-
Notifications
You must be signed in to change notification settings - Fork 59
/
quad_mesh.html
463 lines (425 loc) · 13 KB
/
quad_mesh.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
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
<html>
<head>
<title>
QUAD_MESH - Quadrilateral Meshes
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
QUAD_MESH <br> Quadrilateral Meshes
</h1>
<hr>
<p>
<b>QUAD_MESH</b>
is a FORTRAN90 library which
carries out operations involving meshes of quadrilaterals.
</p>
<p>
The mesh is the collection of quadrilaterals. Each quadrilateral
is termed an "element". The points used to define the shape of the
quadrilateral (the corners, and sometimes a few more points) are called
the "nodes".
</p>
<p>
Routines are available to:
<ul>
<li>
evaluate "quality measures" for the mesh;
</li>
<li>
create a "node neighbor array" for each node;
</li>
<li>
create an "element neighbor array" for each element;
</li>
<li>
estimate the integral of a function over the region covered by the mesh;
</li>
<li>
plot the nodes and elements of a mesh;
</li>
<li>
determine the parts of the mesh that lie on the boundary;
</li>
<li>
sample points at random from the region covered by the mesh;
</li>
<li>
search a mesh to determine which element contains a point.
</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>QUAD_MESH</b> is available in
<a href = "../../cpp_src/quad_mesh/quad_mesh.html">a C++ version</a> and
<a href = "../../f_src/quad_mesh/quad_mesh.html">a FORTRAN90 version</a> and
<a href = "../../m_src/quad_mesh/quad_mesh.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../data/fem2d/fem2d.html">
FEM2D</a>,
a data directory which
contains a description and examples of files that describe a 2D finite element model.
</p>
<p>
<a href = "../../f_src/fem_io/fem_io.html">
FEM_IO</a>,
a FORTRAN90 library which
reads or writes node, element and data files defining a finite element model.
</p>
<p>
<a href = "../../f_src/mesh_bandwidth/mesh_bandwidth.html">
MESH_BANDWIDTH</a>,
a FORTRAN90 program which
returns the geometric bandwidth associated with a mesh of
elements of any order and in a space of arbitrary dimension.
</p>
<p>
<a href = "../../m_src/mesh_display/mesh_display.html">
MESH_DISPLAY</a>,
a MATLAB program which
reads data defining a polygonal mesh and displays it, with optional numbering.
</p>
<p>
<a href = "../../cpp_src/mesh_display_opengl/mesh_display_opengl.html">
MESH_DISPLAY_OPENGL</a>,
a C++ program which
reads files defining a polygonal mesh and displays an image using OpenGL.
</p>
<p>
<a href = "../../data/quad_mesh/quad_mesh.html">
QUAD_MESH</a>,
a data directory which
defines a format for storing meshes of quadrilaterals over a 2D region.
</p>
<p>
<a href = "../../f_src/quad_mesh_rcm/quad_mesh_rcm.html">
QUAD_MESH_RCM</a>,
a FORTRAN90 program which
computes the reverse Cuthill-McKee (RCM) reordering for nodes in a mesh of 4-node
quadrilaterals.
</p>
<p>
<a href = "../../f_src/triangulation/triangulation.html">
TRIANGULATION</a>,
a FORTRAN90 library which
carries out operations involving meshes of triangular elements.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Hans Rudolf Schwarz,<br>
Methode der Finiten Elemente,<br>
Teubner Studienbuecher, 1980,<br>
ISBN: 3-519-02349-0.
</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>
TA640.2.Z54
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "quad_mesh.f90">quad_mesh.f90</a>, the source code.
</li>
<li>
<a href = "quad_mesh.sh">quad_mesh.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "quad_mesh_prb.f90">quad_mesh_prb.f90</a>,
a sample calling program.
</li>
<li>
<a href = "quad_mesh_prb.sh">quad_mesh_prb.sh</a>,
commands to compile and run the sample program.
</li>
<li>
<a href = "quad_mesh_prb_output.txt">quad_mesh_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<p>
<b>EXAMPLE1</b> is a mesh made up of squares of uniform size. The squares
are arranged in a grid with a few irregularities, however. In particular,
there is an interior hole.
<ul>
<li>
<a href = "q4_mesh_ex1_element_neighbors.txt">q4_mesh_ex1_element_neighbors.txt</a>,
element neighbors for example 1 Q4 mesh.
</li>
<li>
<a href = "q4_mesh_ex1_elements.txt">q4_mesh_ex1_elements.txt</a>,
elements for example 1 Q4 mesh.
</li>
<li>
<a href = "q4_mesh_ex1_xy.txt">q4_mesh_ex1_xy.txt</a>,
node coordinates for example 1 Q4 mesh.
</li>
<li>
<a href = "q4_mesh_ex1.png">q4_mesh_ex1.png</a>,
a PNG image of example 1 Q4 mesh.
</li>
</ul>
</p>
<p>
<b>EXAMPLE2</b> is a mesh made up of quadrilaterals that are "trying" to tile a
semicircle. The row of elements that touches the origin is degenerate, and
are essentially triangles. The elements vary in area.
<ul>
<li>
<a href = "q4_mesh_ex2_element_neighbors.txt">q4_mesh_ex2_element_neighbors.txt</a>,
element neighbors for example 2 Q4 mesh.
</li>
<li>
<a href = "q4_mesh_ex2_elements.txt">q4_mesh_ex2_elements.txt</a>,
elements for example 2 Q4 mesh.
