void Foam::LUscalarMatrix::solve
(
Field<Type>& x,
const Field<Type>& source
) const
{
// If x and source are different initialize x = source
if (&x != &source)
{
x = source;
}
if (Pstream::parRun())
{
Field<Type> X(m());
if (Pstream::master(comm_))
{
typename Field<Type>::subField
(
X,
x.size()
) = x;
for
(
int slave=Pstream::firstSlave();
slave<=Pstream::lastSlave(comm_);
slave++
)
{
IPstream::read
(
Pstream::scheduled,
slave,
reinterpret_cast<char*>
(
&(X[procOffsets_[slave]])
),
(procOffsets_[slave+1]-procOffsets_[slave])*sizeof(Type),
Pstream::msgType(),
comm_
);
}
}
else
{
OPstream::write
(
Pstream::scheduled,
Pstream::masterNo(),
reinterpret_cast<const char*>(x.begin()),
x.byteSize(),
Pstream::msgType(),
comm_
);
}
if (Pstream::master(comm_))
{
LUBacksubstitute(*this, pivotIndices_, X);
x = typename Field<Type>::subField
(
X,
x.size()
);
for
(
int slave=Pstream::firstSlave();
slave<=Pstream::lastSlave(comm_);
slave++
)
{
OPstream::write
(
Pstream::scheduled,
slave,
reinterpret_cast<const char*>
(
&(X[procOffsets_[slave]])
),
(procOffsets_[slave + 1]-procOffsets_[slave])*sizeof(Type),
Pstream::msgType(),
comm_
);
}
}
else
{
IPstream::read
(
Pstream::scheduled,
Pstream::masterNo(),
reinterpret_cast<char*>(x.begin()),
x.byteSize(),
Pstream::msgType(),
comm_
);
}
}
else
{
LUBacksubstitute(*this, pivotIndices_, x);
}
}
void Foam::SIBS::SIMPR
(
const ODE& ode,
const scalar xStart,
const scalarField& y,
const scalarField& dydx,
const scalarField& dfdx,
const scalarSquareMatrix& dfdy,
const scalar deltaX,
const label nSteps,
scalarField& yEnd
) const
{
scalar h = deltaX/nSteps;
scalarSquareMatrix a(n_);
for (register label i=0; i<n_; i++)
{
for (register label j=0; j<n_; j++)
{
a[i][j] = -h*dfdy[i][j];
}
++a[i][i];
}
labelList pivotIndices(n_);
LUDecompose(a, pivotIndices);
for (register label i=0; i<n_; i++)
{
yEnd[i] = h*(dydx[i] + h*dfdx[i]);
}
LUBacksubstitute(a, pivotIndices, yEnd);
scalarField del(yEnd);
scalarField ytemp(n_);
for (register label i=0; i<n_; i++)
{
ytemp[i] = y[i] + del[i];
}
scalar x = xStart + h;
ode.derivatives(x, ytemp, yEnd);
for (register label nn=2; nn<=nSteps; nn++)
{
for (register label i=0; i<n_; i++)
{
yEnd[i] = h*yEnd[i] - del[i];
}
LUBacksubstitute(a, pivotIndices, yEnd);
for (register label i=0; i<n_; i++)
{
ytemp[i] += (del[i] += 2.0*yEnd[i]);
}
x += h;
ode.derivatives(x, ytemp, yEnd);
}
for (register label i=0; i<n_; i++)
{
yEnd[i] = h*yEnd[i] - del[i];
}
LUBacksubstitute(a, pivotIndices, yEnd);
for (register label i=0; i<n_; i++)
{
yEnd[i] += ytemp[i];
}
}
bool Foam::seulex::seul
(
const scalar x0,
const scalarField& y0,
const scalar dxTot,
const label k,
scalarField& y,
const scalarField& scale
) const
{
label nSteps = nSeq_[k];
scalar dx = dxTot/nSteps;
for (label i=0; i<n_; i++)
