//---------------------------------------------------------------------
// verification routine
//---------------------------------------------------------------------
void verify(int no_time_steps, char *Class, logical *verified)
{
double xcrref[5], xceref[5], xcrdif[5], xcedif[5];
double epsilon, xce[5], xcr[5], dtref = 0.0;
int m;
//---------------------------------------------------------------------
// tolerance level
//---------------------------------------------------------------------
epsilon = 1.0e-08;
//---------------------------------------------------------------------
// compute the error norm and the residual norm, and exit if not printing
//---------------------------------------------------------------------
printf("[%s:%d]\n", __FILE__, __LINE__);
error_norm(xce);
printf("[%s:%d]\n", __FILE__, __LINE__);
copy_faces();
printf("[%s:%d]\n", __FILE__, __LINE__);
rhs_norm(xcr);
printf("[%s:%d]\n", __FILE__, __LINE__);
for (m = 0; m < 5; m++) {
xcr[m] = xcr[m] / dt;
}
*Class = 'U';
*verified = true;
for (m = 0; m < 5; m++) {
xcrref[m] = 1.0;
xceref[m] = 1.0;
}
//---------------------------------------------------------------------
// reference data for 12X12X12 grids after 100 time steps,
// with DT = 1.50e-02
//---------------------------------------------------------------------
if ( (grid_points[0] == 12) && (grid_points[1] == 12) &&
(grid_points[2] == 12) && (no_time_steps == 100) ) {
*Class = 'S';
dtref = 1.5e-2;
//---------------------------------------------------------------------
// Reference values of RMS-norms of residual.
//---------------------------------------------------------------------
xcrref[0] = 2.7470315451339479e-02;
xcrref[1] = 1.0360746705285417e-02;
xcrref[2] = 1.6235745065095532e-02;
xcrref[3] = 1.5840557224455615e-02;
xcrref[4] = 3.4849040609362460e-02;
//---------------------------------------------------------------------
// Reference values of RMS-norms of solution error.
//---------------------------------------------------------------------
xceref[0] = 2.7289258557377227e-05;
xceref[1] = 1.0364446640837285e-05;
xceref[2] = 1.6154798287166471e-05;
xceref[3] = 1.5750704994480102e-05;
xceref[4] = 3.4177666183390531e-05;
//---------------------------------------------------------------------
// reference data for 36X36X36 grids after 400 time steps,
// with DT = 1.5e-03
//---------------------------------------------------------------------
} else if ( (grid_points[0] == 36) && (grid_points[1] == 36) &&
(grid_points[2] == 36) && (no_time_steps == 400) ) {
*Class = 'W';
dtref = 1.5e-3;
//---------------------------------------------------------------------
// Reference values of RMS-norms of residual.
//---------------------------------------------------------------------
xcrref[0] = 0.1893253733584e-02;
xcrref[1] = 0.1717075447775e-03;
xcrref[2] = 0.2778153350936e-03;
xcrref[3] = 0.2887475409984e-03;
xcrref[4] = 0.3143611161242e-02;
//---------------------------------------------------------------------
// Reference values of RMS-norms of solution error.
//---------------------------------------------------------------------
xceref[0] = 0.7542088599534e-04;
xceref[1] = 0.6512852253086e-05;
xceref[2] = 0.1049092285688e-04;
xceref[3] = 0.1128838671535e-04;
xceref[4] = 0.1212845639773e-03;
//---------------------------------------------------------------------
// reference data for 64X64X64 grids after 400 time steps,
// with DT = 1.5e-03
//---------------------------------------------------------------------
} else if ( (grid_points[0] == 64) && (grid_points[1] == 64) &&
(grid_points[2] == 64) && (no_time_steps == 400) ) {
*Class = 'A';
dtref = 1.5e-3;
//---------------------------------------------------------------------
// Reference values of RMS-norms of residual.