</li>
<li>
<a href = "q4_mesh_ex2_xy.txt">q4_mesh_ex2_xy.txt</a>,
node coordinates for example 2 Q4 mesh.
</li>
<li>
<a href = "q4_mesh_ex2.png">q4_mesh_ex2.png</a>,
a PNG image of example 2 Q4 mesh.
</li>
</ul>
</p>
<p>
<b>SAMPLE_QUAD</b> demonstrates how a single quadrilateral can be randomly sampled.
<ul>
<li>
<a href = "sample_quad.txt">sample_quad.txt</a>,
node coordinates for random sample points in a quadrilateral.
</li>
<li>
<a href = "sample_quad.png">sample_quad.png</a>,
a PNG image of the random sample points in a quadrilateral.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>ADJ_SET_Q4_MESH</b> sets adjacencies in a Q4 mesh.
</li>
<li>
<b>ADJ_SIZE_Q4_MESH</b> counts adjacencies in a Q4 mesh.
</li>
<li>
<b>AREA_Q4_MESH</b> computes areas of elements in a Q4 mesh.
</li>
<li>
<b>AREA_QUAD</b> returns the area of a quadrilateral.
</li>
<li>
<b>BANDWIDTH</b> determines the bandwidth associated with a finite element mesh.
</li>
<li>
<b>BOUNDARY_EDGE_COUNT_Q4_MESH</b> counts the boundary edges.
</li>
<li>
<b>BOUNDARY_EDGE_COUNT_EULER_Q4_MESH</b> counts boundary edges by Euler's formula.
</li>
<li>
<b>CH_CAP</b> capitalizes a single character.
</li>
<li>
<b>CH_EQI</b> is a case insensitive comparison of two characters for equality.
</li>
<li>
<b>CH_TO_DIGIT</b> returns the integer value of a base 10 digit.
</li>
<li>
<b>EXAMPLE1_Q4_MESH</b> sets up example #1 Q4 mesh.
</li>
<li>
<b>EXAMPLE1_Q4_MESH_SIZE</b> sets sizes for example #1 Q4 mesh.
</li>
<li>
<b>EXAMPLE2_Q4_MESH</b> sets up example #2 Q4 mesh.
</li>
<li>
<b>EXAMPLE2_Q4_MESH_SIZE</b> sets sizes for example #2 Q4 mesh.
</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_UNIT</b> returns a free FORTRAN unit number.
</li>
<li>
<b>I4_MODP</b> returns the nonnegative remainder of I4 division.
</li>
<li>
<b>I4_WRAP</b> forces an I4 to lie between given limits by wrapping.
</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_SORTED_UNIQUE_COUNT</b> counts unique elements in an I4COL.
</li>
<li>
<b>I4COL_SWAP</b> swaps columns I and J 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.
</li>
<li>
<b>I4MAT_TRANSPOSE_PRINT</b> prints an I4MAT, transposed.
</li>
<li>
<b>I4MAT_TRANSPOSE_PRINT_SOME</b> prints some of the transpose of an I4MAT.
</li>
<li>
<b>I4MAT_WRITE</b> writes an I4MAT file.
</li>
<li>
<b>I4VEC_PRINT</b> prints an I4VEC.
</li>
<li>
<b>MESH_BASE_ONE</b> ensures that the element definition is one-based.
</li>
<li>
<b>NEIGHBOR_ELEMENTS_Q4_MESH</b> determines element neighbors in a Q4 mesh.
</li>
<li>
<b>NODE_ORDER_Q4_MESH</b> determines the order of nodes in a Q4 mesh.
</li>
<li>
<b>PLOT_Q4_MESH</b> plots a Q4 mesh.
</li>
<li>
<b>R8_UNIFORM_01</b> returns a unit pseudorandom R8.
</li>
<li>
<b>R8MAT_DATA_READ</b> reads data from an R8MAT file.
</li>
<li>
<b>R8MAT_HEADER_READ</b> reads the header from an R8MAT file.
</li>
<li>
<b>R8MAT_TRANSPOSE_PRINT</b> prints an R8MAT, transposed.
</li>
<li>
<b>R8MAT_TRANSPOSE_PRINT_SOME</b> prints some of an R8MAT, transposed.
</li>
<li>
<b>R8MAT_WRITE</b> writes an R8MAT file.
</li>
<li>
<b>R8VEC_BRACKET</b> searches a sorted R8VEC for successive brackets of a value.
</li>
<li>
<b>R8VEC_PRINT</b> prints an R8VEC.
</li>
<li>
<b>R8VEC_UNIFORM_01</b> returns a unit pseudorandom R8VEC.
</li>
<li>
<b>REFERENCE_TO_PHYSICAL_Q4</b> maps Q4 reference points to physical points.
</li>
<li>
<b>S_BLANK_DELETE</b> removes blanks from a string, left justifying the remainder.
</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>SAMPLE_Q4_MESH</b> returns random points in a Q4 mesh.
</li>
<li>
<b>SAMPLE_QUAD</b> returns random points in a quadrilateral.
</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>TRIANGLE_AREA</b> computes the area of a triangle.
</li>
<li>
<b>TRIANGLE_SAMPLE</b> returns random points in a triangle.
</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 29 September 2009.
</i>
<!-- John Burkardt -->
</body>
<!-- Initial HTML skeleton created by HTMLINDEX. -->
</html>