rheolef  6.3

`adapt` - mesh adaptation More...

`#include <adapt.h>`

## Public Types

typedef std::vector< int >
::size_type
size_type

## Public Attributes

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 anisomax
bool clean
bool double_precision
Float anglecorner

## Detailed Description

`adapt` - mesh adaptation

SYNOPSYS

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

The metric `M` is determined from `|H|`. Recall that an isotropic metric is such that `M(x)=hloc(x)^(-2)*Id` where `hloc(x)` is the element size field and `Id` is the identity `d*d` matrix, and `d=1,2,3` is the physical space dimension.

GMSH ISOTROPIC METRIC

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).

BAMG ANISOTROPIC METRIC

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 `phi(x)`. The parameter is provided by the optional variable `opts.cutoff`; its default value is `1e-7`. The default strategy is the local normalization. The global normalization can be enforced by setting `opts.additional="-AbsError"`.

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 controled by setting `opts.hmin` not too small.

The local normalization has been choosen 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.

Definition at line 95 of file adapt.h.

## Member Typedef Documentation

Definition at line 96 of file adapt.h.

## Constructor & Destructor Documentation

inline

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## Member Data Documentation

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