forked from johannesgerer/jburkardt-cpp
-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathfem2d_sample.html
379 lines (342 loc) · 10.5 KB
/
fem2d_sample.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
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
<html>
<head>
<title>
FEM2D_SAMPLE - Evaluate a Finite Element Function of a 2D Argument
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
FEM2D_SAMPLE <br> Evaluate a Finite Element Function of a 2D Argument
</h1>
<hr>
<p>
<b>FEM2D_SAMPLE</b>
is a C++ program which
can evaluate a finite element function of a 2D argument.
</p>
<p>
The current version of the program can only handle finite element
meshes which are made of piecewise linear triangles of order 3 or 6.
</p>
<h3 align = "center">
Usage:
</h3>
<p>
<blockquote>
<b>fem2d_sample</b> <i>fem_prefix</i> <i>sample_prefix</i>
</blockquote>
where <i>fem_prefix</i> is the common prefix for the FEM files:
<ul>
<li>
<i>fem_prefix</i><b>_nodes.txt</b>, the node coordinates.
</li>
<li>
<i>fem_prefix</i><b>_elements.txt</b>, the nodes that make up each element;
</li>
<li>
<i>fem_prefix</i><b>_values.txt</b>, the values defined at each node.
</li>
</ul>
and <i>sample_prefix</i> is the common prefix for the SAMPLE files,
for which the node file is input, and the values file is created by the program:
<ul>
<li>
<i>sample_prefix</i><b>_nodes.txt</b>, the node coordinates where samples are desired.
</li>
<li>
<i>sample_prefix</i><b>_values.txt</b>, the values computed at each sample node.
</li>
</ul>
</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>FEM2D_SAMPLE</b> is available in
<a href = "../../cpp_src/fem2d_sample/fem2d_sample.html">a C++ version</a> and
<a href = "../../f77_src/fem2d_sample/fem2d_sample.html">a FORTRAN77 version</a> and
<a href = "../../f_src/fem2d_sample/fem2d_sample.html">a FORTRAN90 version</a> and
<a href = "../../m_src/fem2d_sample/fem2d_sample.html">a MATLAB version.</a>
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../cpp_src/discrete_pdf_sample_2d/discrete_pdf_sample_2d.html">
DISCRETE_PDF_SAMPLE_2D</a>,
a C++ program which
demonstrates how to construct a Probability Density Function (PDF)
from a table of sample data, and then to use that PDF to create new samples.
</p>
<p>
<a href = "../../cpp_src/fem1d_sample/fem1d_sample.html">
FEM1D_SAMPLE</a>,
a C++ program which
samples a scalar or vector finite element function of one variable,
defined by FEM files,
returning interpolated values at the sample points.
</p>
<p>
<a href = "../../data/fem2d/fem2d.html">
FEM2D</a>,
a data directory which
contains examples of 2D FEM files,
three text files that describe a 2D finite element geometry;
</p>
<p>
<a href = "../../cpp_src/fem2d_heat/fem2d_heat.html">
FEM2D_HEAT</a>,
a C++ program which
solves the
time dependent heat equation in the unit square.
</p>
<p>
<a href = "../../cpp_src/fem2d_pack/fem2d_pack.html">
FEM2D_PACK</a>,
a C++ library which
includes utitlies for 2D finite element calculations.
</p>
<p>
<a href = "../../cpp_src/fem2d_poisson/fem2d_poisson.html">
FEM2D_POISSON</a>,
a C++ program which
solves Poisson's equation
on a square, using the finite element method.
</p>
<p>
<a href = "../../cpp_src/fem2d_poisson_linear/fem2d_poisson_linear.html">
FEM2D_POISSON_LINEAR</a>,
a C++ program which
solves the 2D Poisson equation on a rectangle, using the finite element method,
and piecewise linear triangular elements.
</p>
<p>
<a href = "../../cpp_src/fem2d_project/fem2d_project.html">
FEM2D_PROJECT</a>,
a C++ program which
projects a function F(X,Y) into a given finite element space
of piecewise linear triangular elements.
</p>
<p>
<a href = "../../cpp_src/fem3d_sample/fem3d_sample.html">
FEM3D_SAMPLE</a>,
a C++ program which
evaluates a finite element function defined on 3D tetrahedral mesh.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Hans Rudolf Schwarz,<br>
Finite Element Methods,<br>
Academic Press, 1988,<br>
ISBN: 0126330107,<br>
LC: TA347.F5.S3313.
</li>
<li>
Gilbert Strang, George Fix,<br>
An Analysis of the Finite Element Method,<br>
Cambridge, 1973,<br>
ISBN: 096140888X,<br>
LC: TA335.S77.
</li>
<li>
Olgierd Zienkiewicz,<br>
The Finite Element Method,<br>
Sixth Edition,<br>
Butterworth-Heinemann, 2005,<br>
ISBN: 0750663200,<br>
LC: TA640.2.Z54.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "fem2d_sample.cpp">fem2d_sample.cpp</a>, the source code.
