Commit ee7284d4 authored by Henry's avatar Henry
Browse files

seulex ODE solver: further rationalisation

Careful handing of cached state and use of stepState class to carry information between sub-steps.

Also careful debugging of the handling of kTarg to resolve SEGV when running at low tolerance.
parent e026a79e
......@@ -50,16 +50,15 @@ namespace Foam
Foam::seulex::seulex(const ODESystem& ode, const dictionary& dict)
:
ODESolver(ode, dict),
jacRedo_(min(1.0e-4, min(relTol_))),
nSeq_(iMaxx_),
cpu_(iMaxx_),
table_(kMaxx_, n_),
jacRedo_(min(1.0e-4, min(relTol_))),
coeff_(iMaxx_, iMaxx_),
theta_(2.0*jacRedo_),
calcJac_(false),
table_(kMaxx_, n_),
dfdx_(n_),
dfdy_(n_),
a_(n_),
coeff_(iMaxx_, iMaxx_),
pivotIndices_(n_),
dxOpt_(iMaxx_),
temp_(iMaxx_),
......@@ -70,6 +69,7 @@ Foam::seulex::seulex(const ODESystem& ode, const dictionary& dict)
yTemp_(n_),
dydx_(n_)
{
// The CPU time factors for the major parts of the algorithm
const scalar cpuFunc = 1.0, cpuJac = 5.0, cpuLU = 1.0, cpuSolve = 1.0;
nSeq_[0] = 2;
......@@ -86,10 +86,7 @@ Foam::seulex::seulex(const ODESystem& ode, const dictionary& dict)
cpu_[k+1] = cpu_[k] + (nSeq_[k+1]-1)*(cpuFunc + cpuSolve) + cpuLU;
}
//NOTE: the first element of relTol_ and absTol_ are used here.
scalar logTol = -log10(relTol_[0] + absTol_[0])*0.6 + 0.5;
kTarg_ = min(1, min(kMaxx_ - 1, int(logTol)));
// Set the extrapolation coefficients array
for (int k=0; k<iMaxx_; k++)
{
for (int l=0; l<k; l++)
......@@ -142,7 +139,7 @@ bool Foam::seulex::seul
if (nn == 1 && k<=1)
{
scalar dy1 = 0.0;
for (label i = 0; i < n_; i++)
for (label i=0; i<n_; i++)
{
dy1 += sqr(dy_[i]/scale[i]);
}
......@@ -157,7 +154,7 @@ bool Foam::seulex::seul
LUBacksubstitute(a_, pivotIndices_, dy_);
scalar dy2 = 0.0;
for (label i = 0; i <n_ ; i++)
for (label i=0; i<n_; i++)
{
dy2 += sqr(dy_[i]/scale[i]);
}
......@@ -210,30 +207,24 @@ void Foam::seulex::solve
(
scalar& x,
scalarField& y,
scalar& dxTry
stepState& step
) const
{
static bool firstStep = true, lastStep = false;
static bool reject = false, prevReject = false;
temp_[0] = GREAT;
scalar dx = dxTry;
dxTry = -VGREAT;
bool forward = dx > 0 ? true : false;
scalar dx = step.dxTry;
y0_ = y;
dxOpt_[0] = mag(0.1*dx);
if (dx != dxTry && !firstStep)
if (step.first || step.prevReject)
{
lastStep = true;
theta_ = 2.0*jacRedo_;
}
if (reject)
if (step.first)
{
prevReject = true;
lastStep = false;
theta_=2.0*jacRedo_;
// NOTE: the first element of relTol_ and absTol_ are used here.
scalar logTol = -log10(relTol_[0] + absTol_[0])*0.6 + 0.5;
kTarg_ = max(1, min(kMaxx_ - 1, int(logTol)));
}
forAll(scale_, i)
......@@ -241,39 +232,39 @@ void Foam::seulex::solve
scale_[i] = absTol_[i] + relTol_[i]*mag(y[i]);
}
reject = false;
bool firstk = true;
scalar dxNew = mag(dx);
bool jacUpdated = false;
if (theta_ > jacRedo_ && !calcJac_)
if (theta_ > jacRedo_)
{
odes_.jacobian(x, y, dfdx_, dfdy_);
calcJac_ = true;
jacUpdated = true;
}
int k;
scalar errOld;
scalar dxNew = mag(dx);
bool firstk = true;
while (firstk || reject)
while (firstk || step.reject)
{
dx = forward ? dxNew : -dxNew;
dx = step.forward ? dxNew : -dxNew;
firstk = false;
reject = false;
step.reject = false;
if (mag(dx) <= mag(x)*SMALL)
{
WarningIn("seulex::step(const scalar")
<< "step size underflow in step :" << dx << endl;
WarningIn("seulex::solve(scalar& x, scalarField& y, stepState&")
<< "step size underflow :" << dx << endl;
}
for (k = 0; k <= kTarg_ + 1; k++)
scalar errOld;
for (k=0; k<=kTarg_+1; k++)
{
bool success = seul(x, y0_, dx, k, ySequence_, scale_);
if (!success)
{
reject = true;
step.reject = true;
dxNew = mag(dx)*stepFactor5_;
break;
}
......@@ -289,6 +280,7 @@ void Foam::seulex::solve
table_[k-1][i] = ySequence_[i];
}
}
if (k != 0)
{
extrapolate(k, table_, y);
......@@ -301,7 +293,7 @@ void Foam::seulex::solve
err = sqrt(err/n_);
if (err > 1.0/SMALL || (k > 1 && err >= errOld))
{
reject = true;
step.reject = true;
dxNew = mag(dx)*stepFactor5_;
break;
}
......@@ -321,11 +313,17 @@ void Foam::seulex::solve
