def addTime(self, generator):
qShape = (self.numberOf3DBasisFunctions(), self.numberOfQuantities())
dQ0 = OptionalDimTensor('dQ(0)',
self.Q.optName(),
self.Q.optSize(),
self.Q.optPos(),
qShape,
alignStride=True)
power = Scalar('power')
derivatives = [dQ0]
generator.add('derivativeTaylorExpansion(0)',
self.I['kp'] <= power * dQ0['kp'])
for i in range(1, self.order):
derivativeSum = Add()
if self.sourceMatrix():
derivativeSum += derivatives[-1]['kq'] * self.sourceMatrix(
)['qp']
for j in range(3):
derivativeSum += self.db.kDivMT[j][self.t(
'kl')] * derivatives[-1]['lq'] * self.starMatrix(j)['qp']
derivativeSum = DeduceIndices(
self.Q['kp'].indices).visit(derivativeSum)
derivativeSum = EquivalentSparsityPattern().visit(derivativeSum)
dQ = OptionalDimTensor('dQ({})'.format(i),
self.Q.optName(),
self.Q.optSize(),
self.Q.optPos(),
qShape,
spp=derivativeSum.eqspp(),
alignStride=True)
generator.add('derivative({})'.format(i),
dQ['kp'] <= derivativeSum)
generator.add('derivativeTaylorExpansion({})'.format(i),
self.I['kp'] <= self.I['kp'] + power * dQ['kp'])
derivatives.append(dQ)
def add(g):
db = parseXMLMatrixFile('seissol_matrices.xml')
Q = Tensor('Q', (8, 20, 15))
I = Tensor('I', (8, 20, 15))
g.add('seissol_stiffness', Q['skp'] <= db.kXiTDivM['lk'] * I['slq'] * db.star['qp'])
# Reproduces recursive generation of zero blocks in Cauchy-Kowalevski prodedure,
# described in "Sustained Petascale Performance of Seismic Simulations with SeisSol on SuperMUC",
# Breuer et al., ISC 2014.
dQ_shape = (20, 9)
dQ0 = Tensor('dQ(0)', dQ_shape)
star_ela = Tensor('star_ela', (9,9), spp=db.star['qp'].spp().as_ndarray()[0:9,0:9])
dQ_prev = dQ0
for i in range(1,4):
derivativeSum = Add()
for j in range(3):
derivativeSum += db.kDivMT[j]['kl'] * dQ_prev['lq'] * star_ela['qp']
derivativeSum = DeduceIndices('kp').visit(derivativeSum)
derivativeSum = EquivalentSparsityPattern().visit(derivativeSum)
dQ = Tensor('dQ({})'.format(i), dQ_shape, spp=derivativeSum.eqspp())
g.add('derivative({})'.format(i), dQ['kp'] <= derivativeSum)
dQ_prev = dQ
def addLocal(self, generator):
volumeSum = Add()
for i in range(3):
volumeSum += self.db.kDivM[i][self.t('kl')] * self.I['lq'] * self.db.star[i]['qp']
volumeExt = (self.Qext['kp'] <= volumeSum)
generator.add('volumeExt', volumeExt)
localFluxExt = lambda i: self.Qext['kp'] <= self.Qext['kp'] + self.db.rDivM[i][self.t('km')] * self.db.fMrT[i][self.t('ml')] * self.I['lq'] * self.AplusT['qp']
localFluxExtPrefetch = lambda i: self.I if i == 0 else (self.Q if i == 1 else None)
generator.addFamily('localFluxExt', simpleParameterSpace(4), localFluxExt, localFluxExtPrefetch)
generator.add('local', [
self.Qane['kpm'] <= self.Qane['kpm'] + self.w['m'] * self.Qext['kq'] * self.selectAne['qp'] + self.Iane['kpl'] * self.W['lm'],
self.Q['kp'] <= self.Q['kp'] + self.Qext['kq'] * self.selectEla['qp'] + self.Iane['kqm'] * self.E['qmp']
])
def derivative(kthDer):
derivativeSum = Add()
for j in range(3):
derivativeSum += self.db.kDivMT[j][self.t('kl')] * dQ[kthDer-1]['lq'] * self.db.star[j]['qp']
return derivativeSum