-
Notifications
You must be signed in to change notification settings - Fork 41
/
fem1d_sample.html
370 lines (329 loc) · 10.3 KB
/
fem1d_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
<html>
<head>
<title>
FEM1D_SAMPLE - Evaluate a Finite Element Function of a 1D Argument
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
FEM1D_SAMPLE <br> Evaluate a Finite Element Function of a 1D Argument
</h1>
<hr>
<p>
<b>FEM1D_SAMPLE</b>
is a C++ program which
can evaluate a finite element function of one argument.
</p>
<p>
The current version of the program can only handle finite element
meshes which are made of piecewise constant or piecewise linear basis functions.
</p>
<h3 align = "center">
Usage:
</h3>
<p>
<blockquote>
<b>fem1d_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>FEM1D_SAMPLE</b> is available in
<a href = "../../c_src/fem1d_sample/fem1d_sample.html">a C version</a> and
<a href = "../../cpp_src/fem1d_sample/fem1d_sample.html">a C++ version</a> and
<a href = "../../f77_src/fem1d_sample/fem1d_sample.html">a FORTRAN77 version</a> and
<a href = "../../f_src/fem1d_sample/fem1d_sample.html">a FORTRAN90 version</a> and
<a href = "../../m_src/fem1d_sample/fem1d_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 = "../../data/fem1d/fem1d.html">
FEM1D</a>,
a data directory which
contains examples of 1D FEM files,
three text files that describe a 1D finite element model;
</p>
<p>
<a href = "../../cpp_src/fem1d/fem1d.html">
FEM1D</a>,
a C++ program which
applies the finite element method to a 1D linear two point boundary value problem.
</p>
<p>
<a href = "../../cpp_src/fem1d_adaptive/fem1d_adaptive.html">
FEM1D_ADAPTIVE</a>,
a C++ program which
applies the finite element method to a 1D linear two point boundary value problem
using adaptive refinement to improve the solution.
</p>
<p>
<a href = "../../cpp_src/fem1d_bvp_linear/fem1d_bvp_linear.html">
FEM1D_BVP_LINEAR</a>,
a C++ program which
applies the finite element method, with piecewise linear elements,
to a two point boundary value problem in one spatial dimension.
</p>
<p>
<a href = "../../cpp_src/fem1d_heat_steady/fem1d_heat_steady.html">
FEM1D_HEAT_STEADY</a>,
a C++ program which
uses the finite element method to solve the steady (time independent)
heat equation in 1D.
</p>
<p>
<a href = "../../cpp_src/fem1d_nonlinear/fem1d_nonlinear.html">
FEM1D_NONLINEAR</a>,
a C++ program which
applies the finite element method to a 1D nonlinear two point boundary value problem.
</p>
<p>
<a href = "../../cpp_src/fem1d_pack/fem1d_pack.html">
FEM1D_PACK</a>,
a C++ library which
contains utilities for 1D finite element calculations.
</p>
<p>
<a href = "../../cpp_src/fem1d_pmethod/fem1d_pmethod.html">
FEM1D_PMETHOD</a>,
a C++ program which
applies the p-method version of the finite element method to a 1D linear
two point boundary value problem.
</p>
<p>
<a href = "../../cpp_src/fem1d_project/fem1d_project.html">
FEM1D_PROJECT</a>,
a C++ program which
projects data into a finite element space, including the least squares
approximation of data, or the projection of a finite element solution
from one mesh to another.
</p>
<p>
<a href = "../../cpp_src/fem2d_sample/fem2d_sample.html">
FEM2D_SAMPLE</a>,
a C++ library which
evaluates a finite element function defined on an order 3 or order 6 triangulation.
</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 = "fem1d_sample.cpp">fem1d_sample.cpp</a>, the source code.
</li>
<li>
<a href = "fem1d_sample.sh">fem1d_sample.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<b>P1</b> is FEM data for the vector function f(x)=[ 1, x, x^2], on a grid of 11
evenly spaced nodes from -5 to 5, using piecewise constant basis functions.
<ul>
<li>
<a href = "p1_fem_nodes.txt">p1_fem_nodes.txt</a>,
the FEM nodes.
</li>
<li>
<a href = "p1_fem_elements.txt">p1_fem_elements.txt</a>,
the FEM elements.
</li>
<li>
<a href = "p1_fem_values.txt">p1_fem_values.txt</a>,
the FEM nodal values.
</li>
<li>
<a href = "p1_sample_nodes.txt">p1_sample_nodes.txt</a>,
the sample nodes.
</li>
<li>
<a href = "p1_sample_values.txt">p1_sample_values.txt</a>,
the sample nodal values.
</li>
</ul>
</p>
<p>
<b>P2</b> is FEM data for the vector function f(x)=[ 1, x, x^2], on a grid of 11
evenly spaced nodes from -5 to 5, using piecewise linear basis functions.
<ul>
<li>
<a href = "p2_fem_nodes.txt">p2_fem_nodes.txt</a>,
the FEM nodes.
</li>
<li>
<a href = "p2_fem_elements.txt">p2_fem_elements.txt</a>,
the FEM elements.
</li>
<li>
<a href = "p2_fem_values.txt">p2_fem_values.txt</a>,
the FEM nodal values.
</li>
<li>
<a href = "p2_sample_nodes.txt">p2_sample_nodes.txt</a>,
the sample nodes.
</li>
<li>
<a href = "p2_sample_values.txt">p2_sample_values.txt</a>,
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 FEM1D_SAMPLE.
</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>FEM1D_EVALUATE</b> evaluates a 1D FEM function at sample points.
</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>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>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>R8VEC_BRACKET4</b> finds the interval containing or nearest a given value.
</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>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</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 04 July 2013.
</i>
<!-- John Burkardt -->
</body>
<!-- Initial HTML skeleton created by HTMLINDEX. -->
</html>