VISTA offers grid-type specific
interpolation services which are accessed via a generic
opaque interface (GRid Support, GRS
)
so that the application does not have to bother with
any details of the interpolation. These interpolation methods are
well-suited for situations where the attribute information that is
requested by an application is defined on a grid which is unknown or
which can not be handled by the application. By means of the generic
interpolation service the application can simply interpolate all the
input attributes onto a preferred (internal) grid.
The GRS uses a finite-element notion for interpolation. New element types can be registered by providing element type name and interpolation functions. The interpolation functions can be linear or of higher order, corresponding to the the form functions used in finite-element methods.
From a rigorous point of view, finite-difference results should not be interpolated at all, as the values of a quantity are only defined on the grid points. From previous considerations it is, however, obvious that an interpolation method is needed for coupling simulation tools, also when no element-specific interpolation function which is consistent with the application's discretization method is given.
VORONOI is in the advantageous position to utilize target grid information for this interpolation problem. The target (Delaunay) grid is a ``super-grid'' of the input grid (the input grid is a ``sub-grid'' of the Delaunay grid) and the output grid. This means that the Delaunay grid contains (nearly) only grid points that are also grid points of the source grids. For those points which are not contained in the source grid on which an attribute to be interpolated is defined, some means to obtain ``reasonable'' values is required (these are the unknown values).
This situation can be interpreted and reformulated as the search for a solution of a (yet unknown) partial differential equation, where the solution is sought on the grid points with unknown values, the grid points with known values imposing a Dirichlet boundary condition. The motivation to spend these efforts is that the quality of the interpolation may be improved with respect to defaulting to linear interpolation on the (triangulated) source grid.