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optimizedSolidAssemble.pyx
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optimizedSolidAssemble.pyx
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# cython: language_level=3, boundscheck=False
# include math method from C libs.
import numpy as np
cimport numpy as np
from libc.math cimport sqrt
from libc.stdio cimport printf
from cython.parallel import prange
cimport cython
cimport openmp
cdef long nPts # number of nodes in shape
cdef long ndim # number of dimensions
cdef long nSmp # number of samples
# (n,m) (m,d)
@cython.cdivision(True)
@cython.boundscheck(False)
@cython.wraparound(False)
cdef void dot(double[:,::1] A, double[:,::1] B, double[:,::1] C,
long n, long m, long d):
cdef long i, j, k
for i in range(n):
for j in range(d):
C[i,j] = 0.0
for k in range(m):
C[i,j] += A[i,k]*B[k,j]
# (n,m) (m,1)
@cython.cdivision(True)
@cython.boundscheck(False)
@cython.wraparound(False)
cdef void dot1(double[:,::1] A, double[::1] B, double[::1] C,
long n, long m):
cdef long i, j, k
for i in range(n):
C[i] = 0.0
for j in range(m):
C[i] += A[i,j]*B[j]
# (n,m) (n,d)
@cython.cdivision(True)
@cython.boundscheck(False)
@cython.wraparound(False)
cdef void dotT(double[:,::1] A, double[:,::1] B, double[:,::1] C,
long n, long m, long d):
cdef long i, j, k
for i in range(m):
for j in range(d):
C[i,j] = 0.0
for k in range(n):
C[i,j] += A[k,i]*B[k,j]
# (n,m) (n,1)
@cython.cdivision(True)
@cython.boundscheck(False)
@cython.wraparound(False)
cdef void dotT1(double[:,::1] A, double[::1] B, double[::1] C,
long n, long m):
cdef long i, j, k
for i in range(m):
C[i] = 0.0
for j in range(n):
C[i] += A[j,i]*B[j]
@cython.cdivision(True)
@cython.boundscheck(False)
@cython.wraparound(False)
cdef void CoordinateTransformation(double[:,::1] nodes, long[::1] eNIds,
double[:,::1] edges, double[:,::1] T,
double[:,::1] TT):
cdef double edgenorm = 0.0
edges[0,0] = nodes[eNIds[2],0] - nodes[eNIds[1],0]
edges[0,1] = nodes[eNIds[2],1] - nodes[eNIds[1],1]
edges[0,2] = nodes[eNIds[2],2] - nodes[eNIds[1],2]
edges[1,0] = nodes[eNIds[0],0] - nodes[eNIds[2],0]
edges[1,1] = nodes[eNIds[0],1] - nodes[eNIds[2],1]
edges[1,2] = nodes[eNIds[0],2] - nodes[eNIds[2],2]
edgenorm = sqrt(edges[0,0]*edges[0,0] + edges[0,1]*edges[0,1] + edges[0,2]*edges[0,2])
# edgenorm = 1.0 / edgenorm
T[0,0] = edges[0,0]/edgenorm
T[0,1] = edges[0,1]/edgenorm
T[0,2] = edges[0,2]/edgenorm
edgenorm = edges[1,0]*T[0,0] + edges[1,1]*T[0,1] + edges[1,2]*T[0,2]
T[1,0] = edges[1,0] - edgenorm*T[0,0]
T[1,1] = edges[1,1] - edgenorm*T[0,1]
T[1,2] = edges[1,2] - edgenorm*T[0,2]
edgenorm = sqrt(T[1,0]*T[1,0] + T[1,1]*T[1,1] + T[1,2]*T[1,2])
# edgenorm = 1.0 / edgenorm
T[1,0] = T[1,0]/edgenorm
T[1,1] = T[1,1]/edgenorm
T[1,2] = T[1,2]/edgenorm
# set the 3rd to be cross product of first two
T[2,0] = T[0,1]*T[1,2] - T[0,2]*T[1,1] # cx = aybz - azby
T[2,1] = T[0,2]*T[1,0] - T[0,0]*T[1,2] # cy = azbx - axbz
T[2,2] = T[0,0]*T[1,1] - T[0,1]*T[1,0] # cz = axby - aybx
# enlarge the T to be big
TT[0,0] = TT[3,3] = TT[6,6] = T[0,0]
TT[0,1] = TT[3,4] = TT[6,7] = T[0,1]
TT[0,2] = TT[3,5] = TT[6,8] = T[0,2]
TT[1,0] = TT[4,3] = TT[7,6] = T[1,0]
TT[1,1] = TT[4,4] = TT[7,7] = T[1,1]
TT[1,2] = TT[4,5] = TT[7,8] = T[1,2]
TT[2,0] = TT[5,3] = TT[8,6] = T[2,0]
TT[2,1] = TT[5,4] = TT[8,7] = T[2,1]
TT[2,2] = TT[5,5] = TT[8,8] = T[2,2]
@cython.cdivision(True)
@cython.boundscheck(False)
@cython.wraparound(False)
cdef void assembling(long[::1] eNIds, double[:,:,::1] lM,
double[:,:,::1] lK, double[::1] lf,
long[::1] indptr, long[::1] indices,
double[:,:,:,::1] M, double[:,:,:,::1] K, double[::1] f):
nSmp = lM.shape[0]
cdef long a, b, s
cdef long row, col, left, right, ptr
cdef long il, ir, ib
for a in range(3):
row = eNIds[a]
il = row*3
ir = a*3
# Assemble the RHS.
f[il] += lf[ir]
f[il+1] += lf[ir+1]
f[il+2] += lf[ir+2]
for b in range(3):
col = eNIds[b]
