void
AEFVMaterial::computeQpProperties()
{
// initialize the variable
_u[_qp] = _uc[_qp];
// interpolate variable values at face center
if (_bnd)
{
// you should know how many equations you are solving and assign this number
// e.g. = 1 (for the advection equation)
unsigned int nvars = 1;
std::vector<RealGradient> ugrad(nvars, RealGradient(0., 0., 0.));
ugrad = _lslope.getElementSlope(_current_elem->id());
// get the directional vector from cell center to face center
RealGradient dvec = _q_point[_qp] - _current_elem->centroid();
// calculate the variable at face center
_u[_qp] += ugrad[0] * dvec;
// clear the temporary vectors
ugrad.clear();
}
// calculations only for elemental output
else if (!_bnd)
{
}
}
void dtron(int n, double *x, double *xl, double *xu, double gtol, double frtol, double fatol, double fmin, int maxfev, double cgtol)
{
/*
c *********
c
c Subroutine dtron
c
c The optimization problem of BSVM is a bound-constrained quadratic
c optimization problem and its Hessian matrix is positive semidefinite.
c We modified the optimization solver TRON by Chih-Jen Lin and
c Jorge More' into this version which is suitable for this
c special case.
c
c This subroutine implements a trust region Newton method for the
c solution of large bound-constrained quadratic optimization problems
c
c min { f(x)=0.5*x'*A*x + g0'*x : xl <= x <= xu }
c
c where the Hessian matrix A is dense and positive semidefinite. The
c user must define functions which evaluate the function, gradient,
c and the Hessian matrix.
c
c The user must choose an initial approximation x to the minimizer,
c lower bounds, upper bounds, quadratic terms, linear terms, and
c constants about termination criterion.
c
c parameters:
c
c n is an integer variable.
c On entry n is the number of variables.
c On exit n is unchanged.
c
c x is a double precision array of dimension n.
c On entry x specifies the vector x.
c On exit x is the final minimizer.
c
c xl is a double precision array of dimension n.
c On entry xl is the vector of lower bounds.
c On exit xl is unchanged.
c
c xu is a double precision array of dimension n.
c On entry xu is the vector of upper bounds.
c On exit xu is unchanged.
c
c gtol is a double precision variable.
c On entry gtol specifies the relative error of the projected
c gradient.
c On exit gtol is unchanged.
c
c frtol is a double precision variable.
c On entry frtol specifies the relative error desired in the
c function. Convergence occurs if the estimate of the
c relative error between f(x) and f(xsol), where xsol
c is a local minimizer, is less than frtol.
c On exit frtol is unchanged.
c
c fatol is a double precision variable.
c On entry fatol specifies the absolute error desired in the
c function. Convergence occurs if the estimate of the
c absolute error between f(x) and f(xsol), where xsol
c is a local minimizer, is less than fatol.
c On exit fatol is unchanged.
c
c fmin is a double precision variable.
c On entry fmin specifies a lower bound for the function.
c The subroutine exits with a warning if f < fmin.
c On exit fmin is unchanged.
c
c maxfev is an integer variable.
c On entry maxfev specifies the limit of function evaluations.
c On exit maxfev is unchanged.
c
c cgtol is a double precision variable.
c On entry gqttol specifies the convergence criteria for
c subproblems.
c On exit gqttol is unchanged.
c
c **********
*/
/* Parameters for updating the iterates. */
double eta0 = 1e-4, eta1 = 0.25, eta2 = 0.75;
/* Parameters for updating the trust region size delta. */
double sigma1 = 0.25, sigma2 = 0.5, sigma3 = 4;
double p5 = 0.5, one = 1;
double gnorm, gnorm0, delta, snorm;
double alphac = 1, alpha, f, fc, prered, actred, gs;
int search = 1, iter = 1, info, inc = 1;
double *xc = (double *) xmalloc(sizeof(double)*n);
double *s = (double *) xmalloc(sizeof(double)*n);
double *wa = (double *) xmalloc(sizeof(double)*n);
double *g = (double *) xmalloc(sizeof(double)*n);
double *A = NULL;
uhes(n, x, &A);
ugrad(n, x, g);
ufv(n, x, &f);
gnorm0 = F77_CALL(dnrm2)(&n, g, &inc);
delta = 1000*gnorm0;
gnorm = dgpnrm(n, x, xl, xu, g);
if (gnorm <= gtol*gnorm0)
{
/*
//printf("CONVERGENCE: GTOL TEST SATISFIED\n");
*/
search = 0;
}
while (search)
{
/* Save the best function value and the best x. */
fc = f;
memcpy(xc, x, sizeof(double)*n);
/* Compute the Cauchy step and store in s. */
dcauchy(n, x, xl, xu, A, g, delta, &alphac, s, wa);
/* Compute the projected Newton step. */
dspcg(n, x, xl, xu, A, g, delta, cgtol, s, &info);
if (ufv(n, x, &f) > maxfev)
{
/*