//---------------------------------------------------------------------
xcrref[0] = 2.4799822399300195;
xcrref[1] = 1.1276337964368832;
xcrref[2] = 1.5028977888770491;
xcrref[3] = 1.4217816211695179;
xcrref[4] = 2.1292113035138280;
//---------------------------------------------------------------------
// Reference values of RMS-norms of solution error.
//---------------------------------------------------------------------
xceref[0] = 1.0900140297820550e-04;
xceref[1] = 3.7343951769282091e-05;
xceref[2] = 5.0092785406541633e-05;
xceref[3] = 4.7671093939528255e-05;
xceref[4] = 1.3621613399213001e-04;
//---------------------------------------------------------------------
// reference data for 102X102X102 grids after 400 time steps,
// with DT = 1.0e-03
//---------------------------------------------------------------------
} else if ( (grid_points[0] == 102) && (grid_points[1] == 102) &&
(grid_points[2] == 102) && (no_time_steps == 400) ) {
*Class = 'B';
dtref = 1.0e-3;
//---------------------------------------------------------------------
// Reference values of RMS-norms of residual.
//---------------------------------------------------------------------
xcrref[0] = 0.6903293579998e+02;
xcrref[1] = 0.3095134488084e+02;
xcrref[2] = 0.4103336647017e+02;
xcrref[3] = 0.3864769009604e+02;
xcrref[4] = 0.5643482272596e+02;
//---------------------------------------------------------------------
// Reference values of RMS-norms of solution error.
//---------------------------------------------------------------------
xceref[0] = 0.9810006190188e-02;
xceref[1] = 0.1022827905670e-02;
xceref[2] = 0.1720597911692e-02;
xceref[3] = 0.1694479428231e-02;
xceref[4] = 0.1847456263981e-01;
//---------------------------------------------------------------------
// reference data for 162X162X162 grids after 400 time steps,
// with DT = 0.67e-03
//---------------------------------------------------------------------
} else if ( (grid_points[0] == 162) && (grid_points[1] == 162) &&
(grid_points[2] == 162) && (no_time_steps == 400) ) {
*Class = 'C';
dtref = 0.67e-3;
//---------------------------------------------------------------------
// Reference values of RMS-norms of residual.
//---------------------------------------------------------------------
xcrref[0] = 0.5881691581829e+03;
xcrref[1] = 0.2454417603569e+03;
xcrref[2] = 0.3293829191851e+03;
xcrref[3] = 0.3081924971891e+03;
xcrref[4] = 0.4597223799176e+03;
//---------------------------------------------------------------------
// Reference values of RMS-norms of solution error.
//---------------------------------------------------------------------
xceref[0] = 0.2598120500183e+00;
xceref[1] = 0.2590888922315e-01;
xceref[2] = 0.5132886416320e-01;
xceref[3] = 0.4806073419454e-01;
xceref[4] = 0.5483377491301e+00;
//---------------------------------------------------------------------
// reference data for 408X408X408 grids after 500 time steps,
// with DT = 0.3e-03
//---------------------------------------------------------------------
} else if ( (grid_points[0] == 408) && (grid_points[1] == 408) &&
(grid_points[2] == 408) && (no_time_steps == 500) ) {
*Class = 'D';
dtref = 0.30e-3;
//---------------------------------------------------------------------
// Reference values of RMS-norms of residual.
//---------------------------------------------------------------------
xcrref[0] = 0.1044696216887e+05;
xcrref[1] = 0.3204427762578e+04;
xcrref[2] = 0.4648680733032e+04;
xcrref[3] = 0.4238923283697e+04;
xcrref[4] = 0.7588412036136e+04;
//---------------------------------------------------------------------
// Reference values of RMS-norms of solution error.
//---------------------------------------------------------------------
xceref[0] = 0.5089471423669e+01;
xceref[1] = 0.5323514855894e+00;
xceref[2] = 0.1187051008971e+01;
xceref[3] = 0.1083734951938e+01;
xceref[4] = 0.1164108338568e+02;
//---------------------------------------------------------------------
// reference data for 1020X1020X1020 grids after 500 time steps,
// with DT = 0.1e-03
//---------------------------------------------------------------------
} else if ( (grid_points[0] == 1020) && (grid_points[1] == 1020) &&
(grid_points[2] == 1020) && (no_time_steps == 500) ) {
*Class = 'E';
dtref = 0.10e-3;
//---------------------------------------------------------------------
// Reference values of RMS-norms of residual.
