Parameters That Define Boundary Conditions

Developer Reference for Intel® oneAPI Math Kernel Library for C

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Date 11/07/2023

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Parameters That Define Boundary Conditions

Poisson Solver routines for the Cartesian solver use the following common parameters to define the boundary conditions.

Parameters to Define Boundary Conditions for the Cartesian Solver
Parameter	Description
bd_ax	double* for d_commit_Helmholtz_2D/d_commit_Helmholtz_3D and d_Helmholtz_2D/d_Helmholtz_3D, float* for s_commit_Helmholtz_2D/s_commit_Helmholtz_3D and s_Helmholtz_2D/s_Helmholtz_3D. Contains values of the boundary condition on the leftmost boundary of the domain along the `x`-axis. 2D problem: the size of the array is ny+1. Its contents depend on the boundary conditions as follows: Dirichlet boundary condition (value of BCtype[0] is 'D'): values of the function `G`(ax, `y`_j), `j`=0, ..., ny. Neumann boundary condition (value of BCtype[0] is 'N'): values of the function `g`(ax, `y`_j), `j`=0, ..., ny. The value corresponding to the index `j` is placed in bd_ax[`j`]. 3D problem: the size of the array is (ny+1)(nz+1). Its contents depend on the boundary conditions as follows: Dirichlet boundary condition (value of BCtype[0] is 'D'): values of the function `G`(ax, `y`_j, `z`_k), `j`=0, ..., ny, `k`=0, ..., nz. Neumann boundary condition (value of BCtype[0] is 'N'): the values of the function `g`(ax, `y`_j, `z`_k), `j`=0, ..., ny, `k`=0, ..., nz. The values are packed in the array so that the value corresponding to indices `(j, k)` is placed in bd_ax[`j+k`(ny+1)]. For periodic boundary conditions (the value of BCtype[0] is 'P'), this parameter is not used, so it can accept a dummy pointer.
bd_bx	double* for d_commit_Helmholtz_2D/d_commit_Helmholtz_3D and d_Helmholtz_2D/d_Helmholtz_3D, float* for s_commit_Helmholtz_2D/s_commit_Helmholtz_3D and s_Helmholtz_2D/s_Helmholtz_3D. Contains values of the boundary condition on the rightmost boundary of the domain along the `x`-axis. 2D problem: the size of the array is ny+1. Its contents depend on the boundary conditions as follows: Dirichlet boundary condition (value of BCtype[1] is 'D'): values of the function `G`(bx, `y`_j), `j`=0, ..., ny. Neumann boundary condition (value of BCtype[1] is 'N'): values of the function `g`(bx, `y`_j), `j`=0, ..., ny. The value corresponding to the index `j` is placed in bd_bx[`j`]. 3D problem: the size of the array is (ny+1)(nz+1). Its contents depend on the boundary conditions as follows: Dirichlet boundary condition (value of BCtype[1] is 'D'): values of the function `G`(bx, `y`_j, `z`_k), `j`=0, ..., ny, `k`=0, ..., nz. Neumann boundary condition (value of BCtype[1] is 'N'): values of the function `g`(bx, `y`_j, `z`_k), `j`=0, ..., ny, `k`=0, ..., nz. The values are packed in the array so that the value corresponding to indices `(j, k)` is placed in bd_bx[`j+k`(ny+1)]. For periodic boundary conditions (the value of BCtype[1] is 'P'), this parameter is not used, so it can accept a dummy pointer.
bd_ay	double* for d_commit_Helmholtz_2D/d_commit_Helmholtz_3D and d_Helmholtz_2D/d_Helmholtz_3D, float* for s_commit_Helmholtz_2D/s_commit_Helmholtz_3D and s_Helmholtz_2D/s_Helmholtz_3D. Contains values of the boundary condition on the leftmost boundary of the domain along the `y`-axis. 2D problem: the size of the array is nx+1. Its contents depend on the boundary conditions as follows: Dirichlet boundary condition (value of BCtype[2] is 'D'): values of the function `G`(`x`_i, ay), `i`=0, ..., nx. Neumann boundary condition (value of BCtype[2] is 'N'): values of the function `g`(`x`_i, ay), `i`=0, ..., nx. The value corresponding to the index `i` is placed in bd_ay[`i`]. 3D problem: the size of the array is (nx+1)(nz+1). Its contents depend on the boundary conditions as follows: Dirichlet boundary condition (value of BCtype[2] is 'D'): values of the function `G`(`x`_i,ay, `z`_k), `i`=0, ..., nx, `k`=0, ..., nz. Neumann boundary condition (value of BCtype[2] is 'N'): values of the function `g`(`x`_i,ay, `z`_k), `i`=0, ..., nx, `k`=0, ..., nz. The values are packed in the array so that the value corresponding to indices `(i, k)` is placed in bd_ay[`i+k`(nx+1)]. For periodic boundary conditions (the value of BCtype[2] is 'P'), this parameter is not used, so it can accept a dummy pointer.
