Derivatives

Name DerivativesOrder
Section Mesh::Derivatives
Type integer
Default 4

This variable gives the discretization order for the approximation of the differential operators. This means, basically, that DerivativesOrder points are used in each positive/negative spatial direction, e.g. DerivativesOrder = 1 would give the well-known three-point formula in 1D. The number of points actually used for the Laplacian depends on the stencil used. Let $O$ = DerivativesOrder, and $d$ = Dimensions.

• stencil_star: $2 O d + 1$
• stencil_cube: $(2 O + 1)^d$
• stencil_starplus: $2 O d + 1 + n$ with n being 8 in 2D and 24 in 3D.

Name DerivativesStencil
Section Mesh::Derivatives
Type integer
Default stencil_star

Decides what kind of stencil is used, i.e. which points, around each point in the mesh, are the neighboring points used in the expression of the differential operator.

If curvilinear coordinates are to be used, then only the stencil_starplus or the stencil_cube may be used. We only recommend the stencil_starplus, since the cube typically needs far too much memory.

Options:

• stencil_star:
  A star around each point (i.e., only points on the axis).
  
• stencil_variational:
  Same as the star, but with coefficients built in a different way.
  
• stencil_cube:
  A cube of points around each point.
  
• stencil_starplus:
  The star, plus a number of off-axis points.
  
• stencil_stargeneral:
  The general star. Default for non-orthogonal grids.
  

Name MultigridDerivativesOrder
Section Mesh::Derivatives
Type integer
Default 1

This variable gives the discretization order for the approximation of the differential operators on the different levels of the multigrid. For more details, see the variable DerivativesOrder. For star-general stencils, the minimum is set to 2.