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];
}
}
void Foam::ODESolver::solve
(
const ODE& ode,
const scalar xStart,
const scalar xEnd,
scalarField& y,
const scalar eps,
scalar& hEst
) const
{
const label MAXSTP = 10000;
scalar x = xStart;
scalar h = hEst;
scalar hNext = 0;
scalar hPrev = 0;
for (label nStep=0; nStep<MAXSTP; nStep++)
{
ode.derivatives(x, y, dydx_);
for (label i=0; i<n_; i++)
{
yScale_[i] = mag(y[i]) + mag(dydx_[i]*h) + SMALL;
}
if ((x + h - xEnd)*(x + h - xStart) > 0.0)
{
h = xEnd - x;
hPrev = hNext;
}
hNext = 0;
scalar hDid;
solve(ode, x, y, dydx_, eps, yScale_, h, hDid, hNext);
if ((x - xEnd)*(xEnd - xStart) >= 0.0)
{
if (hPrev != 0)
{
hEst = hPrev;
}
else
{
hEst = hNext;
}
return;
}
h = hNext;
}
FatalErrorIn
(
"ODESolver::solve"
"(const ODE& ode, const scalar xStart, const scalar xEnd,"
"scalarField& yStart, const scalar eps, scalar& hEst) const"
) << "Too many integration steps"
<< exit(FatalError);
}
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);
}