//---------------------------------------------------------------------
xcrref[0] = 0.6255387422609e+05;
xcrref[1] = 0.1495317020012e+05;
xcrref[2] = 0.2347595750586e+05;
xcrref[3] = 0.2091099783534e+05;
xcrref[4] = 0.4770412841218e+05;
//---------------------------------------------------------------------
// Reference values of RMS-norms of solution error.
//---------------------------------------------------------------------
xceref[0] = 0.6742735164909e+02;
xceref[1] = 0.5390656036938e+01;
xceref[2] = 0.1680647196477e+02;
xceref[3] = 0.1536963126457e+02;
xceref[4] = 0.1575330146156e+03;
} else {
*verified = false;
}
//---------------------------------------------------------------------
// verification test for residuals if gridsize is one of
// the defined grid sizes above (class .ne. 'U')
//---------------------------------------------------------------------
//---------------------------------------------------------------------
// Compute the difference of solution values and the known reference values.
//---------------------------------------------------------------------
for (m = 0; m < 5; m++) {
xcrdif[m] = fabs((xcr[m]-xcrref[m])/xcrref[m]);
xcedif[m] = fabs((xce[m]-xceref[m])/xceref[m]);
}
//---------------------------------------------------------------------
// Output the comparison of computed results to known cases.
//---------------------------------------------------------------------
if (*Class != 'U') {
printf(" Verification being performed for class %c\n", *Class);
printf(" accuracy setting for epsilon = %20.13E\n", epsilon);
*verified = (fabs(dt-dtref) <= epsilon);
if (!(*verified)) {
*Class = 'U';
printf(" DT does not match the reference value of %15.8E\n", dtref);
}
} else {
printf(" Unknown class\n");
}
if (*Class != 'U') {
printf(" Comparison of RMS-norms of residual\n");
} else {
printf(" RMS-norms of residual\n");
}
for (m = 0; m < 5; m++) {
if (*Class == 'U') {
printf(" %2d%20.13E\n", m+1, xcr[m]);
} else if (xcrdif[m] <= epsilon) {
printf(" %2d%20.13E%20.13E%20.13E\n",
m+1, xcr[m], xcrref[m], xcrdif[m]);
} else {
*verified = false;
printf(" FAILURE: %2d%20.13E%20.13E%20.13E\n",
m+1, xcr[m], xcrref[m], xcrdif[m]);
}
}
if (*Class != 'U') {
printf(" Comparison of RMS-norms of solution error\n");
} else {
printf(" RMS-norms of solution error\n");
}
for (m = 0; m < 5; m++) {
if (*Class == 'U') {
printf(" %2d%20.13E\n", m+1, xce[m]);
} else if (xcedif[m] <= epsilon) {
printf(" %2d%20.13E%20.13E%20.13E\n",
m+1, xce[m], xceref[m], xcedif[m]);
} else {
*verified = false;
printf(" FAILURE: %2d%20.13E%20.13E%20.13E\n",
m+1, xce[m], xceref[m], xcedif[m]);
}
}
if (*Class == 'U') {
printf(" No reference values provided\n");
printf(" No verification performed\n");
} else if (*verified) {
printf(" Verification Successful\n");
} else {
printf(" Verification failed\n");
}
}
void TwostepTimeSolver::solve()
{
libmesh_assert(core_time_solver.get());
// The core_time_solver will handle any first_solve actions
first_solve = false;
// We may have to repeat timesteps entirely if our error is bad
// enough
bool max_tolerance_met = false;
// Calculating error values each time
Real single_norm(0.), double_norm(0.), error_norm(0.),
relative_error(0.);
while (!max_tolerance_met)
{
// If we've been asked to reduce deltat if necessary, make sure
// the core timesolver does so
core_time_solver->reduce_deltat_on_diffsolver_failure =
this->reduce_deltat_on_diffsolver_failure;
if (!quiet)
{
libMesh::out << "\n === Computing adaptive timestep === "
<< std::endl;
}
// Use the double-length timestep first (so the
// old_nonlinear_solution won't have to change)
core_time_solver->solve();
// Save a copy of the double-length nonlinear solution
// and the old nonlinear solution
std::unique_ptr<NumericVector<Number>> double_solution =
_system.solution->clone();
std::unique_ptr<NumericVector<Number>> old_solution =
_system.get_vector("_old_nonlinear_solution").clone();
double_norm = calculate_norm(_system, *double_solution);
if (!quiet)
{
libMesh::out << "Double norm = " << double_norm << std::endl;
}
// Then reset the initial guess for our single-length calcs
*(_system.solution) = _system.get_vector("_old_nonlinear_solution");
// Call two single-length timesteps
// Be sure that the core_time_solver does not change the
// timestep here. (This is unlikely because it just succeeded
// with a timestep twice as large!)
