adapt(4rheolef) | rheolef-7.0 | adapt(4rheolef) |
adapt - mesh adaptation
geo adapt (const field& phi);
geo adapt (const field& phi, const adapt_option& opts);
The function adapt implements the mesh adaptation
procedure,
based on the gmsh (isotropic) or bamg (anisotropic) mesh
generators.
The bamg mesh generator is the default in two dimension.
For dimension one or three, gmsh is the only generator supported yet.
In the two dimensional case, the gmsh correspond to the
opts.generator="gmsh".
The strategy based on a metric determined from the Hessian of
a scalar governing field, denoted as phi, and that is supplied by the
user.
Let us denote by H=Hessian(phi) the Hessian tensor of the field
phi.
Then, |H| denote the tensor that has the same eigenvector as H,
but with absolute value of its eigenvalues:
|H| = Q*diag(|lambda_i|)*Qt
max_(i=0..d-1)(|lambda_i(x)|)*Id
M(x) = -----------------------------------------
err*hcoef^2*(sup_y(phi(y))-inf_y(phi(y)))
Notice that the denominator involves a global (absolute)
normalization
sup_y(phi(y))-inf_y(phi(y)) of the governing field phi
and the two parameters opts.err, the target error,
and opts.hcoef, a secondary normalization parameter (defaults to
1).
There are two approach for the normalization of the metric.
The first one involves a global (absolute) normalization:
|H(x))|
M(x) = -----------------------------------------
err*hcoef^2*(sup_y(phi(y))-inf_y(phi(y)))
|H(x))|
M(x) = -----------------------------------------
err*hcoef^2*(|phi(x)|, cutoff*max_y|phi(y)|)
When choosing global or local normalization ?
When the governing field phi is bounded,
i.e. when err*hcoef^2*(sup_y(phi(y))-inf_y(phi(y)))
will converge versus mesh refinement to a bounded value,
the global normalization defines a metric that is mesh-independent
and thus the adaptation loop will converge.
Otherwise, when phi presents singularities, with unbounded
values (such as corner singularity, i.e. presents peacks when represented
in elevation view), then the mesh adaptation procedure
is more difficult. The global normalization
divides by quantities that can be very large and the mesh adaptation
can diverges when focusing on the singularities.
In that case, the local normalization is preferable.
Moreover, the focus on singularities can also be controlled
by setting opts.hmin not too small.
The local normalization has been chosen as the default since it is
more robust. When your field phi does not present singularities,
then you can swith to the global numbering that leads to a best
equirepartition of the error over the domain.
struct adapt_option {
typedef std::vector<int>::size_type size_type;
std::string generator;
bool isotropic;
Float err;
Float errg;
Float hcoef;
Float hmin;
Float hmax;
Float ratio;
Float cutoff;
size_type n_vertices_max;
size_type n_smooth_metric;
bool splitpbedge;
Float thetaquad;
Float anisomax;
bool clean;
std::string additional;
bool double_precision;
Float anglecorner; // angle below which bamg considers 2 consecutive edge to be part of
// the same spline
adapt_option() :
generator(""),
isotropic(true), err(1e-2), errg(1e-1), hcoef(1), hmin(0.0001), hmax(0.3), ratio(0), cutoff(1e-7),
n_vertices_max(50000), n_smooth_metric(1),
splitpbedge(true), thetaquad(std::numeric_limits<Float>::max()),
anisomax(1e6), clean(false), additional("-RelError"), double_precision(false),
anglecorner(0)
{} }; template <class T, class M> geo_basic<T,M> adapt (
const field_basic<T,M>& phi,
const adapt_option& options = adapt_option());
Copyright (C) 2000-2018 Pierre Saramito <Pierre.Saramito@imag.fr> GPLv3+: GNU GPL version 3 or later <http://gnu.org/licenses/gpl.html>. This is free software: you are free to change and redistribute it. There is NO WARRANTY, to the extent permitted by law.
rheolef-7.0 | rheolef-7.0 |