bd_by	double* for d_commit_Helmholtz_2D/d_commit_Helmholtz_3D and d_Helmholtz_2D/d_Helmholtz_3D, float* for s_commit_Helmholtz_2D/s_commit_Helmholtz_3D and s_Helmholtz_2D/s_Helmholtz_3D. Contains values of the boundary condition on the rightmost boundary of the domain along the `y`-axis. 2D problem: the size of the array is nx+1. Its contents depend on the boundary conditions as follows: Dirichlet boundary condition (value of BCtype[3] is 'D'): values of the function `G`(`x`_i, by), `i`=0, ..., nx. Neumann boundary condition (value of BCtype[3] is 'N'): values of the function `g`(`x`_i, by), `i`=0, ..., nx. The value corresponding to the index `i` is placed in bd_by[`i`]. 3D problem: the size of the array is (nx+1)(nz+1). Its contents depend on the boundary conditions as follows: Dirichlet boundary condition (value of BCtype[3] is 'D'): values of the function `G`(`x`_i,by, `z`_k), `i`=0, ..., nx, `k`=0, ..., nz. Neumann boundary condition (value of BCtype[3] is 'N'): values of the function `g`(`x`_i,by, `z`_k), `i`=0, ..., nx, `k`=0, ..., nz. The values are packed in the array so that the value corresponding to indices `(i, k)` is placed in bd_by[`i+k`(nx+1)]. For periodic boundary conditions (the value of BCtype[3] is 'P'), this parameter is not used, so it can accept a dummy pointer.
bd_az	double* for d_commit_Helmholtz_3D and d_Helmholtz_3D, float* for s_commit_Helmholtz_3D and s_Helmholtz_3D. Used only by ?_commit_Helmholtz_3D and ?_Helmholtz_3D. Contains values of the boundary condition on the leftmost boundary of the domain along the `z`-axis. The size of the array is (nx+1)(ny+1). Its contents depend on the boundary conditions as follows: Dirichlet boundary condition (value of BCtype[4] is 'D'): values of the function `G`(`x`_i, `y`_j,az), `i`=0, ..., nx, `j`=0, ..., ny. Neumann boundary condition (value of BCtype[4] is 'N'), values of the function `g`(`x`_i, `y`_j,az), `i`=0, ..., nx, `j`=0, ..., ny. The values are packed in the array so that the value corresponding to indices `(i, j)` is placed in bd_az[`i+j`(nx+1)]. For periodic boundary conditions (the value of BCtype[4] is 'P'), this parameter is not used, so it can accept a dummy pointer.
bd_bz	double* for d_commit_Helmholtz_3D and d_Helmholtz_3D, float* for s_commit_Helmholtz_3D and s_Helmholtz_3D. Used only by ?_commit_Helmholtz_3D and ?_Helmholtz_3D. Contains values of the boundary condition on the rightmost boundary of the domain along the `z`-axis. The size of the array is (nx+1)(ny+1). Its contents depend on the boundary conditions as follows: Dirichlet boundary condition (value of BCtype[5] is 'D'): values of the function `G`(`x`_i, `y`_j,bz), `i`=0, ..., nx, `j`=0, ..., ny. Neumann boundary condition (value of BCtype[5] is 'N'): values of the function `g`(`x`_i, `y`_j,bz), `i`=0, ..., nx, `j`=0, ..., ny. The values are packed in the array so that the value corresponding to indices `(i, j)` is placed in bd_bz[`i+j`(nx+1)]. For periodic boundary conditions (the value of BCtype[5] is 'P'), this parameter is not used, so it can accept a dummy pointer.

Parent topic: Common Parameters for the Poisson Solver

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Developer Reference for Intel® oneAPI Math Kernel Library for C

Parameters That Define Boundary Conditions

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