Rbfstring Module

class ammorph.rbfstring.RBF

Class to provide strings that can be passed to as rbf_function to Stages

static beckert_wendland_c2_basis(epsilon)

Beckert Wendland Splin C2. This is a compact RBF, it can be used for sparse assembly.

\[\begin{split}\phi(r) = \begin{cases} \left(4 \cdot \frac{r}{\varepsilon} + 1 \right) \cdot \left( 1 - \frac{r}{\varepsilon}\right)^4 & \text{for } \left(1 - \frac{r}{\varepsilon}\right) > 0 \\ 0 & \text{else} \end{cases}\end{split}\]
Parameters

epsilon (float) – epsilon that controls the effect radius of the RBF

Returns

rbf

Return type

str

static gaussian_spline(epsilon)

Returns Gaussian spline function.

\[\phi(r) = \mathrm{e}^{-\left(\frac{r}{\varepsilon}\right)^2}\]
Parameters

epsilon (float) – epsilon that controls the effect radius of the RBF

Returns

rbf

Return type

str

static multi_quadratic_biharmonic_spline(epsilon)

Returns Multi Quadratic Biharmonic Spline string.

\[\phi(r) = \sqrt{r^2 + \varepsilon^2}\]
Parameters

epsilon (float) – epsilon that controls the effect radius of the RBF

Returns

rbf

Return type

str

static thin_plate_spline(epsilon)

Returns Thin Plate Spline (TPS).

This is RBF is very recommended for first studies.

\[\begin{split}\phi(r) = \begin{cases} \left(\frac{r}{\varepsilon}\right)^2 \ln \left(\frac{r}{\varepsilon}\right)^2 & \text{for } r/\varepsilon > 0 \\ \left(\frac{r}{\varepsilon}\right)^2 & \text{ else} \end{cases}\end{split}\]
Parameters

epsilon (float) – epsilon that controls the effect radius of the RBF

Returns

rbf

Return type

str