// FIXME: even if diffsolver failure is unlikely, we ought to
// do *something* if it happens
core_time_solver->reduce_deltat_on_diffsolver_failure = 0;
Real old_time = _system.time;
Real old_deltat = _system.deltat;
_system.deltat *= 0.5;
core_time_solver->solve();
core_time_solver->advance_timestep();
core_time_solver->solve();
single_norm = calculate_norm(_system, *_system.solution);
if (!quiet)
{
libMesh::out << "Single norm = " << single_norm << std::endl;
}
// Reset the core_time_solver's reduce_deltat... value.
core_time_solver->reduce_deltat_on_diffsolver_failure =
this->reduce_deltat_on_diffsolver_failure;
// But then back off just in case our advance_timestep() isn't
// called.
// FIXME: this probably doesn't work with multistep methods
_system.get_vector("_old_nonlinear_solution") = *old_solution;
_system.time = old_time;
_system.deltat = old_deltat;
// Find the relative error
*double_solution -= *(_system.solution);
error_norm = calculate_norm(_system, *double_solution);
relative_error = error_norm / _system.deltat /
std::max(double_norm, single_norm);
// If the relative error makes no sense, we're done
if (!double_norm && !single_norm)
return;
if (!quiet)
{
libMesh::out << "Error norm = " << error_norm << std::endl;
libMesh::out << "Local relative error = "
<< (error_norm /
std::max(double_norm, single_norm))
<< std::endl;
libMesh::out << "Global relative error = "
<< (error_norm / _system.deltat /
std::max(double_norm, single_norm))
<< std::endl;
libMesh::out << "old delta t = " << _system.deltat << std::endl;
}
// If our upper tolerance is negative, that means we want to set
// it based on the first successful time step
if (this->upper_tolerance < 0)
this->upper_tolerance = -this->upper_tolerance * relative_error;
// If we haven't met our upper error tolerance, we'll have to
// repeat this timestep entirely
if (this->upper_tolerance && relative_error > this->upper_tolerance)
{
// Reset the initial guess for our next try
*(_system.solution) =
_system.get_vector("_old_nonlinear_solution");
// Chop delta t in half
_system.deltat /= 2.;
if (!quiet)
{
libMesh::out << "Failed to meet upper error tolerance"
<< std::endl;
libMesh::out << "Retrying with delta t = "
<< _system.deltat << std::endl;
}
}
else
max_tolerance_met = true;
}
// Otherwise, compare the relative error to the tolerance
// and adjust deltat
last_deltat = _system.deltat;
// If our target tolerance is negative, that means we want to set
// it based on the first successful time step
if (this->target_tolerance < 0)
this->target_tolerance = -this->target_tolerance * relative_error;
const Real global_shrink_or_growth_factor =
std::pow(this->target_tolerance / relative_error,
static_cast<Real>(1. / core_time_solver->error_order()));
const Real local_shrink_or_growth_factor =
std::pow(this->target_tolerance /
(error_norm/std::max(double_norm, single_norm)),
static_cast<Real>(1. / (core_time_solver->error_order()+1.)));
if (!quiet)
{
libMesh::out << "The global growth/shrink factor is: "
<< global_shrink_or_growth_factor << std::endl;
libMesh::out << "The local growth/shrink factor is: "
<< local_shrink_or_growth_factor << std::endl;
}
// The local s.o.g. factor is based on the expected **local**
// truncation error for the timestepping method, the global
// s.o.g. factor is based on the method's **global** truncation
// error. You can shrink/grow the timestep to attempt to satisfy
// either a global or local time-discretization error tolerance.
