?_Helmholtz_2D/?_Helmholtz

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 10/15/2026

Version

Public

?_Helmholtz_2D/?_Helmholtz_3D

Computes the solution of the 2D/3D Helmholtz problem specified by the parameters.

Syntax

void d_Helmholtz_2D(double* f, const double* bd_ax, const double* bd_bx, const double* bd_ay,
                    const double* bd_by, DFTI_DESCRIPTOR_HANDLE* xhandle, MKL_INT* ipar,
                    const double* dpar, MKL_INT* stat);

void s_Helmholtz_2D(float* f, const float* bd_ax, const float* bd_bx, const float* bd_ay,
                    const float* bd_by, DFTI_DESCRIPTOR_HANDLE* xhandle, MKL_INT* ipar,
                    const float* spar, MKL_INT* stat);

void d_Helmholtz_3D(double* f, const double* bd_ax, const double* bd_bx, const double* bd_ay,
                    const double* bd_by, const double* bd_az, const double* bd_bz,
                    DFTI_DESCRIPTOR_HANDLE* xhandle, DFTI_DESCRIPTOR_HANDLE* yhandle,
                    MKL_INT* ipar, const double* dpar, MKL_INT* stat);

void s_Helmholtz_3D(float* f, const float* bd_ax, const float* bd_bx, const float* bd_ay,
                    const float* bd_by, const float* bd_az, const float* bd_bz,
                    DFTI_DESCRIPTOR_HANDLE* xhandle, DFTI_DESCRIPTOR_HANDLE* yhandle,
                    MKL_INT* ipar, const float* spar, MKL_INT* stat);

Include Files

mkl_poisson.f90

Input Parameters

Parameter Name	Description
`f`	`double` for `d_Helmholtz_2D/d_Helmholtz_3D`, `float` for `s_Helmholtz_2D/s_Helmholtz_3D`. Contains the right-hand side of the problem packed in a single vector and modified by the appropriate ?_commit_Helmholtz_2D/?_commit_Helmholtz_3D routine. Note that an attempt to substitute the original right-hand side vector, which was passed to the `?_commit_Helmholtz_2D/?_commit_Helmholtz_3D` routine, at this point results in an incorrect solution. 2D problem: the size of the vector is `(nx+1)(ny+1)`. The value of the modified right-hand side in the mesh point `\((i, j)\)` is stored in `f[i+j(nx+1)]`. 3D problem: the size of the vector is `(nx+1)(ny+1)(nz+1)`. The value of the modified right-hand side in the mesh point `\((i, j, k)\)` is stored in `f[i+j(nx+1)+k(nx+1)*(ny+1)]`.
`xhandle`, `yhandle`	`DFTI_DESCRIPTOR_HANDLE *`. Data structures used by the Intel® oneAPI Math Kernel Library (oneMKL) FFT interface (for details, refer to FFT Functions). `yhandle` is used only by `?_Helmholtz_3D`.
`ipar`	`MKL_INT` array of size 128. Contains integer data to be used by Fast Helmholtz Solver (for details, refer to ipar).
`dpar`	`double` array of size depending on the dimension of the problem: 2D problem: `5nx/2+7` 3D problem: `5(nx+ny)/2+9` Contains double-precision data to be used by Fast Helmholtz Solver (for details, refer to dpar and spar).
`spar`	`float` array of size depending on the dimension of the problem: 2D problem: `5nx/2+7` 3D problem: `5(nx+ny)/2+9` Contains single-precision data to be used by Fast Helmholtz Solver (for details, refer to dpar and spar).
`bd_ax`	`double ` for `d_Helmholtz_2D/d_Helmholtz_3D`, `float ` for `s_Helmholtz_2D/s_Helmholtz_3D`. Contains values of the boundary condition on the leftmost boundary of the domain along the x-axis (for more information, refer to the table Parameters to Define Boundary Conditions for the Cartesian Solver).
`bd_bx`	`double ` for `d_Helmholtz_2D/d_Helmholtz_3D`, `float ` for `s_Helmholtz_2D/s_Helmholtz_3D`. Contains values of the boundary condition on the rightmost boundary of the domain along the x-axis (for more information, refer to the table Parameters to Define Boundary Conditions for the Cartesian Solver).
`bd_ay`	`double ` for `d_Helmholtz_2D/d_Helmholtz_3D`, `float ` for `s_Helmholtz_2D/s_Helmholtz_3D`. Contains values of the boundary condition on the leftmost boundary of the domain along the y-axis (for more information, refer to the table Parameters to Define Boundary Conditions for the Cartesian Solver).
`bd_by`	`double ` for `d_Helmholtz_2D/d_Helmholtz_3D`, `float ` for `s_Helmholtz_2D/s_Helmholtz_3D`. Contains values of the boundary condition on the rightmost boundary of the domain along the y-axis (for more information, refer to the table Parameters to Define Boundary Conditions for the Cartesian Solver).
`bd_az`	`double ` for `d_Helmholtz_3D`, `float ` for `s_Helmholtz_3D`. Used only by `?_Helmholtz_3D`. Contains values of the boundary condition on the leftmost boundary of the domain along the z-axis (for more information, refer to the table Parameters to Define Boundary Conditions for the Cartesian Solver).
`bd_bz`	`double ` for `d_Helmholtz_3D`, `float ` for `s_Helmholtz_3D`. Used only by `?_Helmholtz_3D`. Contains values of the boundary condition on the rightmost boundary of the domain along the z-axis (for more information, refer to the table Parameters to Define Boundary Conditions for the Cartesian Solver).

