-
Notifications
You must be signed in to change notification settings - Fork 59
/
felippa.html
530 lines (483 loc) · 15.6 KB
/
felippa.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
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
<html>
<head>
<title>
FELIPPA - Finite Element Quadrature Rules
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
FELIPPA <br> Finite Element Quadrature Rules
</h1>
<hr>
<p>
<b>FELIPPA</b>
is a FORTRAN90 library which
generates the points and weights of a quadrature rule for a variety
of 1D, 2D and 3D regions of interest for computations
involving the finite element method (FEM).
</p>
<p>
Regions for which rules are available, with a count of Corners, Edges, and Faces, include:
<table border = 1>
<tr>
<th>Name</th><th>Acronym</th><th>C+E+F</th>
</tr>
<tr>
<td>Line segment</td><td><b>Line</b></td><td>2+1+0</td>
</tr>
<tr>
<td>Triangle</td><td><b>Trig</b></td><td>3+3+1</td>
</tr>
<tr>
<td>Quadrilateral</td><td><b>Quad</b></td><td>4+4+1</td>
</tr>
<tr>
<td>Tetrahedron</td><td><b>Tetr</b></td><td>4+6+4</td>
</tr>
<tr>
<td>Wedge</td><td><b>Wedg</b></td><td>6+9+5</td>
</tr>
<tr>
<td>Pyramid</td><td><b>Pyra</b></td><td>5+8+5</td>
</tr>
<tr>
<td>Hexahedron</td><td><b>Hexa</b></td><td>8+12+6</td>
</tr>
</table>
</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>FELIPPA</b> is available in
<a href = "../../cpp_src/felippa/felippa.html">a C++ version</a> and
<a href = "../../f_src/felippa/felippa.html">a FORTRAN90 version</a> and
<a href = "../../math_src/felippa/felippa.html">a MATHEMATICA version</a> and
<a href = "../../m_src/felippa/felippa.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/dunavant/dunavant.html">
DUNAVANT</a>,
a FORTRAN90 library which
defines Dunavant rules for quadrature on a triangle.
</p>
<p>
<a href = "../../f_src/fekete/fekete.html">
FEKETE</a>,
a FORTRAN90 library which
defines a Fekete rule for quadrature or interpolation over a triangle.
</p>
<p>
<a href = "../../f_src/gm_rule/gm_rule.html">
GM_RULE</a>,
a FORTRAN90 library which
defines Grundmann-Moeller rules for quadrature over a triangle, tetrahedron,
or general M-dimensional simplex.
</p>
<p>
<a href = "../../f_src/keast/keast.html">
KEAST</a>,
a FORTRAN90 library which
defines quadrature rules for a tetrahedron.
</p>
<p>
<a href = "../../f_src/lyness_rule/lyness_rule.html">
LYNESS_RULE</a>,
a FORTRAN90 library which
returns Lyness-Jespersen quadrature rules for the triangle.
</p>
<p>
<a href = "../../f_src/ncc_tetrahedron/ncc_tetrahedron.html">
NCC_TETRAHEDRON</a>,
a FORTRAN90 library which
defines Newton-Cotes closed quadrature rules on a tetrahedron.
</p>
<p>
<a href = "../../f_src/ncc_triangle/ncc_triangle.html">
NCC_TRIANGLE</a>,
a FORTRAN90 library which
defines Newton-Cotes closed quadrature rules on a triangle.
</p>
<p>
<a href = "../../f_src/nco_tetrahedron/nco_tetrahedron.html">
NCO_TETRAHEDRON</a>,
a FORTRAN90 library which
defines Newton-Cotes open quadrature rules on a tetrahedron.
</p>
<p>
<a href = "../../f_src/nco_triangle/nco_triangle.html">
NCO_TRIANGLE</a>,
a FORTRAN90 library which
defines Newton-Cotes open quadrature rules on a triangle.
