secondderivative.h

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#ifndef _SECOND_DERIV_H_
#define _SECOND_DERIV_H_

#define _SECOND_ORDER_CENTRAL_  "2"

#define _FOURTH_ORDER_CENTRAL_  "4"

/* One-dimensional second derivative functions: Functions to calculate the
 * finite-difference approximation to the second derivative along a given 
 * dimension at the cell-centers / grid points.
 *
 * Arguments:-
 *  
 *  Df        double*     array containing the approximation to the second derivative
 *                        (1D array representing an n-D solution)
 *
 *  f         double*     array containing the function whose second derivative is to
 *                        be computed.
 *                        (1D array representing an n-D solution)
 *
 *  dir       int         dimension (x/y/z/...) along which to compute the second derivative
 *
 *  s         void*       pointer to an object providing the solver context. The object must
 *                        contain at least the following:
 *                        ndims     int       number of dimensions
 *                        nvars     int       number of elements at each grid location
 *                        dim       int*      array of grid size along each dimension 
 *                                            (integer array of size ndims)
 *                        ghosts    int       number of ghost points
 *
 *  m         void*       Pointer to an object providing the MPI context. Current not being 
 *                        used. This will be required for compact finite-difference methods.
 *
 *
 * Notes:
 *
 *  + Df and f are arrays with halos / ghost points. However, the second derivative is computed
 *    only in the interior. So the ghost points of Df contain uninitialized/unusable values.
*/

/* Second derivative functions */
int SecondDerivativeSecondOrderCentral (double*,double*,int,void*,void*); 
int SecondDerivativeFourthOrderCentral (double*,double*,int,void*,void*); 
int SecondDerivativeSecondOrderCentralNoGhosts (double*,double*,int,int,int*,int,int,void*); 
#endif