adapt(4rheolef) | rheolef-6.7 | adapt(4rheolef) |

geo adapt (const field& phi);

geo adapt (const field& phi, const adapt_option_type& opts);

The function

based on the

The

For dimension one or three,

In the two dimensional case, the

The strategy based on a metric determined from the Hessian of

a scalar governing field, denoted as

Let us denote by

Then,

but with absolute value of its eigenvalues:

|H| = Q*diag(|lambda_i|)*QtThe metric

Recall that an isotropic metric is such that

where

identity

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

and the two parameters

and

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)))The first one involves a local (relative) normalization:

|H(x))| M(x) = ----------------------------------------- err*hcoef^2*(|phi(x)|, cutoff*max_y|phi(y)|)Notice that the denominator involves a local value

The parameter is provided by the optional variable

its default value is

The default strategy is the local normalization.

The global normalization can be enforced by setting

When choosing global or local normalization ?

When the governing field

i.e. when

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

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 controled

by setting

The local normalization has been choosen as the default since it is

more robust. When your field

then you can swith to the global numbering that leads to a best

equirepartition of the error over the domain.

struct adapt_option_type { 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_type() : 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_type& options = adapt_option_type());

rheolef-6.7 | rheolef-6.7 |