ib = b*3
# Search and assemble.
left = indptr[row]
right = indptr[row+1]
ptr = (left + right) / 2
while indices[ptr] != col:
if indices[ptr] > col:
right = ptr
else:
left = ptr
ptr = (left + right) / 2
for s in range(nSmp):
M[ptr,s,0,0] += lM[s,ir,ib]
M[ptr,s,0,1] += lM[s,ir,ib+1]
M[ptr,s,0,2] += lM[s,ir,ib+2]
M[ptr,s,1,0] += lM[s,ir+1,ib]
M[ptr,s,1,1] += lM[s,ir+1,ib+1]
M[ptr,s,1,2] += lM[s,ir+1,ib+2]
M[ptr,s,2,0] += lM[s,ir+2,ib]
M[ptr,s,2,1] += lM[s,ir+2,ib+1]
M[ptr,s,2,2] += lM[s,ir+2,ib+2]
K[ptr,s,0,0] += lK[s,ir,ib]
K[ptr,s,0,1] += lK[s,ir,ib+1]
K[ptr,s,0,2] += lK[s,ir,ib+2]
K[ptr,s,1,0] += lK[s,ir+1,ib]
K[ptr,s,1,1] += lK[s,ir+1,ib+1]
K[ptr,s,1,2] += lK[s,ir+1,ib+2]
K[ptr,s,2,0] += lK[s,ir+2,ib]
K[ptr,s,2,1] += lK[s,ir+2,ib+1]
K[ptr,s,2,2] += lK[s,ir+2,ib+2]
@cython.cdivision(True)
@cython.boundscheck(False)
@cython.wraparound(False)
cdef void lumping(long[::1] indptr,
double[:,:,:,::1] M, double[:,::1] lumpM):
nSmp = M.shape[1]
cdef long nNodes = len(indptr) - 1
cdef long i, j, ik, jk, s
for i in range(nNodes):
for j in range(indptr[i], indptr[i+1]):
for ik in range(3):
for jk in range(3):
for s in range(nSmp):
lumpM[3*i+ik,s] += M[j,s,ik,jk]
@cython.cdivision(True)
@cython.boundscheck(False)
@cython.wraparound(False)
def OptimizedSolidAssemble(double[:,::1] nodes, long[:,::1] elements,
double[::1] coefs, double[::1] wt, double[:,:,::1] tM,
double[:,::1] D, double[:,::1] coefK, double[:,:,::1] elmGThick,
long[::1] indptr, long[::1] indices,
double[:,:,:,::1] M, double[:,:,:,::1] K,
double[::1] f, double[:,::1] lumpM):
cdef long nElms = elements.shape[0]
cdef long iElm, iSmp
nPts = elements.shape[1]
ndim = nodes.shape[1]
nSmp = elmGThick.shape[1]
cdef double trac = coefs[0]
cdef long nGps = wt.shape[0]
cdef long[::1] eNIds = np.empty(nPts, dtype=long)
cdef double[:,::1] T = np.empty((nPts, nPts), dtype=np.float)
cdef double[:,::1] TT = np.zeros((9,9), dtype=np.float)
cdef double[:,::1] lNodes = np.empty((nPts, 2), dtype=np.float)
# cdef double[:,::1] D = np.zeros((5, 5), dtype=np.float)
cdef double[:,::1] B = np.zeros((5, 9), dtype=np.float)
# traction array used for calc f
cdef double[::1] tracArr = np.zeros(9, dtype=np.float)
# no used var for speed up
cdef double[:,::1] edges = np.empty((2,3), dtype=np.float)
# used for temporary value
cdef double[:,::1] BTD = np.empty((9,5), dtype=np.float)
cdef double[:,::1] BTDB = np.empty((9,9), dtype=np.float)
cdef double[:,::1] TTPM = np.empty((9,9), dtype=np.float)
cdef double[:,::1] TTPK = np.empty((9,9), dtype=np.float)
cdef double[:,::1] lM = np.empty((9,9), dtype=np.float)
cdef double[:,::1] lK = np.empty((9,9), dtype=np.float)
cdef double[::1] lf = np.zeros(9, dtype=np.float)
cdef double[:,::1] gM = np.empty((9,9), dtype=np.float)
cdef double[:,::1] gK = np.empty((9,9), dtype=np.float)
cdef double[::1] gf = np.zeros(9, dtype=np.float)
cdef double[:,:,::1] sgM = np.empty((nSmp,9,9), dtype=np.float)
cdef double[:,:,::1] sgK = np.empty((nSmp,9,9), dtype=np.float)
cdef double area
cdef double y23, y31, y12, x32, x13, x21
cdef double c1, c2, c3, c4
cdef long i, j, k
# Calculate the traction vector prepared for f.
tracArr[2] = tracArr[5] = tracArr[8] = trac/3.0
for iElm in range(nElms):
for i in range(nPts):
eNIds[i] = elements[iElm,i]
# Get the transformation matrix T.
CoordinateTransformation(nodes, eNIds, edges, T, TT)
# Transform the triangular to sheer.
lNodes[0,0] = nodes[eNIds[0],0]*T[0,0] + nodes[eNIds[0],1]*T[0,1] + nodes[eNIds[0],2]*T[0,2]
lNodes[0,1] = nodes[eNIds[0],0]*T[1,0] + nodes[eNIds[0],1]*T[1,1] + nodes[eNIds[0],2]*T[1,2]
lNodes[1,0] = nodes[eNIds[1],0]*T[0,0] + nodes[eNIds[1],1]*T[0,1] + nodes[eNIds[1],2]*T[0,2]
lNodes[1,1] = nodes[eNIds[1],0]*T[1,0] + nodes[eNIds[1],1]*T[1,1] + nodes[eNIds[1],2]*T[1,2]
lNodes[2,0] = nodes[eNIds[2],0]*T[0,0] + nodes[eNIds[2],1]*T[0,1] + nodes[eNIds[2],2]*T[0,2]
lNodes[2,1] = nodes[eNIds[2],0]*T[1,0] + nodes[eNIds[2],1]*T[1,1] + nodes[eNIds[2],2]*T[1,2]