dxOpt_[k] = mag(dx*fac);
temp_[k] = cpu_[k]/dxOpt_[k];
if ((firstStep || lastStep) && err <= 1.0)
if ((step.first || step.last) && err <= 1.0)
{
break;
}
if (k == kTarg_-1 && !prevReject && !firstStep && !lastStep)
if
(
k == kTarg_ - 1
&& !step.prevReject
&& !step.first && !step.last
)
{
if (err <= 1.0)
{
......@@ -333,7 +331,7 @@ void Foam::seulex::solve
}
else if (err > nSeq_[kTarg_]*nSeq_[kTarg_ + 1]*4.0)
{
reject = true;
step.reject = true;
kTarg_ = k;
if (kTarg_>1 && temp_[k-1] < kFactor1_*temp_[k])
{
......@@ -343,6 +341,7 @@ void Foam::seulex::solve
break;
}
}
if (k == kTarg_)
{
if (err <= 1.0)
......@@ -351,7 +350,7 @@ void Foam::seulex::solve
}
else if (err > nSeq_[k + 1]*2.0)
{
reject = true;
step.reject = true;
if (kTarg_>1 && temp_[k-1] < kFactor1_*temp_[k])
{
kTarg_--;
......@@ -360,11 +359,12 @@ void Foam::seulex::solve
break;
}
}
if (k == kTarg_+1)
{
if (err > 1.0)
{
reject = true;
step.reject = true;
if
(
kTarg_ > 1
......@@ -379,26 +379,26 @@ void Foam::seulex::solve
}
}
}
if (reject)
if (step.reject)
{
prevReject = true;
if (!calcJac_)
step.prevReject = true;
if (!jacUpdated)
{
theta_ = 2.0*jacRedo_;
if (theta_ > jacRedo_ && !calcJac_)
if (theta_ > jacRedo_ && !jacUpdated)
{
odes_.jacobian(x, y, dfdx_, dfdy_);
calcJac_ = true;
jacUpdated = true;
}
}
}
}
calcJac_ = false;
jacUpdated = false;
step.dxDid = dx;
x += dx;
firstStep = false;
label kopt;
if (k == 1)
......@@ -430,11 +430,11 @@ void Foam::seulex::solve
}
}
if (prevReject)
if (step.prevReject)
{
kTarg_ = min(kopt, k);
dxNew = min(mag(dx), dxOpt_[kTarg_]);
prevReject = false;
step.prevReject = false;
}
else
{
......@@ -456,14 +456,7 @@ void Foam::seulex::solve
kTarg_ = kopt;
}
if (forward)
{
dxTry = dxNew;
}
else
{
dxTry = -dxNew;
}
step.dxTry = step.forward ? dxNew : -dxNew;
}
......
......@@ -28,7 +28,7 @@ Description
An extrapolation-algorithm, based on the linearly implicit Euler method
with step size control and order selection.
The implementation is based on the SEULEX code in
The implementation is based on the SEULEX algorithm in
\verbatim
"Solving Ordinary Differential Equations II: Stiff
and Differential-Algebraic Problems, second edition",
......@@ -65,35 +65,42 @@ class seulex
{
// Private data
// SEULEX constants
static const label kMaxx_ = 12;
static const label iMaxx_ = kMaxx_ + 1;
// Static constants
static const scalar
stepFactor1_, stepFactor2_, stepFactor3_,
stepFactor4_, stepFactor5_,
kFactor1_, kFactor2_;
static const label kMaxx_ = 12;
static const label iMaxx_ = kMaxx_ + 1;
// Temporary fields
mutable label kTarg_;
mutable labelField nSeq_;
mutable scalarField cpu_;
mutable scalarRectangularMatrix table_;
static const scalar
stepFactor1_, stepFactor2_, stepFactor3_,
stepFactor4_, stepFactor5_,
kFactor1_, kFactor2_;
mutable scalar jacRedo_, theta_;
mutable bool calcJac_;
// Evaluated constants
mutable scalarField dfdx_;
mutable scalarSquareMatrix dfdy_;
mutable scalarSquareMatrix a_, coeff_;
mutable labelList pivotIndices_;
scalar jacRedo_;
labelField nSeq_;
scalarField cpu_;
scalarSquareMatrix coeff_;
// Fields space for "solve" function
mutable scalarField dxOpt_, temp_;
mutable scalarField y0_, ySequence_, scale_;
// Temporary storage
// held to avoid dynamic memory allocation between calls
// and to transfer internal values between functions
// Fields used in "dy" function
mutable scalarField dy_, yTemp_, dydx_;
mutable scalar theta_;
mutable label kTarg_;
mutable scalarRectangularMatrix table_;
mutable scalarField dfdx_;
mutable scalarSquareMatrix dfdy_;
mutable scalarSquareMatrix a_;
mutable labelList pivotIndices_;
// Fields space for "solve" function
mutable scalarField dxOpt_, temp_;
mutable scalarField y0_, ySequence_, scale_;
// Fields used in "seul" function
mutable scalarField dy_, yTemp_, dydx_;
// Private Member Functions
......@@ -137,7 +144,7 @@ public:
(
scalar& x,
scalarField& y,
scalar& dxTry
stepState& step
) const;
};
......
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