4.3.0.0.1 Mesh:

The Mesh is an object (providing the mesh interface) that addresses the discretization of the domain $\mathcal {D}$ using a Cartesian mesh. It decomposes the domain into a set of rectangular subdomains called Regions (they have a certain minimum size, so that they do not end up being just a single grid cell) which are then distributed among various processors (see Appendix A). The Mesh also allows the creation of data objects (which provide the FieldVar interface) on the Mesh. FieldVars can hold data at various times (this is required if one uses a multistep time-integrator like Crank-Nicholson) and this is reflected in the Mesh; i.e. it has a concept of time steps. The Mesh also provides the ability to define certain parameters which are common to all FieldVars e.g. the number of cells in the halo around the domain boundary (so that, for example, Neumann boundary conditions may be applied), and the radius of the spatial stencil (which determines the width of the ghost-cell halos one keeps around subdomains when computing in parallel). It also allows the specification of the domain (in terms of size and the N_x x N_y grid cells itself) as well as the Collocation type (see Chapter C).