# Calculate area and matrix B.
area = ((lNodes[1,0]*lNodes[2,1] - lNodes[2,0]*lNodes[1,1])
- (lNodes[0,0]*lNodes[2,1] - lNodes[2,0]*lNodes[0,1])
+ (lNodes[0,0]*lNodes[1,1] - lNodes[1,0]*lNodes[0,1]))*0.5
# if area <= 0.0:
# printf("Element %ld area not valid!\n", iElm)
# if iElm in [184204, 184227, 184239, 118128, 122060, 123569, 122747, 123560]:
# printf("Element %ld area is %.*e\n", iElm, 17, area)
y23 = lNodes[1,1] - lNodes[2,1]
y31 = lNodes[2,1] - lNodes[0,1]
y12 = lNodes[0,1] - lNodes[1,1]
x32 = lNodes[2,0] - lNodes[1,0]
x13 = lNodes[0,0] - lNodes[2,0]
x21 = lNodes[1,0] - lNodes[0,0]
c1 = (2.0*area)
B[0,0] = B[2,1] = B[3,2] = y23/c1
B[0,3] = B[2,4] = B[3,5] = y31/c1
B[0,6] = B[2,7] = B[3,8] = y12/c1
B[1,1] = B[2,0] = B[4,2] = x32/c1
B[1,4] = B[2,3] = B[4,5] = x13/c1
B[1,7] = B[2,6] = B[4,8] = x21/c1
# Calculate local mass matrix.
# Calculate local stiffness matrix.
dotT(B, D, BTD, 5, 9, 5)
dot(BTD, B, BTDB, 9, 5, 9)
# Calculate for samples and assemble them.
for iSmp in range(nSmp):
for i in range(9):
for j in range(9):
lK[i,j] = BTDB[i,j]*coefK[iElm,iSmp]*area
lM[i,j] = 0.0
for k in range(nGps):
# lM[i,j] = (tM[0,i,j]*elmGThick[iElm,iSmp,0]*wt[0] \
# + tM[1,i,j]*elmGThick[iElm,iSmp,1]*wt[1] \
# + tM[2,i,j]*elmGThick[iElm,iSmp,2]*wt[2])*area
lM[i,j] += tM[k,i,j]*elmGThick[iElm,iSmp,k]*wt[k]
lM[i,j] = lM[i,j]*area
# Transform back to global coord.
dotT(TT, lM, TTPM, 9, 9, 9)
dot(TTPM, TT, gM, 9, 9, 9)
dotT(TT, lK, TTPK, 9, 9, 9)
dot(TTPK, TT, gK, 9, 9, 9)
# Assembling.
for i in range(9):
for j in range(9):
sgM[iSmp,i,j] = gM[i,j]
sgK[iSmp,i,j] = gK[i,j]
# Prepare the lf matrix.
lf[2] = tracArr[2]*area
lf[5] = tracArr[5]*area
lf[8] = tracArr[8]*area
# Transform back to global coord.
dotT1(TT, lf, gf, 9, 9)
# Assembling.
assembling(eNIds, sgM, sgK, gf, indptr, indices, M, K, f)
# if iElm == 925:
# print('lNodes: {}'.format(np.asarray(lNodes)))
# print('B: {}'.format(np.asarray(B)))
# print('D: {}'.format(np.asarray(D)))
# print('lK: {}'.format(np.asarray(lK)))
# print('gK: {}'.format(np.asarray(gK)))
# Lump the mass matrix.
lumping(indptr, M, lumpM)
# ----------------------------- Assembling With Damping ----------------------------------------------
@cython.cdivision(True)
@cython.boundscheck(False)
@cython.wraparound(False)
cdef void assemblingWithDamping(long[::1] eNIds, double[:,:,::1] lM, double[:,:,::1] lC,
double[:,:,::1] lK, double[::1] lf,
long[::1] indptr, long[::1] indices,
double[:,:,:,::1] M, double[:,:,:,::1] C,
double[:,:,:,::1] K, double[::1] f):
nSmp = lM.shape[0]
cdef long a, b, s
cdef long row, col, left, right, ptr
cdef long il, ir, ib
for a in range(3):
row = eNIds[a]
il = row*3
ir = a*3
# Assemble the RHS.
f[il] += lf[ir]
f[il+1] += lf[ir+1]
f[il+2] += lf[ir+2]
for b in range(3):
col = eNIds[b]