Real shrink_or_growth_factor =
this->global_tolerance ? global_shrink_or_growth_factor :
local_shrink_or_growth_factor;
if (this->max_growth && this->max_growth < shrink_or_growth_factor)
{
if (!quiet && this->global_tolerance)
{
libMesh::out << "delta t is constrained by max_growth" << std::endl;
}
shrink_or_growth_factor = this->max_growth;
}
_system.deltat *= shrink_or_growth_factor;
// Restrict deltat to max-allowable value if necessary
if ((this->max_deltat != 0.0) && (_system.deltat > this->max_deltat))
{
if (!quiet)
{
libMesh::out << "delta t is constrained by maximum-allowable delta t."
<< std::endl;
}
_system.deltat = this->max_deltat;
}
// Restrict deltat to min-allowable value if necessary
if ((this->min_deltat != 0.0) && (_system.deltat < this->min_deltat))
{
if (!quiet)
{
libMesh::out << "delta t is constrained by minimum-allowable delta t."
<< std::endl;
}
_system.deltat = this->min_deltat;
}
if (!quiet)
{
libMesh::out << "new delta t = " << _system.deltat << std::endl;
}
}
//---------------------------------------------------------------------
// verification routine
//---------------------------------------------------------------------
void verify(int no_time_steps, char *Class, logical *verified)
{
double xcrref[5], xceref[5], xcrdif[5], xcedif[5];
double epsilon, xce[5], xcr[5], dtref = 0.0;
int m;
//---------------------------------------------------------------------
// tolerance level
//---------------------------------------------------------------------
epsilon = 1.0e-08;
//---------------------------------------------------------------------
// compute the error norm and the residual norm, and exit if not printing
//---------------------------------------------------------------------
error_norm(xce);
compute_rhs();
rhs_norm(xcr);
for (m = 0; m < 5; m++) {
xcr[m] = xcr[m] / dt;
}
*Class = 'U';
*verified = true;
for (m = 0; m < 5; m++) {
xcrref[m] = 1.0;
xceref[m] = 1.0;
}
//---------------------------------------------------------------------
// reference data for 12X12X12 grids after 60 time steps, with DT = 1.0e-02
//---------------------------------------------------------------------
if ( (grid_points[0] == 12) && (grid_points[1] == 12) &&
(grid_points[2] == 12) && (no_time_steps == 60)) {
*Class = 'S';
dtref = 1.0e-2;
//---------------------------------------------------------------------
// Reference values of RMS-norms of residual.
//---------------------------------------------------------------------
xcrref[0] = 1.7034283709541311e-01;
xcrref[1] = 1.2975252070034097e-02;
xcrref[2] = 3.2527926989486055e-02;
xcrref[3] = 2.6436421275166801e-02;
xcrref[4] = 1.9211784131744430e-01;
//---------------------------------------------------------------------
// Reference values of RMS-norms of solution error.
