(UNDER CONSTRUCTION)

This library provides a set of functions for computation derivatives using spectral methods. The lib depends on FFTW library. The library is compatible with W-SLDA Toolkit however, it can be used as standalone lib. It is written in C99 standard.

Name convention

Generic name of a function is wderiv_operation_Nd_t, where:

• wderiv: fixed, function belongs to wderiv lib,

• operation:

  • dfdx : \frac{\partial f}{\partial x}
  • dfdy : \frac{\partial f}{\partial y}
  • dfdz : \frac{\partial f}{\partial z}
  • d2fdx2 : \frac{\partial^2 f}{\partial x^2}
  • d2fdy2 : \frac{\partial^2 f}{\partial y^2}
  • d2fdz2 : \frac{\partial^2 f}{\partial z^2}
  • dnfdxn : \frac{\partial^n f}{\partial x^n}
  • dnfdyn : \frac{\partial^n f}{\partial y^n}
  • dnfdzn : \frac{\partial^n f}{\partial z^n}
  • gradient : (\frac{\partial f}{\partial x}, \frac{\partial f}{\partial y}, \frac{\partial f}{\partial z})
  • gradient2 : |\nabla f|^2, see here for computation details
  • laplace : \frac{\partial^2 f}{\partial x^2} + \frac{\partial^2 f}{\partial y^2} + \frac{\partial^2 f}{\partial z^2}
  • divergence : \frac{\partial f}{\partial x} + \frac{\partial f}{\partial y} + \frac{\partial f}{\partial z}
  • curl : (\frac{\partial f_y}{\partial z} - \frac{\partial f_z}{\partial y},\frac{\partial f_z}{\partial x} - \frac{\partial f_x}{\partial z},\frac{\partial f_x}{\partial y} - \frac{\partial f_y}{\partial x})

• N:

  • 3 for 3D problems
  • 2 for 2D problems
  • 1 for 1D problems

• t:

  • r for real problems
  • c for complex problems