</li>
<li>
<a href = "fem2d_sample.sh">fem2d_sample.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<b>SQ</b> is FEM data for the function f(x,y)=x^2+y^2, on a 5x5 grid
of nodes, organized into linear triangles. The sample data seeks the values
of this function on a 4x4 evenly spaced grid.
<ul>
<li>
<a href = "fem_sq_nodes.txt">fem_sq_nodes.txt</a>,
defines the FEM nodes.
</li>
<li>
<a href = "fem_sq_elements.txt">fem_sq_elements.txt</a>,
defines the FEM elements.
</li>
<li>
<a href = "fem_sq_values.txt">fem_sq_values.txt</a>,
defines the FEM nodal values.
</li>
<li>
<a href = "sample_sq_nodes.txt">sample_sq_nodes.txt</a>,
defines the sample nodes.
</li>
<li>
<a href = "sample_sq_values.txt">sample_sq_values.txt</a>,
defines the sample nodal values.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>MAIN</b> is the main program for FEM2D_SAMPLE.
</li>
<li>
<b>BASIS_MN_T3:</b> all bases at N points for a T3 element.
</li>
<li>
<b>BASIS_MN_T6:</b> all bases at N points for a T6 element.
</li>
<li>
<b>CH_CAP</b> capitalizes a single character.
</li>
<li>
<b>CH_EQI</b> is true if two characters are equal, disregarding case.
</li>
<li>
<b>CH_TO_DIGIT</b> returns the integer value of a base 10 digit.
</li>
<li>
<b>GRID_SAMPLE</b> samples a (scalar) FE function on a T3 or T6 triangulation.
</li>
<li>
<b>FILE_COLUMN_COUNT</b> counts the number of columns in the first line of a file.
</li>
<li>
<b>FILE_ROW_COUNT</b> counts the number of row records in a file.
</li>
<li>
<b>GET_SEED</b> returns a random seed for the random number generator.
</li>
<li>
<b>I4_MAX</b> returns the maximum of two integers.
</li>
<li>
<b>I4_MIN</b> returns the smaller of two integers.
</li>
<li>
<b>I4_UNIFORM</b> returns a scaled pseudorandom I4.
</li>
<li>
<b>I4COL_COMPARE</b> compares columns I and J of an I4COL.
</li>
<li>
<b>I4COL_SORT_A</b> ascending sorts an I4COL.
</li>
<li>
<b>I4COL_SWAP</b> swaps two columns of an I4COL.
</li>
<li>
<b>I4MAT_DATA_READ</b> reads data from an I4MAT file.
</li>
<li>
<b>I4MAT_HEADER_READ</b> reads the header from an I4MAT file.
</li>
<li>
<b>R4_ABS</b> returns the absolute value of an R4.
</li>
<li>
<b>R4_NINT</b> returns the nearest integer to an R4.
</li>
<li>
<b>R4_UNIFORM_01</b> returns a unit pseudorandom R4.
</li>
<li>
<b>R8_HUGE</b> returns a "huge" R8.
</li>
<li>
<b>R8_MAX</b> returns the maximum of two R8's.
</li>
<li>
<b>R8_MIN</b> returns the minimum of two R8's.
</li>
<li>
<b>R8_NINT</b> returns the nearest integer to an R8.
</li>
<li>
<b>R8MAT_DATA_READ</b> reads the data from an R8MAT file.
</li>
<li>
<b>R8MAT_HEADER_READ</b> reads the header from an R8MAT file.
</li>
<li>
<b>R8MAT_WRITE</b> writes an R8MAT file.
</li>
<li>
<b>S_LEN_TRIM</b> returns the length of a string to the last nonblank.
</li>
<li>
<b>S_TO_I4</b> reads an I4 from a string.
</li>
<li>
<b>S_TO_I4VEC</b> reads an I4VEC from a string.
</li>
<li>
<b>S_TO_R8</b> reads an R8 from a string.
</li>
<li>
<b>S_TO_R8VEC</b> reads an R8VEC from a string.
</li>
<li>
<b>S_WORD_COUNT</b> counts the number of "words" in a string.
</li>
<li>
<b>SORT_HEAP_EXTERNAL</b> externally sorts a list of items into ascending order.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
<li>
<b>TRIANGULATION_ORDER3_NEIGHBOR_TRIANGLES</b> determines triangle neighbors.
</li>
<li>
<b>TRIANGULATION_ORDER6_NEIGHBOR_TRIANGLES</b> determines triangle neighbors.
</li>
<li>
<b>TRIANGULATION_SEARCH_DELAUNAY</b> searches a triangulation for a point.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../cpp_src.html">
the C++ source codes</a>.
</p>
<hr>
<i>
Last revised on 08 August 2009.
</i>
<!-- John Burkardt -->
</body>
<!-- Initial HTML skeleton created by HTMLINDEX. -->
</html>