</p>
<p>
<a href = "../../f_src/product_rule/product_rule.html">
PRODUCT_RULE</a>,
a FORTRAN90 program which
can create a multidimensional quadrature rule as a product of
one dimensional rules.
</p>
<p>
<a href = "../../f_src/pyramid_rule/pyramid_rule.html">
PYRAMID_RULE</a>,
a FORTRAN90 program which
computes a quadrature rule for a pyramid.
</p>
<p>
<a href = "../../datasets/quadrature_rules_pyramid/quadrature_rules_pyramid.html">
QUADRATURE_RULES_PYRAMID</a>,
a dataset directory which
contains quadrature rules for a pyramid with a square base.
</p>
<p>
<a href = "../../datasets/quadrature_rules_tet/quadrature_rules_tet.html">
QUADRATURE_RULES_TET</a>,
a dataset directory which
contains quadrature rules for tetrahedrons,
stored as a file of abscissas, a file of weights,
and a file of vertices.
</p>
<p>
<a href = "../../datasets/quadrature_rules_tri/quadrature_rules_tri.html">
QUADRATURE_RULES_TRI</a>,
a dataset directory which
contains quadrature rules for triangles,
stored as a file of abscissas, a file of weights,
and a file of vertices.
</p>
<p>
<a href = "../../datasets/quadrature_rules_wedge/quadrature_rules_wedge.html">
QUADRATURE_RULES_WEDGE</a>,
a dataset directory which
contains quadrature rules for a wedge (a triangle x a straight line).
</p>
<p>
<a href = "../../f_src/quadrule/quadrule.html">
QUADRULE</a>,
a FORTRAN90 library which
defines quadrature rules on a
variety of intervals with different weight functions.
</p>
<p>
<a href = "../../f_src/stroud/stroud.html">
STROUD</a>,
a FORTRAN90 library which
defines quadrature rules for a variety of unusual areas, surfaces and volumes in 2D,
3D and N-dimensions.
</p>
<p>
<a href = "../../f_src/tetrahedron_monte_carlo/tetrahedron_monte_carlo.html">
TETRAHEDRON_MONTE_CARLO</a>,
a FORTRAN90 program which
uses the Monte Carlo method to estimate integrals over a tetrahedron.
</p>
<p>
<a href = "../../datasets/tetrahedrons/tetrahedrons.html">
TETRAHEDRONS</a>,
a dataset directory which
contains examplesof tetrahedrons;
</p>
<p>
<a href = "../../f_src/triangle_monte_carlo/triangle_monte_carlo.html">
TRIANGLE_MONTE_CARLO</a>,
a FORTRAN90 program which
uses the Monte Carlo method to estimate integrals over a triangle.
</p>
<p>
<a href = "../../f_src/wandzura/wandzura.html">
WANDZURA</a>,
a FORTRAN90 library which
defines Wandzura rules for quadrature on a triangle.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Carlos Felippa,<br>
A compendium of FEM integration formulas for symbolic work,<br>
Engineering Computation,<br>
Volume 21, Number 8, 2004, pages 867-890.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "felippa.f90">felippa.f90</a>, the source code.
</li>
<li>
<a href = "felippa.sh">felippa.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "felippa_prb.f90">felippa_prb.f90</a>,
a sample calling program.
</li>
<li>
<a href = "felippa_prb.sh">felippa_prb.sh</a>,
commands to compile and run the sample program.
</li>
<li>
<a href = "felippa_prb_output.txt">felippa_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>COMP_NEXT</b> computes the compositions of the integer N into K parts.
</li>
<li>
<b>HEXA_UNIT_MONOMIAL</b> integrates a monomial over the unit hexahedron.
</li>
<li>
<b>HEXA_UNIT_MONOMIAL_TEST</b> tests HEXA_UNIT_MONOMIAL.
</li>
<li>
<b>HEXA_UNIT_QUAD_TEST</b> tests the rules for the unit hexahedron.