ib = b*3
# Search and assemble.
left = indptr[row]
right = indptr[row+1]
ptr = (left + right) / 2
while indices[ptr] != col:
if indices[ptr] > col:
right = ptr
else:
left = ptr
ptr = (left + right) / 2
for s in range(nSmp):
M[ptr,s,0,0] += lM[s,ir,ib]
M[ptr,s,0,1] += lM[s,ir,ib+1]
M[ptr,s,0,2] += lM[s,ir,ib+2]
M[ptr,s,1,0] += lM[s,ir+1,ib]
M[ptr,s,1,1] += lM[s,ir+1,ib+1]
M[ptr,s,1,2] += lM[s,ir+1,ib+2]
M[ptr,s,2,0] += lM[s,ir+2,ib]
M[ptr,s,2,1] += lM[s,ir+2,ib+1]
M[ptr,s,2,2] += lM[s,ir+2,ib+2]
C[ptr,s,0,0] += lC[s,ir,ib]
C[ptr,s,0,1] += lC[s,ir,ib+1]
C[ptr,s,0,2] += lC[s,ir,ib+2]
C[ptr,s,1,0] += lC[s,ir+1,ib]
C[ptr,s,1,1] += lC[s,ir+1,ib+1]
C[ptr,s,1,2] += lC[s,ir+1,ib+2]
C[ptr,s,2,0] += lC[s,ir+2,ib]
C[ptr,s,2,1] += lC[s,ir+2,ib+1]
C[ptr,s,2,2] += lC[s,ir+2,ib+2]
K[ptr,s,0,0] += lK[s,ir,ib]
K[ptr,s,0,1] += lK[s,ir,ib+1]
K[ptr,s,0,2] += lK[s,ir,ib+2]
K[ptr,s,1,0] += lK[s,ir+1,ib]
K[ptr,s,1,1] += lK[s,ir+1,ib+1]
K[ptr,s,1,2] += lK[s,ir+1,ib+2]
K[ptr,s,2,0] += lK[s,ir+2,ib]
K[ptr,s,2,1] += lK[s,ir+2,ib+1]
K[ptr,s,2,2] += lK[s,ir+2,ib+2]
@cython.cdivision(True)
@cython.boundscheck(False)
@cython.wraparound(False)
cdef void lumpingWithDamping(long[::1] indptr,
double[:,:,:,::1] M, double[:,::1] lumpM,
double[:,:,:,::1] C, double[:,::1] lumpC):
nSmp = M.shape[1]
cdef long nNodes = len(indptr) - 1
cdef long i, j, ik, jk, s
for i in range(nNodes):
for j in range(indptr[i], indptr[i+1]):
for ik in range(3):
for jk in range(3):
for s in range(nSmp):
lumpM[3*i+ik,s] += M[j,s,ik,jk]
lumpC[3*i+ik,s] += C[j,s,ik,jk]
@cython.cdivision(True)
@cython.boundscheck(False)
@cython.wraparound(False)
def OptimizedSolidAssembleWithDamping(double[:,::1] nodes, long[:,::1] elements,
double[::1] coefs, double[::1] wt, double[:,:,::1] tM,
double[:,::1] D, double[:,::1] coefK, double[:,:,::1] elmGThick,
long[::1] indptr, long[::1] indices,
double[:,:,:,::1] M, double[:,:,:,::1] C, double[:,:,:,::1] K,
double[::1] f, double[:,::1] lumpM, double[:,::1] lumpC):
cdef long nElms = elements.shape[0]
cdef long iElm, iSmp
nPts = elements.shape[1]
ndim = nodes.shape[1]
nSmp = elmGThick.shape[1]
cdef double trac = coefs[0]
cdef double damp = coefs[1]
cdef long[::1] eNIds = np.empty(nPts, dtype=long)
cdef double[:,::1] T = np.empty((nPts, nPts), dtype=np.float)
cdef double[:,::1] TT = np.zeros((9,9), dtype=np.float)
cdef double[:,::1] lNodes = np.empty((nPts, 2), dtype=np.float)
# cdef double[:,::1] D = np.zeros((5, 5), dtype=np.float)
cdef double[:,::1] B = np.zeros((5, 9), dtype=np.float)
# traction array used for calc f
cdef double[::1] tracArr = np.zeros(9, dtype=np.float)
# no used var for speed up
cdef double[:,::1] edges = np.empty((2,3), dtype=np.float)
# used for temporary value
cdef double[:,::1] BTD = np.empty((9,5), dtype=np.float)
cdef double[:,::1] BTDB = np.empty((9,9), dtype=np.float)
cdef double[:,::1] TTPM = np.empty((9,9), dtype=np.float)
cdef double[:,::1] TTPC = np.empty((9,9), dtype=np.float)
cdef double[:,::1] TTPK = np.empty((9,9), dtype=np.float)
cdef double[:,::1] lM = np.empty((9,9), dtype=np.float)
cdef double[:,::1] lC = np.empty((9,9), dtype=np.float)
cdef double[:,::1] lK = np.empty((9,9), dtype=np.float)
cdef double[::1] lf = np.zeros(9, dtype=np.float)
cdef double[:,::1] gM = np.empty((9,9), dtype=np.float)
cdef double[:,::1] gC = np.empty((9,9), dtype=np.float)
cdef double[:,::1] gK = np.empty((9,9), dtype=np.float)
cdef double[::1] gf = np.zeros(9, dtype=np.float)
cdef double[:,:,::1] sgM = np.empty((nSmp,9,9), dtype=np.float)
cdef double[:,:,::1] sgC = np.empty((nSmp,9,9), dtype=np.float)
cdef double[:,:,::1] sgK = np.empty((nSmp,9,9), dtype=np.float)
cdef double area
cdef double y23, y31, y12, x32, x13, x21
cdef double c1, c2, c3, c4
cdef long i, j
# Calculate the traction vector prepared for f.
tracArr[2] = tracArr[5] = tracArr[8] = trac/3.0
for iElm in range(nElms):
for i in range(nPts):
eNIds[i] = elements[iElm,i]
