adam_bashforth.cl File Reference

Improved Euler time integration scheme. More...

#include "resources/Scripts/types/types.h"

Include dependency graph for adam_bashforth.cl:

Macros
#define	TSCHEME_ADAMS_BASHFORTH_STEPS   5u
#define	DYDT_1(dydt_0)   dydt_0
#define	DYDT_2(dydt_0, dydt_1)   1.5f * dydt_0 - 0.5f * dydt_1
#define	DYDT_3(dydt_0, dydt_1, dydt_2)    23.f / 12.f * dydt_0 - 4.f / 3.f * dydt_1 + 5.f / 12.f * dydt_2
#define	DYDT_4(dydt_0, dydt_1, dydt_2, dydt_3)
#define	DYDT_5(dydt_0, dydt_1, dydt_2, dydt_3, dydt_4)

Functions
__kernel void	predictor (__global vec *r, __global vec *u, __global vec *dudt, __global float *rho, __global float *drhodt, __global vec *r_in, __global vec *u_in, __global vec *dudt_in, __global float *rho_in, __global float *drhodt_in, unsigned int N)
	Adams-Bashforth time integration scheme predictor stage.
__kernel void	sort (const __global vec *dudt_as1_in, __global vec *dudt_as1, const __global vec *dudt_as2_in, __global vec *dudt_as2, const __global vec *dudt_as3_in, __global vec *dudt_as3, const __global vec *dudt_as4_in, __global vec *dudt_as4, const __global float *drhodt_as1_in, __global float *drhodt_as1, const __global float *drhodt_as2_in, __global float *drhodt_as2, const __global float *drhodt_as3_in, __global float *drhodt_as3, const __global float *drhodt_as4_in, __global float *drhodt_as4, const __global unit *id_sorted, unsigned int N)
	Sort the stored Adams-Bashforth stored variation rates.
__kernel void	corrector (__global int *imove, __global unsigned int *iset, __global vec *r, __global vec *u, __global vec *dudt, __global float *rho, __global float *drhodt, __global vec *dudt_as1, __global float *drhodt_as1, __global vec *dudt_as2, __global float *drhodt_as2, __global vec *dudt_as3, __global float *drhodt_as3, __global vec *dudt_as4, __global float *drhodt_as4, unsigned int N, float dt, unsigned int iter)
	Improved Euler time integration scheme corrector stage.
__kernel void	postcorrector (const __global vec *dudt_as1, const __global float *drhodt_as1, const __global vec *dudt_as2, const __global float *drhodt_as2, const __global vec *dudt_as3, const __global float *drhodt_as3, const __global vec *dudt, const __global float *drhodt, __global vec *dudt_as1_in, __global float *drhodt_as1_in, __global vec *dudt_as2_in, __global float *drhodt_as2_in, __global vec *dudt_as3_in, __global float *drhodt_as3_in, __global vec *dudt_as4_in, __global float *drhodt_as4_in, unsigned int N)
	Backup de data for the sorting algorithm.

Detailed Description

Improved Euler time integration scheme.

Time integration is based in the following quasi-second order Predictor-Corrector integration scheme:

• \( \mathbf{u}_{n+1} = \mathbf{u}_{n} + \frac{\Delta t}{2} \left( \left. \frac{\mathrm{d}\mathbf{u}}{\mathrm{d}t} \right\vert_{n+1/2} + \left. \frac{\mathrm{d}\mathbf{u}}{\mathrm{d}t} \right\vert_{n-1/2} \right) \)
• \( \mathbf{r}_{n+1} = \mathbf{r}_{n} + \Delta t \, \mathbf{u}_{n} + \frac{\Delta t^2}{4} \left( \left. \frac{\mathrm{d}\mathbf{u}}{\mathrm{d}t} \right\vert_{n+1/2} + \left. \frac{\mathrm{d}\mathbf{u}}{\mathrm{d}t} \right\vert_{n-1/2} \right) \)
• \( \rho_{n+1} = \rho_{n} + \frac{\Delta t}{2} \left( \left. \frac{\mathrm{d}\rho}{\mathrm{d}t} \right\vert_{n+1/2} + \left. \frac{\mathrm{d}\rho}{\mathrm{d}t} \right\vert_{n-1/2} \right) \)