</li>
<li>
<b>HEXA_UNIT_RULE</b> returns a quadrature rule for the unit hexahedron.
</li>
<li>
<b>HEXA_UNIT_VOLUME:</b> volume of a unit hexahedron.
</li>
<li>
<b>LINE_UNIT_MONOMIAL:</b> monomial integral in a unit line.
</li>
<li>
<b>LINE_UNIT_MONOMIAL_TEST</b> tests LINE_UNIT_MONOMIAL.
</li>
<li>
<b>LINE_UNIT_O01</b> returns a 1 point quadrature rule for the unit line.
</li>
<li>
<b>LINE_UNIT_O02</b> returns a 2 point quadrature rule for the unit line.
</li>
<li>
<b>LINE_UNIT_O03</b> returns a 3 point quadrature rule for the unit line.
</li>
<li>
<b>LINE_UNIT_O04</b> returns a 4 point quadrature rule for the unit line.
</li>
<li>
<b>LINE_UNIT_O05</b> returns a 5 point quadrature rule for the unit line.
</li>
<li>
<b>LINE_UNIT_QUAD_TEST</b> tests the rules for the unit line.
</li>
<li>
<b>LINE_UNIT_VOLUME:</b> volume of a unit line.
</li>
<li>
<b>MONOMIAL_VALUE</b> evaluates a monomial.
</li>
<li>
<b>PYRA_UNIT_MONOMIAL:</b> monomial integral in a unit pyramid.
</li>
<li>
<b>PYRA_UNIT_MONOMIAL_TEST</b> tests PYRA_UNIT_MONOMIAL.
</li>
<li>
<b>PYRA_UNIT_O01</b> returns a 1 point quadrature rule for the unit pyramid.
</li>
<li>
<b>PYRA_UNIT_O05</b> returns a 5 point quadrature rule for the unit pyramid.
</li>
<li>
<b>PYRA_UNIT_O06</b> returns a 6 point quadrature rule for the unit pyramid.
</li>
<li>
<b>PYRA_UNIT_O08</b> returns an 8 point quadrature rule for the unit pyramid.
</li>
<li>
<b>PYRA_UNIT_O08B</b> returns an 8 point quadrature rule for the unit pyramid.
</li>
<li>
<b>PYRA_UNIT_O09</b> returns a 9 point quadrature rule for the unit pyramid.
</li>
<li>
<b>PYRA_UNIT_O13</b> returns a 13 point quadrature rule for the unit pyramid.
</li>
<li>
<b>PYRA_UNIT_O18</b> returns an 18 point quadrature rule for the unit pyramid.
</li>
<li>
<b>PYRA_UNIT_O27</b> returns a 27 point quadrature rule for the unit pyramid.
</li>
<li>
<b>PYRA_UNIT_O48</b> returns a 48 point quadrature rule for the unit pyramid.
</li>
<li>
<b>PYRA_UNIT_QUAD_TEST</b> tests the rules for the unit pyramid.
</li>
<li>
<b>PYRA_UNIT_VOLUME:</b> volume of a unit pyramid with square base.
</li>
<li>
<b>QUAD_UNIT_MONOMIAL</b> integrates a monomial over the unit quadrilateral.
</li>
<li>
<b>QUAD_UNIT_MONOMIAL_TEST</b> tests QUAD_UNIT_MONOMIAL.
</li>
<li>
<b>QUAD_UNIT_QUAD_TEST</b> tests the rules for the unit quadrilateral.
</li>
<li>
<b>QUAD_UNIT_RULE</b> returns a quadrature rule for the unit quadrilateral.
</li>
<li>
<b>QUAD_UNIT_VOLUME:</b> volume of a unit quadrilateral.
</li>
<li>
<b>R8_CHOOSE</b> computes the binomial coefficient C(N,K) as an R8.
</li>
<li>
<b>R8_MOP</b> returns the I-th power of -1 as an R8.