NOTE:

To avoid incorrect computation results, do not change arrays bd_ax, bd_bx, bd_ay, bd_by, bd_az, bd_bz between a call to the ?_commit_Helmholtz_2D/?_commit_Helmholtz_3D routine and a subsequent call to the appropriate ?_Helmholtz_2D/?_Helmholtz_3D routine.

Output Parameters

Parameter Name	Description
`f`	On output, contains the approximate solution to the problem packed the same way as the right-hand side of the problem was packed on input.
`xhandle`, `yhandle`	Data structures used by the Intel® oneAPI Math Kernel Library (oneMKL) FFT interface. Although the addresses do not change, the structures are modified on output.
`ipar`	Contains integer data to be used by Fast Helmholtz Solver. Modified on output as explained in ipar.
`stat`	`MKL_INT *`. Routine completion status, which is also written to `ipar[0]`. Continue to call other Poisson Solver routines only if the status is 0.

Description

The ?_Helmholtz_2D/?_Helmholtz_3D routines compute the approximate solution of the Helmholtz problem defined in the previous calls to the corresponding initialization and commit routines. The solution is computed according to formulas given in Poisson Solver Implementation. The f parameter, which initially holds the packed vector of the right-hand side of the problem, is replaced by the computed solution packed in the same way. Values of ax, bx, ay, by, az, and bz are passed to the routines with the spar/dpar array, and values of nx, ny, nz, and BCtype are passed with the ipar array.

Return Values

Parameter Name	Value	Description
`stat`	`1`	The routine completed without errors but with some warnings.
`stat`	`0`	The routine successfully completed the task.
`stat`	`-2`	The routine stopped because division by zero occurred. It usually happens if the data in the `dpar` or `spar` array was altered by mistake.
`stat`	`-3`	The routine stopped because the sufficient memory was unavailable for the computations.
`stat`	`-100`	The routine stopped because an error in the input data was found or the data in the `dpar`, `spar`, or `ipar` array was altered by mistake.
`stat`	`-1000`	The routine stopped because of the Intel® oneAPI Math Kernel Library (oneMKL) FFT or TT interface error.
`stat`	`-10000`	The routine stopped because the initialization failed to complete or the parameter `ipar[0]` was altered by mistake.
`stat`	`-99999`	The routine failed to complete the task because of a fatal error.

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