{
for (label j=0; j<n_; j++)
{
a_(i, j) = -dfdy_(i, j);
}
a_(i, i) += 1/dx;
}
LUDecompose(a_, pivotIndices_);
scalar xnew = x0 + dx;
odes_.derivatives(xnew, y0, dy_);
LUBacksubstitute(a_, pivotIndices_, dy_);
yTemp_ = y0;
for (label nn=1; nn<nSteps; nn++)
{
yTemp_ += dy_;
xnew += dx;
if (nn == 1 && k<=1)
{
scalar dy1 = 0;
for (label i=0; i<n_; i++)
{
dy1 += sqr(dy_[i]/scale[i]);
}
dy1 = sqrt(dy1);
odes_.derivatives(x0 + dx, yTemp_, dydx_);
for (label i=0; i<n_; i++)
{
dy_[i] = dydx_[i] - dy_[i]/dx;
}
LUBacksubstitute(a_, pivotIndices_, dy_);
const scalar denom = min(1, dy1 + SMALL);
scalar dy2 = 0;
for (label i=0; i<n_; i++)
{
// Test of dy_[i] to avoid overflow
if (mag(dy_[i]) > scale[i]*denom)
{
theta_ = 1;
return false;
}
dy2 += sqr(dy_[i]/scale[i]);
}
dy2 = sqrt(dy2);
theta_ = dy2/denom;
if (theta_ > 1)
{
return false;
}
}
odes_.derivatives(xnew, yTemp_, dy_);
LUBacksubstitute(a_, pivotIndices_, dy_);
}
for (label i=0; i<n_; i++)
{
y[i] = yTemp_[i] + dy_[i];
}
return true;
}
bool Foam::seulex::seul
(
const scalar x0,
const scalarField& y0,
const scalar dxTot,
const label k,
scalarField& y,
const scalarField& scale
) const
{
label nSteps = nSeq_[k];
scalar dx = dxTot/nSteps;
for (label i=0; i<n_; i++)
{
for (label j=0; j<n_; j++)
{
a_[i][j] = -dfdy_[i][j];
}
a_[i][i] += 1.0/dx;
}
LUDecompose(a_, pivotIndices_);
scalar xnew = x0 + dx;
odes_.derivatives(xnew, y0, dy_);
LUBacksubstitute(a_, pivotIndices_, dy_);
yTemp_ = y0;
for (label nn=1; nn<nSteps; nn++)
{
yTemp_ += dy_;
xnew += dx;
if (nn == 1 && k<=1)
{
scalar dy1 = 0.0;
for (label i=0; i<n_; i++)
{
dy1 += sqr(dy_[i]/scale[i]);
}
dy1 = sqrt(dy1);
odes_.derivatives(x0 + dx, yTemp_, dydx_);
for (label i=0; i<n_; i++)
{
dy_[i] = dydx_[i] - dy_[i]/dx;
}
LUBacksubstitute(a_, pivotIndices_, dy_);
scalar dy2 = 0.0;
for (label i=0; i<n_; i++)
{
dy2 += sqr(dy_[i]/scale[i]);
}
dy2 = sqrt(dy2);
theta_ = dy2/min(1.0, dy1 + SMALL);
if (theta_ > 1.0)
{
return false;
}
}
odes_.derivatives(xnew, yTemp_, dy_);
LUBacksubstitute(a_, pivotIndices_, dy_);
}
for (label i=0; i<n_; i++)
{
y[i] = yTemp_[i] + dy_[i];
}
return true;
}
void Foam::LUscalarMatrix::solve(Field<Type>& sourceSol) const
{
if (Pstream::parRun())
{
Field<Type> completeSourceSol(m());
if (Pstream::master(comm_))
{
typename Field<Type>::subField
(
completeSourceSol,
sourceSol.size()
).assign(sourceSol);
for
(
int slave=Pstream::firstSlave();
slave<=Pstream::lastSlave(comm_);
slave++
)
{
IPstream::read
(
Pstream::scheduled,
slave,
reinterpret_cast<char*>
(
&(completeSourceSol[procOffsets_[slave]])
),
(procOffsets_[slave+1]-procOffsets_[slave])*sizeof(Type),
Pstream::msgType(),
comm_
);
}
}
else
{
OPstream::write
(
Pstream::scheduled,
Pstream::masterNo(),
reinterpret_cast<const char*>(sourceSol.begin()),
