.0) / 3.0;
sM[(nodeIds[0]*3)*nSmp] += lm;
sM[(nodeIds[0]*3+1)*nSmp] += lm;
sM[(nodeIds[0]*3+2)*nSmp] += lm;
// ab = 20 with symetrical
sM[(nodeIds[2]*3)*nSmp] += lm;
sM[(nodeIds[2]*3+1)*nSmp] += lm;
sM[(nodeIds[2]*3+2)*nSmp] += lm;
// Row 1
// ab = 11
lm = density * area * (elmThick[0]/8.0 + elmThick[1]/4.0 + elmThick[2]/8.0) / 3.0;
sM[(nodeIds[1]*3)*nSmp] += lm;
sM[(nodeIds[1]*3+1)*nSmp] += lm;
sM[(nodeIds[1]*3+2)*nSmp] += lm;
// ab = 12
lm = density * area * (elmThick[1]/8.0 + elmThick[2]/8.0) / 3.0;
sM[(nodeIds[1]*3)*nSmp] += lm;
sM[(nodeIds[1]*3+1)*nSmp] += lm;
sM[(nodeIds[1]*3+2)*nSmp] += lm;
// ab = 21 with symetrical
sM[(nodeIds[2]*3)*nSmp] += lm;
sM[(nodeIds[2]*3+1)*nSmp] += lm;
sM[(nodeIds[2]*3+2)*nSmp] += lm;
// Row 2
// ab = 22
lm = density * area * (elmThick[0]/8.0 + elmThick[1]/4.0 + elmThick[2]/8.0) / 3.0;
sM[(nodeIds[2]*3)*nSmp] += lm;
sM[(nodeIds[2]*3+1)*nSmp] += lm;
sM[(nodeIds[2]*3+2)*nSmp] += lm;
}
}
/* Assemble matrix K (stiffness) at each time step.
- nodes: (nGNodes, 3) the global coords of all the nodes.
- elmNodeIds: (nElm, 3) the node ids' of each element.
- u: (nGNodes*3, nSmp) the displacement of all samples at each dof.
*/
__kernel void assemble_K_P(const long nElms, const long nSmp, const double pressure,
const __global double *pVals, const __global double *nodes,
const __global long *elmNodeIds, const __global double *elmThicknessE,
const __global double *u, __global double *Ku, __global double *P)
{
for (uint iElm = get_group_id(0); iElm < nElms; iElm += get_num_groups(0))
{
const __global long *nodeIds = elmNodeIds + iElm * 3;
const double density = pVals[0];
// pE[0]: v
// pE[1]: 0.5*(1-v)
// pE[2]: 0.5*k*(1-v)
// pE[3]: (1-v^2)
const __global double *pE = pVals + 1;
double sNodes[9];
double T[9];
double lNodes[6];
double lB[6];
double llK[9] = {0};
double glK[9];
// tmp vars
double tmpVec[3];
double tmpBP[4]; // product of two rows of B
double tmpMat[9];
double area = 0.0;
// tmp vars
double tmpVal = 0.0;
double tmpNorm = 0.0;
for (uint iSmp = get_local_id(0); iSmp < nSmp; iSmp += get_local_size(0))
{
const __global double *su = u + iSmp;
__global double *sKu = Ku + iSmp;
__global double *sP = P + iSmp;
// Get the updated coordinates.
// node 0
sNodes[0] = nodes[nodeIds[0]*3] + su[(nodeIds[0]*3)*nSmp];
sNodes[1] = nodes[nodeIds[0]*3+1] + su[(nodeIds[0]*3+1)*nSmp];
sNodes[2] = nodes[nodeIds[0]*3+2] + su[(nodeIds[0]*3+2)*nSmp];
// node 1
sNodes[3] = nodes[nodeIds[1]*3] + su[(nodeIds[1]*3)*nSmp];
sNodes[4] = nodes[nodeIds[1]*3+1] + su[(nodeIds[1]*3+1)*nSmp];
sNodes[5] = nodes[nodeIds[1]*3+2] + su[(nodeIds[1]*3+2)*nSmp];
// node 2
sNodes[6] = nodes[nodeIds[2]*3] + su[(nodeIds[2]*3)*nSmp];
sNodes[7] = nodes[nodeIds[2]*3+1] + su[(nodeIds[2]*3+1)*nSmp];
sNodes[8] = nodes[nodeIds[2]*3+2] + su[(nodeIds[2]*3+2)*nSmp];
// Transform coordernates to referenced coord.