# Get the transformation matrix T.
CoordinateTransformation(nodes, eNIds, edges, T, TT)
# Transform the triangular to sheer.
lNodes[0,0] = nodes[eNIds[0],0]*T[0,0] + nodes[eNIds[0],1]*T[0,1] + nodes[eNIds[0],2]*T[0,2]
lNodes[0,1] = nodes[eNIds[0],0]*T[1,0] + nodes[eNIds[0],1]*T[1,1] + nodes[eNIds[0],2]*T[1,2]
lNodes[1,0] = nodes[eNIds[1],0]*T[0,0] + nodes[eNIds[1],1]*T[0,1] + nodes[eNIds[1],2]*T[0,2]
lNodes[1,1] = nodes[eNIds[1],0]*T[1,0] + nodes[eNIds[1],1]*T[1,1] + nodes[eNIds[1],2]*T[1,2]
lNodes[2,0] = nodes[eNIds[2],0]*T[0,0] + nodes[eNIds[2],1]*T[0,1] + nodes[eNIds[2],2]*T[0,2]
lNodes[2,1] = nodes[eNIds[2],0]*T[1,0] + nodes[eNIds[2],1]*T[1,1] + nodes[eNIds[2],2]*T[1,2]
# Calculate area and matrix B.
area = ((lNodes[1,0]*lNodes[2,1] - lNodes[2,0]*lNodes[1,1])
- (lNodes[0,0]*lNodes[2,1] - lNodes[2,0]*lNodes[0,1])
+ (lNodes[0,0]*lNodes[1,1] - lNodes[1,0]*lNodes[0,1]))*0.5
y23 = lNodes[1,1] - lNodes[2,1]
y31 = lNodes[2,1] - lNodes[0,1]
y12 = lNodes[0,1] - lNodes[1,1]
x32 = lNodes[2,0] - lNodes[1,0]
x13 = lNodes[0,0] - lNodes[2,0]
x21 = lNodes[1,0] - lNodes[0,0]
c1 = (2.0*area)
B[0,0] = B[2,1] = B[3,2] = y23/c1
B[0,3] = B[2,4] = B[3,5] = y31/c1
B[0,6] = B[2,7] = B[3,8] = y12/c1
B[1,1] = B[2,0] = B[4,2] = x32/c1
B[1,4] = B[2,3] = B[4,5] = x13/c1
B[1,7] = B[2,6] = B[4,8] = x21/c1
# Calculate local mass matrix.
# Calculate local stiffness matrix.
dotT(B, D, BTD, 5, 9, 5)
dot(BTD, B, BTDB, 9, 5, 9)
# Calculate for samples and assemble them.
for iSmp in range(nSmp):
for i in range(9):
for j in range(9):
lM[i,j] = (tM[0,i,j]*elmGThick[iElm,iSmp,0]*wt[0] \
+ tM[1,i,j]*elmGThick[iElm,iSmp,1]*wt[1] \
+ tM[2,i,j]*elmGThick[iElm,iSmp,2]*wt[2])*area
# TODO:: divide by density
lC[i,j] = lM[i,j]*damp
lK[i,j] = BTDB[i,j]*coefK[iElm,iSmp]*area
# Transform back to global coord.
dotT(TT, lM, TTPM, 9, 9, 9)
dot(TTPM, TT, gM, 9, 9, 9)
dotT(TT, lC, TTPC, 9, 9, 9)
dot(TTPC, TT, gC, 9, 9, 9)
dotT(TT, lK, TTPK, 9, 9, 9)
dot(TTPK, TT, gK, 9, 9, 9)
# Assembling.
for i in range(9):
for j in range(9):
sgM[iSmp,i,j] = gM[i,j]
sgC[iSmp,i,j] = gC[i,j]
sgK[iSmp,i,j] = gK[i,j]
# Prepare the lf matrix.
lf[2] = tracArr[2]*area
lf[5] = tracArr[5]*area
lf[8] = tracArr[8]*area
# Transform back to global coord.
dotT1(TT, lf, gf, 9, 9)
# Assembling.
assemblingWithDamping(eNIds, sgM, sgC, sgK, gf, indptr, indices, M, C, K, f)
# if iElm == 925:
# print('lNodes: {}'.format(np.asarray(lNodes)))
# print('B: {}'.format(np.asarray(B)))
# print('D: {}'.format(np.asarray(D)))
# print('lK: {}'.format(np.asarray(lK)))
# print('gK: {}'.format(np.asarray(gK)))
# Lump the mass matrix.
lumpingWithDamping(indptr, M, lumpM, C, lumpC)
# ----------------------------- Assembling Updating ----------------------------------------------
@cython.cdivision(True)
@cython.boundscheck(False)
@cython.wraparound(False)
cdef void CoordinateTransformationUpdate(double[:,:,::1] nodes, long s, long[::1] eNIds,
double[:,::1] edges, double[:,::1] T,
double[:,::1] TT):
cdef double edgenorm = 0.0
edges[0,0] = nodes[s,eNIds[2],0] - nodes[s,eNIds[1],0]
edges[0,1] = nodes[s,eNIds[2],1] - nodes[s,eNIds[1],1]
edges[0,2] = nodes[s,eNIds[2],2] - nodes[s,eNIds[1],2]
edges[1,0] = nodes[s,eNIds[0],0] - nodes[s,eNIds[2],0]
edges[1,1] = nodes[s,eNIds[0],1] - nodes[s,eNIds[2],1]
edges[1,2] = nodes[s,eNIds[0],2] - nodes[s,eNIds[2],2]
edgenorm = sqrt(edges[0,0]*edges[0,0] + edges[0,1]*edges[0,1] + edges[0,2]*edges[0,2])
# edgenorm = 1.0 / edgenorm
T[0,0] = edges[0,0]/edgenorm
T[0,1] = edges[0,1]/edgenorm
T[0,2] = edges[0,2]/edgenorm
edgenorm = edges[1,0]*T[0,0] + edges[1,1]*T[0,1] + edges[1,2]*T[0,2]
T[1,0] = edges[1,0] - edgenorm*T[0,0]
T[1,1] = edges[1,1] - edgenorm*T[0,1]
T[1,2] = edges[1,2] - edgenorm*T[0,2]
edgenorm = sqrt(T[1,0]*T[1,0] + T[1,1]*T[1,1] + T[1,2]*T[1,2])
# edgenorm = 1.0 / edgenorm
T[1,0] = T[1,0]/edgenorm
T[1,1] = T[1,1]/edgenorm
T[1,2] = T[1,2]/edgenorm
# set the 3rd to be cross product of first two
T[2,0] = T[0,1]*T[1,2] - T[0,2]*T[1,1] # cx = aybz - azby
T[2,1] = T[0,2]*T[1,0] - T[0,0]*T[1,2] # cy = azbx - axbz
T[2,2] = T[0,0]*T[1,1] - T[0,1]*T[1,0] # cz = axby - aybx
# enlarge the T to be big
TT[0,0] = TT[3,3] = TT[6,6] = T[0,0]
TT[0,1] = TT[3,4] = TT[6,7] = T[0,1]
TT[0,2] = TT[3,5] = TT[6,8] = T[0,2]
TT[1,0] = TT[4,3] = TT[7,6] = T[1,0]
TT[1,1] = TT[4,4] = TT[7,7] = T[1,1]
TT[1,2] = TT[4,5] = TT[7,8] = T[1,2]
TT[2,0] = TT[5,3] = TT[8,6] = T[2,0]
TT[2,1] = TT[5,4] = TT[8,7] = T[2,1]
TT[2,2] = TT[5,5] = TT[8,8] = T[2,2]
@cython.cdivision(True)
@cython.boundscheck(False)
@cython.wraparound(False)
cdef void assemblingUpdate(long[::1] eNIds,
double[:,:,::1] lK, double[:,::1] lf,
long[::1] indptr, long[::1] indices,
double[:,:,:,::1] K, double[:,::1] f):
nSmp = lK.shape[0]
cdef long a, b, s
cdef long row, col, left, right, ptr
cdef long il, ir, ib
for a in range(3):
row = eNIds[a]
il = row*3
ir = a*3
for s in range(nSmp):
