31.3 Usage

To include the cubic interpolation tool into your FLASH development, add the line

REQUIRES numericalTools/Interpolate

into the Config file of the directory where the global API's of the interpolation unit will be used. Another way would be to include the option

-with-unit=numericalTools/Interpolate

into your command line when you configure the code with setup. Both ways will give you access to the following cubic interpolation tools in order of their application, where XX stand for the 3 rectangular domain geometries 1D,2D and 3D:

• Interpolate_cubicXXmonoDerv: Handles the logistics for producing optimum sets of mixed vertex derivatives for a (sub)grid from vertex functional values to ensure monotonicity of the generated $C^1$ cubic interpolation surfaces. Note that in oder to generate these mixed derivatives the user needs to provide the vertex function values on a larger (sub)grid than the target (sub)grid: 1,2,3 extra vertex layers for 1D,2D,3D rectangular geometries.
• Interpolate_cubicXXcoeffs: Calculate the cubic expansion coefficients $a_{ij}$ in equation 31.1 from user provided sets of vertex data ${\bf b}$, arranged as shown in 31.4. The calculation is performed in situ, i.e. the input vector ${\bf b}$ is overwritten by the cubic expansion coefficient vector ${\bf a}$ using equation 31.8. The routine accepts a collection of different ${\bf b}$ vectors and processes them all at once. For XX = 2D or 3D, the code allows for multithreading.
• Interpolate_cubicXXF(d1)(d2): For a specific cubic expansion coefficient vector ${\bf a}$ and a set of up to three $[0,1]$ rescaled coordinates $x,y,z$, these function routines calculate the functional value $F$ using equation 31.1 and additionally the complete set of 1st ($dx$,$dy$,$dz$) and 2nd ($d^2x$,$d^2y$,$d^2z$,$dxdy$,$dxdz$,$dydz$) order $[0,1]$ rescaled coordinate derivatives using equation 31.13. Transformation to global coordinate derivatives via equation 31.12 is not done here and has to be done by the user in his specific application.