### Matrix flattening into a vector

Be *d *the mesh dimension and the metric that we want to impose at the mesh node.

*M* is a metric tensor so it is a symmetric matrix and we can choose to only provide the lower triangular part of *M* to Mmg. We flatten this lower triangular matrix to a vector using the following convention:

##### 2D

##### 3D

### Anisotropic metric prescription at mesh nodes

Be the flattened metric that we want to prescribe at the mesh node and *nbvals *the number of mesh nodes.

There is two ways to provide your metrics: using a solution file at the medit format (for command line interface) or using the API function (for library users).

##### Using an input file at medit format (.sol extension)

The medit solution file describes the metric precision, dimension, size and type (in the following example, the user must fill the fields in italic and comments must be removed):

MeshVersionFormatted# nprec=1: simple precision, nprec=2: double precisionnprecDimension# metric dimensiond:must match with the mesh dimensionSolAtVertices# For now, Mmg works only with metrics defined at mesh verticesnumber of metrics: must match with the number of nodes in the mesh filenbvals#1 3# number of solutions per node (always 1 for Mmg) and type of each solution (1:scalar, 2:vector, 3:tensor) # metric at first node # metric at second node ... # metric at last nodeEnd

##### Using the API functions

We suppose here that we want to adapt a three-dimensional volumic mesh, thus we call the Mmg3d library.

We call **mmgMesh** the mesh structure at the Mmg format and **mmgSol** the metric structure at the Mmg format.

In a first step, we must give the solution size and type:

if (MMG3D_Set_solSize(mmgMesh,mmgSol,MMG5_Vertex,,nbvalsMMG5_Tensor)!= 1 ) exit(EXIT_FAILURE);

**MMG5_Vertex** is keyword to say that the metrics are provided at mesh nodes (mandatory for now) and** MMG5_Tensor** a keyword to specify that we want to impose a tensorial metric at nodes (note that we don’t need to specify the metric dimension because this information is redundant with the mesh dimension).

In a last step, we can provide the metric at each node:

for ( i=1; i<=nbvals;++i ) if (MMG3D_Set_tensorSol(mmgSol,,i)!= 1 ) exit(EXIT_FAILURE);