# Assemble the RHS.
f[il,s] += lf[s,ir]
f[il+1,s] += lf[s,ir+1]
f[il+2,s] += lf[s,ir+2]
for b in range(3):
col = eNIds[b]
ib = b*3
# Search and assemble.
left = indptr[row]
right = indptr[row+1]
ptr = (left + right) / 2
while indices[ptr] != col:
if indices[ptr] > col:
right = ptr
else:
left = ptr
ptr = (left + right) / 2
for s in range(nSmp):
K[ptr,s,0,0] += lK[s,ir,ib]
K[ptr,s,0,1] += lK[s,ir,ib+1]
K[ptr,s,0,2] += lK[s,ir,ib+2]
K[ptr,s,1,0] += lK[s,ir+1,ib]
K[ptr,s,1,1] += lK[s,ir+1,ib+1]
K[ptr,s,1,2] += lK[s,ir+1,ib+2]
K[ptr,s,2,0] += lK[s,ir+2,ib]
K[ptr,s,2,1] += lK[s,ir+2,ib+1]
K[ptr,s,2,2] += lK[s,ir+2,ib+2]
@cython.cdivision(True)
@cython.boundscheck(False)
@cython.wraparound(False)
def OptimizedSolidAssembleUpdate(double[:,:,::1] nodes, long[:,::1] elements,
double[::1] coefs, double[:,::1] D, double[:,::1] coefK,
long[::1] indptr, long[::1] indices,
double[:,:,:,::1] K, double[:,::1] f):
cdef long nElms = elements.shape[0]
cdef long iElm, iSmp
nPts = elements.shape[1]
ndim = nodes.shape[2]
nSmp = coefK.shape[1]
cdef double trac = coefs[0]
cdef long[::1] eNIds = np.empty(nPts, dtype=long)
cdef double[:,::1] T = np.empty((nPts, nPts), dtype=np.float)
cdef double[:,::1] TT = np.zeros((9,9), dtype=np.float)
cdef double[:,::1] lNodes = np.empty((nPts, 2), dtype=np.float)
# cdef double[:,::1] D = np.zeros((5, 5), dtype=np.float)
cdef double[:,::1] B = np.zeros((5, 9), dtype=np.float)
# traction array used for calc f
cdef double[::1] tracArr = np.zeros(9, dtype=np.float)
# no used var for speed up
cdef double[:,::1] edges = np.empty((2,3), dtype=np.float)
# used for temporary value
cdef double[:,::1] BTD = np.empty((9,5), dtype=np.float)
cdef double[:,::1] BTDB = np.empty((9,9), dtype=np.float)
cdef double[:,::1] TTPK = np.empty((9,9), dtype=np.float)
cdef double[:,::1] lK = np.empty((9,9), dtype=np.float)
cdef double[::1] lf = np.zeros(9, dtype=np.float)
cdef double[:,::1] gK = np.empty((9,9), dtype=np.float)
cdef double[::1] gf = np.zeros(9, dtype=np.float)
cdef double[:,:,::1] sgK = np.empty((nSmp,9,9), dtype=np.float)
cdef double[:,::1] sgf = np.empty((nSmp,9), dtype=np.float)
cdef double area
cdef double y23, y31, y12, x32, x13, x21
cdef double c1, c2, c3, c4
cdef long i, j
# Calculate the traction vector prepared for f.
tracArr[2] = tracArr[5] = tracArr[8] = trac/3.0
for iElm in range(nElms):
for i in range(nPts):
eNIds[i] = elements[iElm,i]
for iSmp in range(nSmp):