// 1. Get coordinate transformation matrix T.
// T : x 0 1 2
// y 3 4 5
// z 6 7 8
// x
tmpVec[0] = sNodes[6] - sNodes[3];
tmpVec[1] = sNodes[7] - sNodes[4];
tmpVec[2] = sNodes[8] - sNodes[5];
tmpNorm = sqrt(pow(tmpVec[0],2) + pow(tmpVec[1],2) + pow(tmpVec[2],2));
T[0] = tmpVec[0] / tmpNorm;
T[1] = tmpVec[1] / tmpNorm;
T[2] = tmpVec[2] / tmpNorm;
// y
tmpVec[0] = sNodes[0] - sNodes[6];
tmpVec[1] = sNodes[1] - sNodes[7];
tmpVec[2] = sNodes[2] - sNodes[8];
tmpVal = T[0]*tmpVec[0] + T[1]*tmpVec[1] + T[2]*tmpVec[2];
tmpVec[0] -= tmpVal*T[0];
tmpVec[1] -= tmpVal*T[1];
tmpVec[2] -= tmpVal*T[2];
tmpNorm = sqrt(pow(tmpVec[0],2) + pow(tmpVec[1],2) + pow(tmpVec[2],2));
T[3] = tmpVec[0] / tmpNorm;
T[4] = tmpVec[1] / tmpNorm;
T[5] = tmpVec[2] / tmpNorm;
// z, the cross product of x and y
T[6] = T[1]*T[5] - T[2]*T[4];
T[7] = T[2]*T[3] - T[0]*T[5];
T[8] = T[0]*T[4] - T[1]*T[3];
// 2. Transform triangle in 3D to local 2D coord.
// node 0 : 0 1 0 1
// node 1 : 0 1 2 3
// node 2 : 0 1 4 5
lNodes[0] = sNodes[0]*T[0] + sNodes[1]*T[1] + sNodes[2]*T[2];
lNodes[1] = sNodes[0]*T[3] + sNodes[1]*T[4] + sNodes[2]*T[5];
lNodes[2] = sNodes[3]*T[0] + sNodes[4]*T[1] + sNodes[5]*T[2];
lNodes[3] = sNodes[3]*T[3] + sNodes[4]*T[4] + sNodes[5]*T[5];
lNodes[4] = sNodes[6]*T[0] + sNodes[7]*T[1] + sNodes[8]*T[2];
lNodes[5] = sNodes[6]*T[3] + sNodes[7]*T[4] + sNodes[8]*T[5];
// 3. Calculate area by |x1 y1 1| lNodes[0] lNodes[1] 1
// 0.5*|x2 y2 1| lNodes[2] lNodes[3] 1
// |x3 y3 1| lNodes[4] lNodes[5] 1
area = 0.5*(lNodes[0]*(lNodes[3]-lNodes[5]) - lNodes[2]*(lNodes[1]-lNodes[5]) + lNodes[4]*(lNodes[1]-lNodes[3]));
// 4. Compute local B (strain matrix).
lB[0] = lNodes[3] - lNodes[5]; // y23: y2 - y3
lB[1] = lNodes[4] - lNodes[2]; // x32: x3 - x2
lB[2] = lNodes[5] - lNodes[1]; // y31: y3 - y1
lB[3] = lNodes[0] - lNodes[4]; // x13: x1 - x3
lB[4] = lNodes[1] - lNodes[3]; // y12: y1 - y2
lB[5] = lNodes[2] - lNodes[0]; // x21: x2 - x1
// Loop through the nodes and "assemble" K
// 5. Compute local K (stiffness) matrix.
tmpVal = elmThicknessE[iElm*nSmp+iSmp]/(4.0*area*pE[3]);
for (uint i = 0; i < 3; i++)
{
for (uint j = i; j < 3; j++)
{
tmpBP[0] = lB[i*2]*lB[j*2];
tmpBP[1] = lB[i*2]*lB[j*2+1];
tmpBP[2] = lB[i*2+1]*lB[j*2];
tmpBP[3] = lB[i*2+1]*lB[j*2+1];
llK[0] = tmpBP[0] + tmpBP[3]*pE[1];
llK[1] = tmpBP[1]*pE[0] + tmpBP[2]*pE[1];
llK[3] = tmpBP[2]*pE[0] + tmpBP[1]*pE[1];
llK[4] = tmpBP[3] + tmpBP[0]*pE[1];
llK[8] = (tmpBP[0] + tmpBP[3])*pE[2];
// 6. Transform to global coord, gK = TtKT.
