forked from johannesgerer/jburkardt-f
-
Notifications
You must be signed in to change notification settings - Fork 1
/
poisson_serial.html
227 lines (194 loc) · 6.54 KB
/
poisson_serial.html
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
<html>
<head>
<title>
POISSON_SERIAL - A Program for the Poisson Equation in a Rectangle
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
POISSON_SERIAL <br> A Program for the Poisson Equation in a Rectangle
</h1>
<hr>
<p>
<b>POISSON_SERIAL</b>
is a FORTRAN90 program which
computes an approximate solution to the Poisson equation in a rectangular region.
</p>
<p>
The version of Poisson's equation being solved here is
<pre>
- ( d/dx d/dx + d/dy d/dy ) U(x,y) = F(x,y)
</pre>
over the rectangle 0 <= X <= 1, 0 <= Y <= 1, with exact solution
<pre>
U(x,y) = sin ( pi * x * y )
</pre>
so that
<pre>
F(x,y) = pi^2 * ( x^2 + y^2 ) * sin ( pi * x * y )
</pre>
and with Dirichlet boundary conditions along the lines x = 0, x = 1,
y = 0 and y = 1. (The boundary conditions will actually be zero in
this case, but we write up the problem as though we didn't know that,
which makes it easy to change the problem later.)
</p>
<p>
We compute an approximate solution by discretizing the geometry,
assuming that DX = DY, and approximating the Poisson operator by
<pre>
( U(i-1,j) + U(i+1,j) + U(i,j-1) + U(i,j+1) - 4*U(i,j) ) / dx /dy
</pre>
Along with the boundary conditions at the boundary nodes, we have
a linear system for U. We can apply the Jacobi iteration to estimate
the solution to the linear system.
</p>
<p>
<b>POISSON_SERIAL</b> is intended as a starting point for the implementation of a
parallel version, using, for instance, MPI.
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this
web page are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>POISSON_SERIAL</b> is available in
<a href = "../../c_src/poisson_serial/poisson_serial.html">a C version</a> and
<a href = "../../cpp_src/poisson_serial/poisson_serial.html">a C++ version</a> and
<a href = "../../f77_src/poisson_serial/poisson_serial.html">a FORTRAN77 version</a> and
<a href = "../../f_src/poisson_serial/poisson_serial.html">a FORTRAN90 version</a> and
<a href = "../../m_src/poisson_serial/poisson_serial.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/fem2d_poisson_rectangle/fem2d_poisson_rectangle.html">
FEM2D_POISSON_RECTANGLE</a>,
a FORTRAN90 program which
solves the 2D Poisson equation on a rectangle,
using the finite element method,
and piecewise quadratic triangular elements.
</p>
<p>
<a href = "../../f_src/fft_serial/fft_serial.html">
FFT_SERIAL</a>,
a FORTRAN90 program which
demonstrates the computation of a Fast Fourier Transform,
and is intended as a starting point for implementing a parallel version.
</p>
<p>
<a href = "../../f_src/heated_plate/heated_plate.html">
HEATED_PLATE</a>,
a FORTRAN90 program which
solves the steady (time independent) heat equation in a 2D
rectangular region, and is intended as
a starting point for implementing a parallel version.
</p>
<p>
<a href = "../../f_src/md/md.html">
MD</a>,
a FORTRAN90 program which
carries out a molecular dynamics simulation, and is intended as
a starting point for implementing a parallel version.
</p>
<p>
<a href = "../../f_src/mpi/mpi.html">
MPI</a>,
FORTRAN90 programs which
illustrate the use of the MPI application program interface
for carrying out parallel computations in a distributed memory environment.
</p>
<p>
<a href = "../../f_src/mxm_serial/mxm_serial.html">
MXM_SERIAL</a>,
a FORTRAN90 program which
sets up a matrix multiplication problem A=B*C,
intended as a starting point for implementing a parallel version.
</p>
<p>
<a href = "../../f_src/poisson_openmp/poisson_openmp.html">
POISSON_OPENMP</a>,
a FORTRAN90 program which
computes an approximate solution to the Poisson equation in a rectangle,
using the Jacobi iteration to solve the linear system, and OpenMP to
carry out the Jacobi iteration in parallel.
</p>
<p>
<a href = "../../f_src/prime_serial/prime_serial.html">
PRIME_SERIAL</a>,
a FORTRAN90 program which
counts the number of primes between 1 and N,
intended as a starting point for the creation of a parallel version.
</p>
<p>
<a href = "../../f_src/quad_serial/quad_serial.html">
QUAD_SERIAL</a>,
a FORTRAN90 program which
approximates an integral using a quadrature rule,
and is intended as a starting point for parallelization exercises.
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "poisson_serial.f90">poisson_serial.f90</a>, the source code.
</li>
<li>
<a href = "poisson_serial.sh">poisson_serial.sh</a>,
BASH commands to compile the source code.
</li>
<li>
<a href = "poisson_serial_output.txt">poisson_serial_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>MAIN</b> is the main program for POISSON_SERIAL.
</li>
<li>
<b>R8VEC_NORM</b> returns the L2 norm of an R8VEC.
</li>
<li>
<b>RHS</b> initializes the right hand side "vector".
</li>
<li>
<b>SWEEP</b> carries out one step of the Jacobi iteration.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
<li>
<b>U_EXACT</b> evaluates the exact solution.
</li>
<li>
<b>UXXYY_EXACT</b> evaluates - ( d/dx d/dx + d/dy d/dy ) of the exact solution.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../f_src.html">
the FORTRAN90 source codes</a>.
</p>
<hr>
<i>
Last revised on 23 October 2011.
</i>
<!-- John Burkardt -->
</body>
<!-- Initial HTML skeleton created by HTMLINDEX. -->
</html>