Contains structures for time integration. More...

#include <sys/time.h>
#include <basic.h>

Data Structures
struct	TimeIntegration
	Structure of variables/parameters and function pointers for time integration. More...

struct	ExplicitRKParameters
	Structure containing the parameters for an explicit Runge-Kutta method. More...

struct	GLMGEEParameters
	Structure containing the parameters for the General Linear Methods with Global Error Estimators (GLM-GEE) More...

Macros
#define	_FORWARD_EULER_ "euler"

#define	_RK_ "rk"

#define	_GLM_GEE_ "glm-gee"

#define	_RK_1FE_ "1fe"

#define	_RK_22_ "22"

#define	_RK_33_ "33"

#define	_RK_44_ "44"

#define	_RK_SSP3_ "ssprk3"

#define	_RK_TVD3_ "tvdrk3"

#define	_GLM_GEE_YYT_ "yyt"

#define	_GLM_GEE_YEPS_ "yeps"

#define	_GLM_GEE_23_ "23"

#define	_GLM_GEE_24_ "24"

#define	_GLM_GEE_25I_ "25i"

#define	_GLM_GEE_35_ "35"

#define	_GLM_GEE_EXRK2A_ "exrk2a"

#define	_GLM_GEE_RK32G1_ "rk32g1"

#define	_GLM_GEE_RK285EX_ "rk285ex"

Detailed Description

Contains structures for time integration.

Author: Debojyoti Ghosh

Definition in file timeintegration_struct.h.

Data Structure Documentation

struct ExplicitRKParameters

Structure containing the parameters for an explicit Runge-Kutta method.

Contains the parameters defining an explicit Runge Kutta time integration method.

See Also: TimeRK()

Definition at line 177 of file timeintegration_struct.h.

Data Fields
int	nstages	number of stages
double *	A	Stage computation coefficients (Butcher tableau form), saved as a 1D-array in row-major form
double *	b	Step completion coefficients (Butcher tableau form)
double *	c	Stage time coefficients (Butcher tableau form)

struct GLMGEEParameters

Structure containing the parameters for the General Linear Methods with Global Error Estimators (GLM-GEE)

Contains the parameters defining a General Linear time-integration method with global error estimators.

See Also: TimeGLMGEE()

Definition at line 267 of file timeintegration_struct.h.

Data Fields
int	nstages	Number of stages
int	r	Number of auxiliary solutions propagated with solution
char	ee_mode[_MAX_STRING_SIZE_]	Error estimation mode (_GLM_GEE_YYT_ or _GLM_GEE_YEPS_)
double *	A_yyt	Stage computation coefficients ( \(y-\tilde{y}\) error-estimation mode) (row-major)
double *	B_yyt	Step completion coefficients ( \(y-\tilde{y}\) error-estimation mode) (row-major)
double *	C_yyt	Stage computation coefficients ( \(y-\tilde{y}\) error-estimation mode) (row-major)
double *	D_yyt	Step completion coefficients ( \(y-\tilde{y}\) error-estimation mode) (row-major)
double *	c_yyt	Stage time coefficients ( \(y-\tilde{y}\) error-estimation mode) (row-major)
double *	A_yeps	Stage computation coefficients ( \(y-\epsilon\) error-estimation mode) (row-major)
double *	B_yeps	Step completion coefficients ( \(y-\epsilon\) error-estimation mode) (row-major)
double *	C_yeps	Stage computation coefficients ( \(y-\epsilon\) error-estimation mode) (row-major)
double *	D_yeps	Step completion coefficients ( \(y-\epsilon\) error-estimation mode) (row-major)
double *	c_yeps	Stage time coefficients ( \(y-\epsilon\) error-estimation mode) (row-major)
double *	A	Pointer to the stage computation coefficients
double *	B	Pointer to the step completion coefficients
double *	C	Pointer to the stage computation coefficients
double *	D	Pointer to the step completion coefficients
double *	c	Pointer to stage time coefficients
double	gamma	Gamma parameter

Macro Definition Documentation

#define _FORWARD_EULER_ "euler"

Forward Euler time integration

See Also: TimeForwardEuler()

Definition at line 14 of file timeintegration_struct.h.

#define _RK_ "rk"

Runge-Kutta time integration method

See Also: TimeRK()

Definition at line 16 of file timeintegration_struct.h.

#define _GLM_GEE_ "glm-gee"

General Linear Methods with Global Error Estimators

See Also: TimeGLMGEE()

Definition at line 18 of file timeintegration_struct.h.

#define _RK_1FE_ "1fe"

Forward Euler, written as a Runge Kutta method (1 stage, 1st order)

\(\begin{array}{c|c} 0 & 0 \\ \hline & 1 \end{array}\)

See Also: TimeExplicitRKInitialize()

Definition at line 128 of file timeintegration_struct.h.

#define _RK_22_ "22"

2-stage, 2nd order Runge Kutta method, often known as "RK2a"

\(\begin{array}{c|cc} 0 & & \\ 1 & 1 & \\ \hline & \frac{1}{2} & \frac{1}{2}\end{array}\)

See Also: TimeExplicitRKInitialize()

Definition at line 136 of file timeintegration_struct.h.

#define _RK_33_ "33"

3-stage, 3rd order Runge Kutta method

\(\begin{array}{c|ccc} 0 & & & \\ \frac{2}{3} & \frac{2}{3} & & \\ \frac{2}{3} & \frac{5}{12} & \frac{1}{4} & \\ \hline & \frac{1}{4} & -\frac{1}{4} & 1\end{array}\)

See Also: TimeExplicitRKInitialize()

Definition at line 144 of file timeintegration_struct.h.

#define _RK_44_ "44"

The classical 4-stage, 4th order Runge Kutta method

\( \begin{array}{c|cccc} 0 & & & & \\ \frac{1}{2} & \frac{1}{2} & & & \\ \frac{1}{2} & & \frac{1}{2} & & \\ 1 & & & 1 & \\ \hline & \frac{1}{6} & \frac{1}{3} & \frac{1}{3} & \frac{1}{6} \end{array} \)

See Also: TimeExplicitRKInitialize()

Definition at line 152 of file timeintegration_struct.h.

#define _RK_SSP3_ "ssprk3"

Strong-Stability-Preserving (SSP) 3-stage, 3rd order Runge Kutta method

\( \begin{array}{c|ccc} 0 & & & \\ 1 & 1 & & \\ \frac{1}{2} & \frac{1}{4} & \frac{1}{4} & \\ \hline & \frac{1}{6} & \frac{1}{6} & \frac{2}{3} \end{array}\)

See Also: TimeExplicitRKInitialize()

Reference:

Gottlieb, S., Ketcheson, D. I., and Shu, C.-W., High Order Strong Stability Preserving Time Discretizations, J. Sci. Comput., 38 (3), 2009, pp. 251-289, http://dx.doi.org/10.1007/s10915-008-9239-z.

Definition at line 165 of file timeintegration_struct.h.

#define _RK_TVD3_ "tvdrk3"

Same as _RK_SSP3_

Definition at line 166 of file timeintegration_struct.h.

#define _GLM_GEE_YYT_ "yyt"

\(y-\tilde{y}\) form