TtKT(T, llK, tmpMat, glK);
// 7. Calculate Ku, then assemble to vector 'Ku'.
sKu[(nodeIds[i]*3)*nSmp] += (glK[0]*su[(nodeIds[j]*3)*nSmp] \
+ glK[1]*su[(nodeIds[j]*3+1)*nSmp] \
+ glK[2]*su[(nodeIds[j]*3+2)*nSmp])*tmpVal;
sKu[(nodeIds[i]*3+1)*nSmp] += (glK[3]*su[(nodeIds[j]*3)*nSmp] \
+ glK[4]*su[(nodeIds[j]*3+1)*nSmp] \
+ glK[5]*su[(nodeIds[j]*3+2)*nSmp])*tmpVal;
sKu[(nodeIds[i]*3+2)*nSmp] += (glK[6]*su[(nodeIds[j]*3)*nSmp] \
+ glK[7]*su[(nodeIds[j]*3+1)*nSmp] \
+ glK[8]*su[(nodeIds[j]*3+2)*nSmp])*tmpVal;
// use symetrical char. to save computation
if (j > i)
{
sKu[(nodeIds[j]*3)*nSmp] += (glK[0]*su[(nodeIds[i]*3)*nSmp] \
+ glK[3]*su[(nodeIds[i]*3+1)*nSmp] \
+ glK[6]*su[(nodeIds[i]*3+2)*nSmp])*tmpVal;
sKu[(nodeIds[j]*3+1)*nSmp] += (glK[1]*su[(nodeIds[i]*3)*nSmp] \
+ glK[4]*su[(nodeIds[i]*3+1)*nSmp] \
+ glK[7]*su[(nodeIds[i]*3+2)*nSmp])*tmpVal;
sKu[(nodeIds[j]*3+2)*nSmp] += (glK[2]*su[(nodeIds[i]*3)*nSmp] \
+ glK[5]*su[(nodeIds[i]*3+1)*nSmp] \
+ glK[8]*su[(nodeIds[i]*3+2)*nSmp])*tmpVal;
}
}
// 'Assemble' the force vector.
sP[nodeIds[i]*3*nSmp] += T[6] * pressure * area / 3.0;
sP[(nodeIds[i]*3+1)*nSmp] += T[7] * pressure * area / 3.0;
sP[(nodeIds[i]*3+2)*nSmp] += T[8] * pressure * area / 3.0;
}
}
}
}
/* Calculate acceleration ddu at the initial.
- each group loop through columns (nSmp)
*/
__kernel void calc_ddu(const long nSmp, const long ndof,
const __global double *P0, const __global double *Ku,
const __global double *LHS, __global double *ddu)
{
for (uint i = get_group_id(0); i < ndof; i += get_num_groups(0))
{
for (uint j = get_local_id(0); j < nSmp; j += get_local_size(0))
{
ddu[i*nSmp+j] = (P0[i*nSmp+j] - Ku[i*nSmp+j]) / LHS[i*nSmp+j];
}
}
}
/* Calculate u of next time step.
- each group loop through columns (nSmp)
*/
__kernel void calc_u(const long nSmp, const long ndof, const double dt, const double damp,
const __global double *P, const __global double *Ku,
const __global double *LM, const __global double *LHS,
const __global double *u, const __global double *up,
__global double *ures)
{
for (uint i = get_group_id(0); i < ndof; i += get_num_groups(0))
{
for (uint j = get_local_id(0); j < nSmp; j += get_local_size(0))
{
ures[i*nSmp+j] = (dt*dt*((P[i*nSmp+j]-damp*(u[i*nSmp+j]-up[i*nSmp+j])/dt) - Ku[i*nSmp+j]) + LM[i*nSmp+j]*(2.0*u[i*nSmp+j] - up[i*nSmp+j])) / LHS[i*nSmp+j];
}
}
}
/* Calculate u of next time step, add on the appTrac
- each group loop through columns (nSmp)
*/
__kernel void calc_u_appTrac(const long nSmp, const long ndof, const double dt,
const __global double *LHS, const __global double *appTrac,
__global double *ures)
{
for (uint i = get_group_id(0); i < ndof; i += get_num_groups(0))
{
for (uint j = get_local_id(0); j < nSmp; j += get_local_size(0))
{
ures[i*nSmp+j] += dt*dt*appTrac[i] / LHS[i*nSmp+j];
}
}
}