//---------------------------------------------------------------------
xceref[0] = 4.9976913345811579e-04;
xceref[1] = 4.5195666782961927e-05;
xceref[2] = 7.3973765172921357e-05;
xceref[3] = 7.3821238632439731e-05;
xceref[4] = 8.9269630987491446e-04;
//---------------------------------------------------------------------
// reference data for 24X24X24 grids after 200 time steps,
// with DT = 0.8e-3
//---------------------------------------------------------------------
} else if ( (grid_points[0] == 24) && (grid_points[1] == 24) &&
(grid_points[2] == 24) && (no_time_steps == 200) ) {
*Class = 'W';
dtref = 0.8e-3;
//---------------------------------------------------------------------
// Reference values of RMS-norms of residual.
//---------------------------------------------------------------------
xcrref[0] = 0.1125590409344e+03;
xcrref[1] = 0.1180007595731e+02;
xcrref[2] = 0.2710329767846e+02;
xcrref[3] = 0.2469174937669e+02;
xcrref[4] = 0.2638427874317e+03;
//---------------------------------------------------------------------
// Reference values of RMS-norms of solution error.
//---------------------------------------------------------------------
xceref[0] = 0.4419655736008e+01;
xceref[1] = 0.4638531260002e+00;
xceref[2] = 0.1011551749967e+01;
xceref[3] = 0.9235878729944e+00;
xceref[4] = 0.1018045837718e+02;
//---------------------------------------------------------------------
// reference data for 64X64X64 grids after 200 time steps,
// with DT = 0.8e-3
//---------------------------------------------------------------------
} else if ( (grid_points[0] == 64) && (grid_points[1] == 64) &&
(grid_points[2] == 64) && (no_time_steps == 200) ) {
*Class = 'A';
dtref = 0.8e-3;
//---------------------------------------------------------------------
// Reference values of RMS-norms of residual.
//---------------------------------------------------------------------
xcrref[0] = 1.0806346714637264e+02;
xcrref[1] = 1.1319730901220813e+01;
xcrref[2] = 2.5974354511582465e+01;
xcrref[3] = 2.3665622544678910e+01;
xcrref[4] = 2.5278963211748344e+02;
//---------------------------------------------------------------------
// Reference values of RMS-norms of solution error.
//---------------------------------------------------------------------
xceref[0] = 4.2348416040525025e+00;
xceref[1] = 4.4390282496995698e-01;
xceref[2] = 9.6692480136345650e-01;
xceref[3] = 8.8302063039765474e-01;
xceref[4] = 9.7379901770829278e+00;
//---------------------------------------------------------------------
// reference data for 102X102X102 grids after 200 time steps,
// with DT = 3.0e-04
//---------------------------------------------------------------------
} else if ( (grid_points[0] == 102) && (grid_points[1] == 102) &&
(grid_points[2] == 102) && (no_time_steps == 200) ) {
*Class = 'B';
dtref = 3.0e-4;
//---------------------------------------------------------------------
// Reference values of RMS-norms of residual.
//---------------------------------------------------------------------
xcrref[0] = 1.4233597229287254e+03;
xcrref[1] = 9.9330522590150238e+01;
xcrref[2] = 3.5646025644535285e+02;
xcrref[3] = 3.2485447959084092e+02;
xcrref[4] = 3.2707541254659363e+03;
//---------------------------------------------------------------------
// Reference values of RMS-norms of solution error.
//---------------------------------------------------------------------
xceref[0] = 5.2969847140936856e+01;
xceref[1] = 4.4632896115670668e+00;
xceref[2] = 1.3122573342210174e+01;
xceref[3] = 1.2006925323559144e+01;
xceref[4] = 1.2459576151035986e+02;
//---------------------------------------------------------------------
// reference data for 162X162X162 grids after 200 time steps,
// with DT = 1.0e-04
//---------------------------------------------------------------------
} else if ( (grid_points[0] == 162) && (grid_points[1] == 162) &&
(grid_points[2] == 162) && (no_time_steps == 200) ) {
*Class = 'C';
dtref = 1.0e-4;
//---------------------------------------------------------------------
// Reference values of RMS-norms of residual.
