Module: FFT

Fast fourier transform related variables and subroutines.

Cluster distributed FFT

In intel MKL, the MPI slicing happens along the first dimension in C, or the last dimension in Fortran. Note, this is the most natural way to do the slicing, because you want to keep the contingent data in memory on the same core. In the Mu-PRO PhaseFieldSDK, since we also support thin-film boundary conditions in many of our solvers and in most cases x dimension is larger than z, thus it is not a good choice to slice along the Z direction. As a result, all of the real space allocated arrays in Mu-PRO PhaseFieldSDK is defined as (z, y, x) rather than (x, y, z), so that the slicing happens along the x dimension instead of z.

Important

FFT module is also the base for many other modules. You must call the mupro_fft_setup subroutine before you can use the solvers in the SDK.

Name

mod_mupro_fft

Depends on

mod_mupro_size, mod_mupro_print

Defined variables

None

Defined types

type_mupro_FFContext

Defined subroutines

mupro_fft_setup, mupro_fft_forward, mupro_fft_backward ,mupro_fitted_derivative, mupro_fitted_curvature

Defined Types

type_mupro_FFTContext

Variable	Type	Meaning
Rn1	int32	Size of real space x dimension on the current core
Rn2	int32	Size of real space y dimension on the current core
Rn3	int32	Size of real space z dimension on the current core
Cn1	int32	Size of fourier space x dimension on the current core
Cn2	int32	Size of fourier space y dimension on the current core
Cn3	int32	Size of fourier space z dimension on the current core
lstart	int32	Starting index of the data along x on the current core

Important

MPI slicing in FFT only happens along the last dimension of Fortran array, so to have such slicing happens along the x direction, we have to define the x as the last dimension, y as the second to last, and so on. To give an example, the dimension for polarization is (3,z,y,x).

Note

Since MPI slicing happens along the last dimension of Fortran array (which is x in our convention), so \(\text{Rn3}=\text{nz}\), \(\text{Rn2}=\text{ny}\), \(\text{Rn1}\neq \text{nx}\), and \(\text{lstartR} = \text{0}\) for rank 0, and \(\text{lstartR}\neq \text{0}\) for other ranks.

Defined Subroutines

mupro_fft_setup

Initialize cluster distributed FFT, so that we can use forward and backward functions afterwards.

call mupro_fft_setup(context)

Important

You must call this fft setup subroutine after mupro_size_setup and mupro_mpi_setup but before all other subroutines that involves 3D data.

Argument	Type(Intent)	Meaning
context	type_mupro_FFTContext, intent(OUT)	The initialized FFT system information

mupro_fft_forward(real_space, fourier_space )

Forward fft from real space to fourier space.

Argument	Type(Intent)	Meaning
real_space	real(kind=rdp),intent(in),dimension(Rn3,Rn2,Rn1)	Data in real space
fourier_space	complex(kind=rdp),intent(out),dimension(Cn3,Cn2,Cn1)	Data in fourier space

mupro_fft_backward(fourier_space, real_space )

Backward fft from fourier space to real space.

Argument	Type(Intent)	Meaning
fourier_space	complex(kind=rdp),intent(in),dimension(Cn3,Cn2,Cn1)	Data in fourier space
real_space	real(kind=rdp),intent(out),dimension(Rn3,Rn2,Rn1)	Data in real space

mupro_fitted_derivative(data, derivative, order, direction)

Calculate derivate of 3D data. This function can be called in both thin film and bulk cases. In the thin film case, due to the sudden change in data across the film interface and surface, a special fitting step is included, which is also why the subroutine is called mupro_fitted_derivative.

Argument	Type(Intent)	Meaning
data	real(kind=rdp),intent(in),dimension(Rn3,Rn2,Rn1)	Data in real space
derivate	real(kind=rdp),intent(out),dimension(3, Rn3,Rn2,Rn1 )	Derivative in real space, in the order of \(\frac{d}{dx}\), \(\frac{d}{dy}\), \(\frac{d}{dz}\)
order	integer,intent(in)	Order for the fitting along z direction in the thin film case, you can choose from 0 to 4
direction	integer,intent(in)	The direction to calculate derivative, 1: only \(\frac{d}{dx}\), 2: only \(\frac{d}{dy}\), 3: only \(\frac{d}{dz}\), 4: all derivates, 5: \(\frac{d}{dx}\) and \(\frac{d}{dy}\)

mupro_fitted_curvature(data, curvature, order, direction)

Calculate curvature of 3D data. This function can be called in both thin film and bulk cases. In the thin film case, due to the sudden change in data across the film interface and surface, a special fitting step is included, which is also why the subroutine is called mupro_fitted_curvature.

Argument	Type(Intent)	Meaning
data	real(kind=rdp),intent(in),dimension(Rn3,Rn2,Rn1)	Data in real space
derivate	real(kind=rdp),intent(out),dimension(6, Rn3,Rn2,Rn1 )	Curvature in real space, in the order of \(\frac{d^2}{dx^2}\), \(\frac{d^2}{dy^2}\), \(\frac{d^2}{dz^2}\), \(\frac{d^2}{dydz}\) , \(\frac{d^2}{dxdz}\), \(\frac{d^2}{dxdy}\)
order	integer,intent(in)	Order for the fitting along z direction in the thin film case, you can choose from 0 to 4
direction	integer,intent(in)	The direction to calculate Curvature, 1 for \(\frac{d^2}{dxdy}\), 2 for \(\frac{d^2}{dxdz}\), 4 for \(\frac{d^2}{dydz}\), 8 for \(\frac{d^2}{dz^2}\), 16 for \(\frac{d^2}{dy^2}\), 32 for \(\frac{d^2}{dx^2}\). To request multiple second derivatives these numbers should be added together