//printf("ERROR: NFEV > MAXFEV\n");
*/
search = 0;
continue;
}
/* Compute the predicted reduction. */
memcpy(wa, g, sizeof(double)*n);
F77_CALL(dsymv)("U", &n, &p5, A, &n, s, &inc, &one, wa, &inc);
prered = -F77_CALL(ddot)(&n, s, &inc, wa, &inc);
/* Compute the actual reduction. */
actred = fc - f;
/* On the first iteration, adjust the initial step bound. */
snorm = F77_CALL(dnrm2)(&n, s, &inc);
if (iter == 1)
delta = mymin(delta, snorm);
/* Compute prediction alpha*snorm of the step. */
gs = F77_CALL(ddot)(&n, g, &inc, s, &inc);
if (f - fc - gs <= 0)
alpha = sigma3;
else
alpha = mymax(sigma1, -0.5*(gs/(f - fc - gs)));
/* Update the trust region bound according to the ratio
of actual to predicted reduction. */
if (actred < eta0*prered)
/* Reduce delta. Step is not successful. */
delta = mymin(mymax(alpha, sigma1)*snorm, sigma2*delta);
else
{
if (actred < eta1*prered)
/* Reduce delta. Step is not sufficiently successful. */
delta = mymax(sigma1*delta, mymin(alpha*snorm, sigma2*delta));
else
if (actred < eta2*prered)
/* The ratio of actual to predicted reduction is in
the interval (eta1,eta2). We are allowed to either
increase or decrease delta. */
delta = mymax(sigma1*delta, mymin(alpha*snorm, sigma3*delta));
else
/* The ratio of actual to predicted reduction exceeds eta2.
Do not decrease delta. */
delta = mymax(delta, mymin(alpha*snorm, sigma3*delta));
}
/* Update the iterate. */
if (actred > eta0*prered)
{
/* Successful iterate. */
iter++;
/*
uhes(n, x, &A);
*/
ugrad(n, x, g);
gnorm = dgpnrm(n, x, xl, xu, g);
if (gnorm <= gtol*gnorm0)
{
/*
//printf("CONVERGENCE: GTOL = %g TEST SATISFIED\n", gnorm/gnorm0);
*/
search = 0;
continue;
}
}
else
{
/* Unsuccessful iterate. */
memcpy(x, xc, sizeof(double)*n);
f = fc;
}
/* Test for convergence */
if (f < fmin)
{
//printf("WARNING: F .LT. FMIN\n");
search = 0; /* warning */
continue;
}
if (fabs(actred) <= fatol && prered <= fatol)
{
//printf("CONVERGENCE: FATOL TEST SATISFIED\n");
search = 0;
continue;
}
if (fabs(actred) <= frtol*fabs(f) && prered <= frtol*fabs(f))
{
/*
//printf("CONVERGENCE: FRTOL TEST SATISFIED\n");
*/
search = 0;
continue;
}
}
free(g);
free(xc);
free(s);
free(wa);
}
std::vector<RealGradient>
CNSFVMinmaxSlopeLimiting::limitElementSlope() const
{
const Elem * elem = _current_elem;
/// current element id
dof_id_type _elementID = elem->id();
/// current element centroid coordinte
Point ecent = elem->centroid();
/// number of sides surrounding an element
unsigned int nside = elem->n_sides();
/// number of conserved variables
unsigned int nvars = 5;
/// vector for the centroid of the sides surrounding an element
std::vector<Point> scent(nside, Point(0., 0., 0.));
/// vector for the limited gradients of the conserved variables
std::vector<RealGradient> ugrad(nvars, RealGradient(0., 0., 0.));
/// a flag to indicate the boundary side of the current cell
bool bflag = false;
/// initialize local minimum variable values
std::vector<Real> umin(nvars, 0.);
/// initialize local maximum variable values
std::vector<Real> umax(nvars, 0.);
/// initialize local cache for element variable values
std::vector<Real> uelem(nvars, 0.);
/// initialize local cache for reconstructed element gradients
std::vector<RealGradient> rugrad(nvars, RealGradient(0., 0., 0.));
/// initialize local cache for element slope limitor values
std::vector<std::vector<Real>> limit(nside + 1, std::vector<Real>(nvars, 1.));
Real dij = 0.;
uelem = _rslope.getElementAverageValue(_elementID);
for (unsigned int iv = 0; iv < nvars; iv++)
{
umin[iv] = uelem[iv];
umax[iv] = uelem[iv];
}
/// loop over the sides to find the min and max cell-average values
for (unsigned int is = 0; is < nside; is++)
{
const Elem * neighbor = elem->neighbor_ptr(is);
if (neighbor != nullptr && this->hasBlocks(neighbor->subdomain_id()))
{
dof_id_type _neighborID = neighbor->id();
uelem = _rslope.getElementAverageValue(_neighborID);
scent[is] = _rslope.getSideCentroid(_elementID, _neighborID);
}
else
{
uelem = _rslope.getBoundaryAverageValue(_elementID, is);
scent[is] = _rslope.getBoundarySideCentroid(_elementID, is);
}
for (unsigned int iv = 0; iv < nvars; iv++)
{
if (uelem[iv] < umin[iv])
umin[iv] = uelem[iv];
if (uelem[iv] > umax[iv])
umax[iv] = uelem[iv];
}
}
/// loop over the sides to compute the limiter values
rugrad = _rslope.getElementSlope(_elementID);
uelem = _rslope.getElementAverageValue(_elementID);
for (unsigned int is = 0; is < nside; is++)
{
for (unsigned int iv = 0; iv < nvars; iv++)
{
dij = (scent[is] - ecent) * rugrad[iv];
if (dij > 0.)