# Get the transformation matrix T.
CoordinateTransformationUpdate(nodes, iSmp, eNIds, edges, T, TT)
# Transform the triangular to sheer.
lNodes[0,0] = nodes[iSmp,eNIds[0],0]*T[0,0] + nodes[iSmp,eNIds[0],1]*T[0,1] + nodes[iSmp,eNIds[0],2]*T[0,2]
lNodes[0,1] = nodes[iSmp,eNIds[0],0]*T[1,0] + nodes[iSmp,eNIds[0],1]*T[1,1] + nodes[iSmp,eNIds[0],2]*T[1,2]
lNodes[1,0] = nodes[iSmp,eNIds[1],0]*T[0,0] + nodes[iSmp,eNIds[1],1]*T[0,1] + nodes[iSmp,eNIds[1],2]*T[0,2]
lNodes[1,1] = nodes[iSmp,eNIds[1],0]*T[1,0] + nodes[iSmp,eNIds[1],1]*T[1,1] + nodes[iSmp,eNIds[1],2]*T[1,2]
lNodes[2,0] = nodes[iSmp,eNIds[2],0]*T[0,0] + nodes[iSmp,eNIds[2],1]*T[0,1] + nodes[iSmp,eNIds[2],2]*T[0,2]
lNodes[2,1] = nodes[iSmp,eNIds[2],0]*T[1,0] + nodes[iSmp,eNIds[2],1]*T[1,1] + nodes[iSmp,eNIds[2],2]*T[1,2]
# Calculate area and matrix B.
area = ((lNodes[1,0]*lNodes[2,1] - lNodes[2,0]*lNodes[1,1])
- (lNodes[0,0]*lNodes[2,1] - lNodes[2,0]*lNodes[0,1])
+ (lNodes[0,0]*lNodes[1,1] - lNodes[1,0]*lNodes[0,1]))*0.5
y23 = lNodes[1,1] - lNodes[2,1]
y31 = lNodes[2,1] - lNodes[0,1]
y12 = lNodes[0,1] - lNodes[1,1]
x32 = lNodes[2,0] - lNodes[1,0]
x13 = lNodes[0,0] - lNodes[2,0]
x21 = lNodes[1,0] - lNodes[0,0]
c1 = (2.0*area)
B[0,0] = B[2,1] = B[3,2] = y23/c1
B[0,3] = B[2,4] = B[3,5] = y31/c1
B[0,6] = B[2,7] = B[3,8] = y12/c1
B[1,1] = B[2,0] = B[4,2] = x32/c1
B[1,4] = B[2,3] = B[4,5] = x13/c1
B[1,7] = B[2,6] = B[4,8] = x21/c1
# Prepare the lf matrix.
lf[2] = tracArr[2]*area
lf[5] = tracArr[5]*area
lf[8] = tracArr[8]*area
# Calculate local mass matrix.
# Calculate local stiffness matrix.
dotT(B, D, BTD, 5, 9, 5)
dot(BTD, B, BTDB, 9, 5, 9)
# Calculate for samples and assemble them.
for i in range(9):
for j in range(9):
lK[i,j] = BTDB[i,j]*coefK[iElm,iSmp]*area
# Transform back to global coord.
dotT(TT, lK, TTPK, 9, 9, 9)
dot(TTPK, TT, gK, 9, 9, 9)
dotT1(TT, lf, gf, 9, 9)
# Assembling.
for i in range(9):
sgf[iSmp,i] = gf[i]
for j in range(9):
sgK[iSmp,i,j] = gK[i,j]
# Assembling.
assemblingUpdate(eNIds, sgK, sgf, indptr, indices, K, f)
# ----------------------------- Assembling Updating with Damping force ----------------------------------------------
@cython.cdivision(True)
@cython.boundscheck(False)
@cython.wraparound(False)
cdef void assemblingUpdateWithDampingForce(long[::1] eNIds,
double[:,:,::1] lK, double[:,::1] lf, double[:,::1] ldf,
long[::1] indptr, long[::1] indices,
double[:,:,:,::1] K, double[:,::1] f, double[:,::1] df):
nSmp = lK.shape[0]
cdef long a, b, s
cdef long row, col, left, right, ptr
cdef long il, ir, ib
for a in range(3):
row = eNIds[a]
il = row*3
ir = a*3
for s in range(nSmp):
# Assemble the RHS.
f[il,s] += lf[s,ir]
f[il+1,s] += lf[s,ir+1]
f[il+2,s] += lf[s,ir+2]
# Assemble the RHS.
df[il,s] += ldf[s,ir]
df[il+1,s] += ldf[s,ir+1]
df[il+2,s] += ldf[s,ir+2]
for b in range(3):
col = eNIds[b]
ib = b*3
# Search and assemble.
left = indptr[row]
right = indptr[row+1]
ptr = (left + right) / 2
while indices[ptr] != col:
if indices[ptr] > col:
right = ptr
else:
left = ptr
ptr = (left + right) / 2
for s in range(nSmp):
K[ptr,s,0,0] += lK[s,ir,ib]
K[ptr,s,0,1] += lK[s,ir,ib+1]
K[ptr,s,0,2] += lK[s,ir,ib+2]
K[ptr,s,1,0] += lK[s,ir+1,ib]
K[ptr,s,1,1] += lK[s,ir+1,ib+1]
K[ptr,s,1,2] += lK[s,ir+1,ib+2]
K[ptr,s,2,0] += lK[s,ir+2,ib]
K[ptr,s,2,1] += lK[s,ir+2,ib+1]
K[ptr,s,2,2] += lK[s,ir+2,ib+2]
@cython.cdivision(True)
@cython.boundscheck(False)
@cython.wraparound(False)
def OptimizedSolidAssembleUpdateWithDampingForce(double[:,:,::1] nodes, long[:,::1] elements,
double[::1] coefs, double[:,::1] D, double[:,::1] coefK,
double[:,::1] acc, double[:,::1] mass,
long[::1] indptr, long[::1] indices,
double[:,:,:,::1] K, double[:,::1] f, double[:,::1] df):
cdef long nElms = elements.shape[0]
cdef long iElm, iSmp
nPts = elements.shape[1]
