You can use this function to load mesh from different formats

In order to load only .msh file, you can also use the loadGMSHMesh.

Interface:

Required Parameters:

Optional Parameters:

The file you want to load has to be in an appropriate repository. See LoadMesh.

From doc/manual/heatns.cpp

From applications/check/check.cpp

Use this function to create a description from a .geo file.

Use this function to generate a simple geometrical domain from parameters.

Feel++ allows also to select an extended sets of entities from the mesh, you can extract entities which belongs to the local process but also ghost entities which satisfy the same property as the local ones.

Actually you can select both or one one of them thanks to the enum data structure entity_process_t which provides the following options

Here is how to select both local and ghost elements from a Mesh

Denote \(\mathcal{E}_{1}, \ldots ,\mathcal{E}_{n}\) \(n\) disjoints sets of the same type of entities (eg elements, faces,edges or points), \(\cup_{i=1}^{n} \mathcal{E}_i\) with \(\cap_{i=0}^{n} \mathcal{E}_i = \emptyset\).

We wish to concatenate these \(n\) sets. To this end, we use concatenate which takes an arbitrary number of disjoints sets.

Denote \(\mathcal{E}\) a set of entities, eg. the set of all faces (both internal and boundary faces). Denote \(\mathcal{E}_\Gamma\) a set of entities marked by \(\Gamma\). We wish to build \({\Gamma}^c=\mathcal{E}\backslash\Gamma\). To compute the complement, Feel++ provides a complement template function that requires \(\mathcal{E}\) and a predicate that return true if an entity of \(\mathcal{E}\) belongs to \(\Gamma\), false otherwise. The function returns mesh iterators over \(\Gamma^c\).

Feel++ provides some helper functions to apply on set of entities. We denote by range_t the type of the entities set.

A range can be also build directly by the user. This customized range is stored in a std container which contains the c++ references of entity object. We use boost::reference_wrapper for take c++ references and avoid copy of mesh data. All entities enumerated in the range must have same type (elements,faces,edges,points). Below we have an example which select all active elements in mesh for the current partition (i.e. identical to elements(mesh)).

Next, this range can be used in feel++ language.

One of the optimisations that allows to have a huge gain in computational effort is to straighten all the high order elements except for the boundary faces of the computational mesh. This is achieved by moving all the nodes associated to the high order transformation to the position these nodes would have if a first order geometrical transformation were applied. This procedure can be formalized in the following operator

where \(\mathbf{x}^*\) is any point in \(K^*\) and \(\mathbf{\varphi}^1_{K}(\mathbf{x}^*)\) and \(\mathbf{\varphi}^N_{K}(\mathbf{x}^*)\) its images by the geometrical transformation of order one and order \(N\), respectively. On one hand, the first two terms ensure that for all \(K\) not intersecting \(\Gamma\), the order one and \(N\) transformations produce the same image. On the other hand, the last two terms are 0 unless the image of \(\mathbf{x}^*\) in on \(\Gamma\) and, in this case, we don’t move the high order image of \(\mathbf{x}^*\). This allows to have straight internal elements and elements touching the boundary to remain high order. When applying numerical integration, specific quadratures are considered when dealing with internal elements or elements sharing a face with the boundary. The performances, thanks to this transformation, are similar to the ones obtained with first order meshes. However, it needs to be used with care as it can generate folded meshes.

In multiphysics applications or using advanced numerical methods e.g. involving Lagrange multipliers, it is often required to define Function Spaces on different meshes. Theses meshes are often related. Consider for example a heat transfer problem on a domain \(\Omega\) coupled with fluid flow problem on a domain \(\Omega_f \subset \Omega\) as in the Heat Transfer benchmarks. createSubmesh allows to extract \(\Omega_f\) out of \(\Omega\) while keeping information on the relation between the two meshes to be able to transfer data between these meshes very efficiently.