sourceSol.byteSize(),
Pstream::msgType(),
comm_
);
}
if (Pstream::master(comm_))
{
LUBacksubstitute(*this, pivotIndices_, completeSourceSol);
sourceSol = typename Field<Type>::subField
(
completeSourceSol,
sourceSol.size()
);
for
(
int slave=Pstream::firstSlave();
slave<=Pstream::lastSlave(comm_);
slave++
)
{
OPstream::write
(
Pstream::scheduled,
slave,
reinterpret_cast<const char*>
(
&(completeSourceSol[procOffsets_[slave]])
),
(procOffsets_[slave + 1]-procOffsets_[slave])*sizeof(Type),
Pstream::msgType(),
comm_
);
}
}
else
{
IPstream::read
(
Pstream::scheduled,
Pstream::masterNo(),
reinterpret_cast<char*>(sourceSol.begin()),
sourceSol.byteSize(),
Pstream::msgType(),
comm_
);
}
}
else
{
LUBacksubstitute(*this, pivotIndices_, sourceSol);
}
}
void Foam::KRR4::solve
(
const ODE& ode,
scalar& x,
scalarField& y,
scalarField& dydx,
const scalar eps,
const scalarField& yScale,
const scalar hTry,
scalar& hDid,
scalar& hNext
) const
{
scalar xTemp = x;
yTemp_ = y;
dydxTemp_ = dydx;
ode.jacobian(xTemp, yTemp_, dfdx_, dfdy_);
scalar h = hTry;
for (register label jtry=0; jtry<maxtry; jtry++)
{
for (register label i=0; i<n_; i++)
{
for (register label j=0; j<n_; j++)
{
a_[i][j] = -dfdy_[i][j];
}
a_[i][i] += 1.0/(gamma*h);
}
LUDecompose(a_, pivotIndices_);
for (register label i=0; i<n_; i++)
{
g1_[i] = dydxTemp_[i] + h*c1X*dfdx_[i];
}
LUBacksubstitute(a_, pivotIndices_, g1_);
for (register label i=0; i<n_; i++)
{
y[i] = yTemp_[i] + a21*g1_[i];
}
x = xTemp + a2X*h;
ode.derivatives(x, y, dydx_);
for (register label i=0; i<n_; i++)
{
g2_[i] = dydx_[i] + h*c2X*dfdx_[i] + c21*g1_[i]/h;
}
LUBacksubstitute(a_, pivotIndices_, g2_);
for (register label i=0; i<n_; i++)
{
y[i] = yTemp_[i] + a31*g1_[i] + a32*g2_[i];
}
x = xTemp + a3X*h;
ode.derivatives(x, y, dydx_);
for (register label i=0; i<n_; i++)
{
g3_[i] = dydx[i] + h*c3X*dfdx_[i] + (c31*g1_[i] + c32*g2_[i])/h;
}
LUBacksubstitute(a_, pivotIndices_, g3_);
for (register label i=0; i<n_; i++)
{
g4_[i] = dydx_[i] + h*c4X*dfdx_[i]
+ (c41*g1_[i] + c42*g2_[i] + c43*g3_[i])/h;
}
LUBacksubstitute(a_, pivotIndices_, g4_);
for (register label i=0; i<n_; i++)
{
y[i] = yTemp_[i] + b1*g1_[i] + b2*g2_[i] + b3*g3_[i] + b4*g4_[i];
yErr_[i] = e1*g1_[i] + e2*g2_[i] + e3*g3_[i] + e4*g4_[i];
}
x = xTemp + h;
if (x == xTemp)
{
FatalErrorIn("ODES::KRR4")
<< "stepsize not significant"
<< exit(FatalError);
}
scalar maxErr = 0.0;
for (register label i=0; i<n_; i++)
{
maxErr = max(maxErr, mag(yErr_[i]/yScale[i]));
}
maxErr /= eps;
if (maxErr <= 1.0)
{
hDid = h;
hNext = (maxErr > errcon ? safety*h*pow(maxErr, pgrow) : grow*h);
return;
}
else
{
hNext = safety*h*pow(maxErr, pshrink);
h = (h >= 0.0 ? max(hNext, shrink*h) : min(hNext, shrink*h));
}
}
FatalErrorIn("ODES::KRR4")
<< "exceeded maxtry"
<< exit(FatalError);
}