//---------------------------------------------------------------------
xcrref[0] = 0.62398116551764615e+04;
xcrref[1] = 0.50793239190423964e+03;
xcrref[2] = 0.15423530093013596e+04;
xcrref[3] = 0.13302387929291190e+04;
xcrref[4] = 0.11604087428436455e+05;
//---------------------------------------------------------------------
// Reference values of RMS-norms of solution error.
//---------------------------------------------------------------------
xceref[0] = 0.16462008369091265e+03;
xceref[1] = 0.11497107903824313e+02;
xceref[2] = 0.41207446207461508e+02;
xceref[3] = 0.37087651059694167e+02;
xceref[4] = 0.36211053051841265e+03;
//---------------------------------------------------------------------
// reference data for 408x408x408 grids after 250 time steps,
// with DT = 0.2e-04
//---------------------------------------------------------------------
} else if ( (grid_points[0] == 408) && (grid_points[1] == 408) &&
(grid_points[2] == 408) && (no_time_steps == 250) ) {
*Class = 'D';
dtref = 0.2e-4;
//---------------------------------------------------------------------
// Reference values of RMS-norms of residual.
//---------------------------------------------------------------------
xcrref[0] = 0.2533188551738e+05;
xcrref[1] = 0.2346393716980e+04;
xcrref[2] = 0.6294554366904e+04;
xcrref[3] = 0.5352565376030e+04;
xcrref[4] = 0.3905864038618e+05;
//---------------------------------------------------------------------
// Reference values of RMS-norms of solution error.
//---------------------------------------------------------------------
xceref[0] = 0.3100009377557e+03;
xceref[1] = 0.2424086324913e+02;
xceref[2] = 0.7782212022645e+02;
xceref[3] = 0.6835623860116e+02;
xceref[4] = 0.6065737200368e+03;
//---------------------------------------------------------------------
// reference data for 1020x1020x1020 grids after 250 time steps,
// with DT = 0.4e-05
//---------------------------------------------------------------------
} else if ( (grid_points[0] == 1020) && (grid_points[1] == 1020) &&
(grid_points[2] == 1020) && (no_time_steps == 250) ) {
*Class = 'E';
dtref = 0.4e-5;
//---------------------------------------------------------------------
// Reference values of RMS-norms of residual.
//---------------------------------------------------------------------
xcrref[0] = 0.9795372484517e+05;
xcrref[1] = 0.9739814511521e+04;
xcrref[2] = 0.2467606342965e+05;
xcrref[3] = 0.2092419572860e+05;
xcrref[4] = 0.1392138856939e+06;
//---------------------------------------------------------------------
// Reference values of RMS-norms of solution error.
//---------------------------------------------------------------------
xceref[0] = 0.4327562208414e+03;
xceref[1] = 0.3699051964887e+02;
xceref[2] = 0.1089845040954e+03;
xceref[3] = 0.9462517622043e+02;
xceref[4] = 0.7765512765309e+03;
} else {
*verified = false;
}
//---------------------------------------------------------------------
// verification test for residuals if gridsize is one of
// the defined grid sizes above (*Class != 'U')
//---------------------------------------------------------------------
//---------------------------------------------------------------------
// Compute the difference of solution values and the known reference values.
//---------------------------------------------------------------------
for (m = 0; m < 5; m++) {
xcrdif[m] = fabs((xcr[m]-xcrref[m])/xcrref[m]);
xcedif[m] = fabs((xce[m]-xceref[m])/xceref[m]);
}
//---------------------------------------------------------------------
// Output the comparison of computed results to known cases.