limit[is + 1][iv] = std::min(1., (umax[iv] - uelem[iv]) / dij);
else if (dij < 0.)
limit[is + 1][iv] = std::min(1., (umin[iv] - uelem[iv]) / dij);
}
}
/// loop over the sides to get the final limiter of this cell
for (unsigned int is = 0; is < nside; is++)
{
for (unsigned int iv = 0; iv < nvars; iv++)
{
if (limit[0][iv] > limit[is + 1][iv])
limit[0][iv] = limit[is + 1][iv];
}
}
/// get the limited slope of this cell
if (!_include_bc && bflag)
{
for (unsigned int iv = 0; iv < nvars; iv++)
ugrad[iv] = RealGradient(0., 0., 0.);
}
else
{
for (unsigned int iv = 0; iv < nvars; iv++)
ugrad[iv] = rugrad[iv] * limit[0][iv];
}
return ugrad;
}
std::vector<RealGradient>
CNSFVWENOSlopeLimiting::limitElementSlope() const
{
const Elem * elem = _current_elem;
/// current element id
dof_id_type _elementID = elem->id();
/// number of conserved variables
unsigned int nvars = 5;
/// number of sides surrounding an element
unsigned int nside = elem->n_sides();
/// vector for the limited gradients of the conserved variables
std::vector<RealGradient> ugrad(nvars, RealGradient(0., 0., 0.));
/// initialize local cache for reconstructed element gradients
std::vector<RealGradient> rugrad(nvars, RealGradient(0., 0., 0.));
/// a small number to avoid dividing by zero
Real eps = 1e-7;
/// initialize oscillation indicator
std::vector<std::vector<Real>> osci(nside + 1, std::vector<Real>(nvars, 0.));
/// initialize weight coefficients
std::vector<std::vector<Real>> weig(nside + 1, std::vector<Real>(nvars, 0.));
/// initialize summed coefficients
std::vector<Real> summ(nvars, 0.);
/// compute oscillation indicators, nonlinear weights and their summ for each stencil
rugrad = _rslope.getElementSlope(_elementID);
for (unsigned int iv = 0; iv < nvars; iv++)
{
osci[0][iv] = std::sqrt(rugrad[iv] * rugrad[iv]);
weig[0][iv] = _lweig / std::pow(eps + osci[0][iv], _dpowe);
summ[iv] = weig[0][iv];
}
for (unsigned int is = 0; is < nside; is++)
{
unsigned int in = is + 1;
if (elem->neighbor(is) != NULL)
{
dof_id_type _neighborID = elem->neighbor(is)->id();
rugrad = _rslope.getElementSlope(_neighborID);
for (unsigned int iv = 0; iv < nvars; iv++)
{
osci[in][iv] = std::sqrt(rugrad[iv] * rugrad[iv]);
weig[in][iv] = 1. / std::pow(eps + osci[in][iv], _dpowe);
summ[iv] += weig[in][iv];
}
}
}
/// compute the normalized weight
for (unsigned int iv = 0; iv < nvars; iv++)
weig[0][iv] = weig[0][iv] / summ[iv];
for (unsigned int is = 0; is < nside; is++)
{
unsigned int in = is + 1;
if (elem->neighbor(is) != NULL)
for (unsigned int iv = 0; iv < nvars; iv++)
weig[in][iv] = weig[in][iv] / summ[iv];
}
/// compute the limited slope
rugrad = _rslope.getElementSlope(_elementID);
for (unsigned int iv = 0; iv < nvars; iv++)
ugrad[iv] = weig[0][iv] * rugrad[iv];
for (unsigned int is = 0; is < nside; is++)
{
unsigned int in = is + 1;
if (elem->neighbor(is) != NULL)
{
dof_id_type _neighborID = elem->neighbor(is)->id();
rugrad = _rslope.getElementSlope(_neighborID);
for (unsigned int iv = 0; iv < nvars; iv++)
ugrad[iv] += weig[in][iv] * rugrad[iv];
}
}
return ugrad;
}
