Contents

# 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
 is 'D'): values of the function
G
(
ax
,
y
j
),
j
=0, ...,
ny
.
• Neumann boundary condition (value of
BCtype
 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
 is 'D'): values of the function
G
(
ax
,
y
j
,
z
k
),
j
=0, ...,
ny
,
k
=0, ...,
nz
.
• Neumann boundary condition (value of
BCtype
 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
 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
 is 'D'): values of the function
G
(
bx
,
y
j
),
j
=0, ...,
ny
.
• Neumann boundary condition (value of
BCtype
 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
 is 'D'): values of the function
G
(
bx
,
y
j
,
z
k
),
j
=0, ...,
ny
,
k
=0, ...,
nz
.
• Neumann boundary condition (value of
BCtype
 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
 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
 is 'D'): values of the function
G
(
x
i
,
ay
),
i
=0, ...,
nx
.
• Neumann boundary condition (value of
BCtype
 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
 is 'D'): values of the function
G
(
x
i
,
ay
,
z
k
),
i
=0, ...,
nx
,
k
=0, ...,
nz
.
• Neumann boundary condition (value of
BCtype
 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
 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
 is 'D'): values of the function
G
(
x
i
,
by
),
i
=0, ...,
nx
.
• Neumann boundary condition (value of
BCtype
 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
 is 'D'): values of the function
G
(
x
i
,
by
,
z
k
),
i
=0, ...,
nx
,
k
=0, ...,
nz
.
• Neumann boundary condition (value of
BCtype
 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
 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
 is 'D'): values of the function
G
(
x
i
,
y
j
,
az
),
i
=0, ...,
nx
,
j
=0, ...,
ny
.
• Neumann boundary condition (value of
BCtype
 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
 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
 is 'D'): values of the function
G
(
x
i
,
y
j
,
bz
),
i
=0, ...,
nx
,
j
=0, ...,
ny
.
• Neumann boundary condition (value of
BCtype
 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
 is 'P'), this parameter is not used, so it can accept a dummy pointer.

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