//---------------------------------------------------------------------
if (*Class != 'U') {
printf(" Verification being performed for class %c\n", *Class);
printf(" accuracy setting for epsilon = %20.13E\n", epsilon);
*verified = (fabs(dt-dtref) <= epsilon);
if (!(*verified)) {
*Class = 'U';
printf(" DT does not match the reference value of %15.8E\n", dtref);
}
} else {
printf(" Unknown class\n");
}
if (*Class != 'U') {
printf(" Comparison of RMS-norms of residual\n");
} else {
printf(" RMS-norms of residual\n");
}
for (m = 0; m < 5; m++) {
if (*Class == 'U') {
printf(" %2d%20.13E\n", m+1, xcr[m]);
} else if (xcrdif[m] <= epsilon) {
printf(" %2d%20.13E%20.13E%20.13E\n",
m+1, xcr[m], xcrref[m], xcrdif[m]);
} else {
*verified = false;
printf(" FAILURE: %2d%20.13E%20.13E%20.13E\n",
m+1, xcr[m], xcrref[m], xcrdif[m]);
}
}
if (*Class != 'U') {
printf(" Comparison of RMS-norms of solution error\n");
} else {
printf(" RMS-norms of solution error\n");
}
for (m = 0; m < 5; m++) {
if (*Class == 'U') {
printf(" %2d%20.13E\n", m+1, xce[m]);
} else if (xcedif[m] <= epsilon) {
printf(" %2d%20.13E%20.13E%20.13E\n",
m+1, xce[m], xceref[m], xcedif[m]);
} else {
*verified = false;
printf(" FAILURE: %2d%20.13E%20.13E%20.13E\n",
m+1, xce[m], xceref[m], xcedif[m]);
}
}
if (*Class == 'U') {
printf(" No reference values provided\n");
printf(" No verification performed\n");
} else if (*verified) {
printf(" Verification Successful\n");
} else {
printf(" Verification failed\n");
}
}
void verify(int no_time_steps, char *class_r, int *verified_r) {
//---------------------------------------------------------------------
//---------------------------------------------------------------------
//---------------------------------------------------------------------
// verification routine
//---------------------------------------------------------------------
double xcrref[5],xceref[5],xcrdif[5],xcedif[5],
epsilon, xce[5], xcr[5], dtref;
int m;
char class;
int verified;
#define xcrref(m) xcrref[m-1]
#define xceref(m) xceref[m-1]
#define xcrdif(m) xcrdif[m-1]
#define xcedif(m) xcedif[m-1]
#define xce(m) xce[m-1]
#define xcr(m) xcr[m-1]
//---------------------------------------------------------------------
// tolerance level
//---------------------------------------------------------------------
epsilon = 1.0e-08;
verified = 1;
//---------------------------------------------------------------------
// compute the error norm and the residual norm, and exit if not printing
//---------------------------------------------------------------------
error_norm(xce);
copy_faces();
rhs_norm(xcr);
for (m = 1; m <= 5; m++) {
xcr(m) = xcr(m) / dt;
}
if (node != root) return;
class = 'U';
for (m = 1; m <= 5; m++) {
xcrref(m) = 1.0;
xceref(m) = 1.0;
}
//---------------------------------------------------------------------
// reference data for 12X12X12 grids after 60 time steps, with DT = 1.0e-02
//---------------------------------------------------------------------
if ( (grid_points(1) == 12 ) &&
(grid_points(2) == 12 ) &&
(grid_points(3) == 12 ) &&
(no_time_steps == 60 )) {
class = 'S';
dtref = 1.0e-2;
//---------------------------------------------------------------------
// Reference values of RMS-norms of residual.
//---------------------------------------------------------------------
xcrref(1) = 1.7034283709541311e-01;
xcrref(2) = 1.2975252070034097e-02;
xcrref(3) = 3.2527926989486055e-02;
xcrref(4) = 2.6436421275166801e-02;
xcrref(5) = 1.9211784131744430e-01;
//---------------------------------------------------------------------
// Reference values of RMS-norms of solution error.
//---------------------------------------------------------------------
xceref(1) = 4.9976913345811579e-04;
xceref(2) = 4.5195666782961927e-05;
xceref(3) = 7.3973765172921357e-05;
xceref(4) = 7.3821238632439731e-05;
xceref(5) = 8.9269630987491446e-04;
//---------------------------------------------------------------------
// reference data for 24X24X24 grids after 200 time steps, with DT = 0.8e-3
//---------------------------------------------------------------------
} else if ( (grid_points(1) == 24) &&