ndim = nodes.shape[2]
nSmp = coefK.shape[1]
cdef double trac = coefs[0]
cdef long[::1] eNIds = np.empty(nPts, dtype=long)
cdef double[:,::1] T = np.empty((nPts, nPts), dtype=np.float)
cdef double[:,::1] TT = np.zeros((9,9), dtype=np.float)
cdef double[:,::1] lNodes = np.empty((nPts, 2), dtype=np.float)
# cdef double[:,::1] D = np.zeros((5, 5), dtype=np.float)
cdef double[:,::1] B = np.zeros((5, 9), dtype=np.float)
# traction array used for calc f
cdef double[::1] tracArr = np.zeros(9, dtype=np.float)
# no used var for speed up
cdef double[:,::1] edges = np.empty((2,3), dtype=np.float)
# used for temporary value
cdef double[:,::1] BTD = np.empty((9,5), dtype=np.float)
cdef double[:,::1] BTDB = np.empty((9,9), dtype=np.float)
cdef double[:,::1] TTPK = np.empty((9,9), dtype=np.float)
cdef double[:,::1] lK = np.empty((9,9), dtype=np.float)
cdef double[::1] lf = np.zeros(9, dtype=np.float)
cdef double[:,::1] gK = np.empty((9,9), dtype=np.float)
cdef double[::1] gf = np.zeros(9, dtype=np.float)
cdef double[:,:,::1] sgK = np.empty((nSmp,9,9), dtype=np.float)
cdef double[:,::1] sgf = np.empty((nSmp,9), dtype=np.float)
# things related with damping force
cdef double[::1] gAcc = np.empty(9, dtype=np.float)
cdef double[::1] lAcc = np.empty(9, dtype=np.float)
cdef double[::1] ldf = np.zeros(9, dtype=np.float)
cdef double[::1] gdf = np.zeros(9, dtype=np.float)
cdef double[:,::1] sgdf = np.empty((nSmp,9), dtype=np.float)
cdef double area
cdef double y23, y31, y12, x32, x13, x21
cdef double c1, c2, c3, c4
cdef long i, j
# Calculate the traction vector prepared for f.
tracArr[2] = tracArr[5] = tracArr[8] = trac/3.0
for iElm in range(nElms):
for i in range(nPts):
eNIds[i] = elements[iElm,i]
for iSmp in range(nSmp):
for i in range(nPts):
gAcc[i*3] = acc[eNIds[i]*3,iSmp]
gAcc[i*3+1] = acc[eNIds[i]*3+1,iSmp]
gAcc[i*3+2] = acc[eNIds[i]*3+2,iSmp]
# Get the transformation matrix T.
CoordinateTransformationUpdate(nodes, iSmp, eNIds, edges, T, TT)
# Transform the triangular to sheer.
lNodes[0,0] = nodes[iSmp,eNIds[0],0]*T[0,0] + nodes[iSmp,eNIds[0],1]*T[0,1] + nodes[iSmp,eNIds[0],2]*T[0,2]
lNodes[0,1] = nodes[iSmp,eNIds[0],0]*T[1,0] + nodes[iSmp,eNIds[0],1]*T[1,1] + nodes[iSmp,eNIds[0],2]*T[1,2]
lNodes[1,0] = nodes[iSmp,eNIds[1],0]*T[0,0] + nodes[iSmp,eNIds[1],1]*T[0,1] + nodes[iSmp,eNIds[1],2]*T[0,2]
lNodes[1,1] = nodes[iSmp,eNIds[1],0]*T[1,0] + nodes[iSmp,eNIds[1],1]*T[1,1] + nodes[iSmp,eNIds[1],2]*T[1,2]
lNodes[2,0] = nodes[iSmp,eNIds[2],0]*T[0,0] + nodes[iSmp,eNIds[2],1]*T[0,1] + nodes[iSmp,eNIds[2],2]*T[0,2]
lNodes[2,1] = nodes[iSmp,eNIds[2],0]*T[1,0] + nodes[iSmp,eNIds[2],1]*T[1,1] + nodes[iSmp,eNIds[2],2]*T[1,2]
# Calculate area and matrix B.
area = ((lNodes[1,0]*lNodes[2,1] - lNodes[2,0]*lNodes[1,1])
- (lNodes[0,0]*lNodes[2,1] - lNodes[2,0]*lNodes[0,1])
+ (lNodes[0,0]*lNodes[1,1] - lNodes[1,0]*lNodes[0,1]))*0.5
y23 = lNodes[1,1] - lNodes[2,1]
y31 = lNodes[2,1] - lNodes[0,1]
y12 = lNodes[0,1] - lNodes[1,1]
x32 = lNodes[2,0] - lNodes[1,0]
x13 = lNodes[0,0] - lNodes[2,0]
x21 = lNodes[1,0] - lNodes[0,0]
c1 = (2.0*area)
B[0,0] = B[2,1] = B[3,2] = y23/c1
B[0,3] = B[2,4] = B[3,5] = y31/c1
B[0,6] = B[2,7] = B[3,8] = y12/c1
B[1,1] = B[2,0] = B[4,2] = x32/c1
B[1,4] = B[2,3] = B[4,5] = x13/c1
B[1,7] = B[2,6] = B[4,8] = x21/c1
# Prepare the lf matrix.
lf[2] = tracArr[2]*area
lf[5] = tracArr[5]*area
lf[8] = tracArr[8]*area
# Calculating the local acc.
dot1(TT, gAcc, lAcc, 9, 9)
ldf[2] = -0.1*lAcc[2]*mass[iElm,iSmp]
ldf[5] = -0.1*lAcc[5]*mass[iElm,iSmp]
ldf[8] = -0.1*lAcc[8]*mass[iElm,iSmp]
# Calculate local mass matrix.
# Calculate local stiffness matrix.
dotT(B, D, BTD, 5, 9, 5)
dot(BTD, B, BTDB, 9, 5, 9)
# Calculate for samples and assemble them.
for i in range(9):
for j in range(9):
lK[i,j] = BTDB[i,j]*coefK[iElm,iSmp]*area