</li>
<li>
<b>R8MAT_DET_4D</b> computes the determinant of a 4 by 4 matrix.
</li>
<li>
<b>R8MAT_WRITE</b> writes an R8MAT file.
</li>
<li>
<b>R8VEC_DIRECT_PRODUCT</b> creates a direct product of R8VEC's.
</li>
<li>
<b>R8VEC_DIRECT_PRODUCT2</b> creates a direct product of R8VEC's.
</li>
<li>
<b>SUBCOMP_NEXT</b> computes the next subcomposition of N into K parts.
</li>
<li>
<b>TETR_UNIT_MONOMIAL</b> integrates a monomial over the unit tetrahedron.
</li>
<li>
<b>TETR_UNIT_MONOMIAL_TEST</b> tests TETR_UNIT_MONOMIAL.
</li>
<li>
<b>TETR_UNIT_O01</b> returns a 1 point quadrature rule for the unit tetrahedron.
</li>
<li>
<b>TETR_UNIT_O04</b> returns a 4 point quadrature rule for the unit tetrahedron.
</li>
<li>
<b>TETR_UNIT_O08</b> returns an 8 point quadrature rule for the unit tetrahedron.
</li>
<li>
<b>TETR_UNIT_O08B</b> returns an 8 point quadrature rule for the unit tetrahedron.
</li>
<li>
<b>TETR_UNIT_O14</b> returns a 14 point quadrature rule for the unit tetrahedron.
</li>
<li>
<b>TETR_UNIT_O14B</b> returns a 14 point quadrature rule for the unit tetrahedron.
</li>
<li>
<b>TETR_UNIT_O15</b> returns a 15 point quadrature rule for the unit tetrahedron.
</li>
<li>
<b>TETR_UNIT_O15B</b> returns a 15 point quadrature rule for the unit tetrahedron.
</li>
<li>
<b>TETR_UNIT_O24</b> returns a 24 point quadrature rule for the unit tetrahedron.
</li>
<li>
<b>TETR_UNIT_QUAD_TEST</b> tests the rules for the unit tetrahedron.
</li>
<li>
<b>TETR_UNIT_VOLUME</b> returns the volume of the unit tetrahedron.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
<li>
<b>TRIG_UNIT_MONOMIAL</b> integrates a monomial over the unit triangle.
</li>
<li>
<b>TRIG_UNIT_MONOMIAL_TEST</b> tests TRIG_UNIT_MONOMIAL.
</li>
<li>
<b>TRIG_UNIT_O01</b> returns a 1 point quadrature rule for the unit triangle.
</li>
<li>
<b>TRIG_UNIT_O03</b> returns a 3 point quadrature rule for the unit triangle.
</li>
<li>
<b>TRIG_UNIT_O03B</b> returns a 3 point quadrature rule for the unit triangle.
</li>
<li>
<b>TRIG_UNIT_O06</b> returns a 6 point quadrature rule for the unit triangle.
</li>
<li>
<b>TRIG_UNIT_O06B</b> returns a 6 point quadrature rule for the unit triangle.
</li>
<li>
<b>TRIG_UNIT_O07</b> returns a 7 point quadrature rule for the unit triangle.
</li>
<li>
<b>TRIG_UNIT_O12</b> returns a 12 point quadrature rule for the unit triangle.
</li>
<li>
<b>TRIG_UNIT_QUAD_TEST</b> tests the rules for the unit triangle.
</li>
<li>
<b>TRIG_UNIT_VOLUME:</b> volume of a unit triangle.
</li>
<li>
<b>WEDG_UNIT_MONOMIAL:</b> monomial integral in a unit wedge.
</li>
<li>
<b>WEDG_UNIT_MONOMIAL_TEST</b> tests WEDG_UNIT_MONOMIAL.
</li>
<li>
<b>WEDG_UNIT_QUAD_TEST</b> tests the rules for the unit wedge.
</li>
<li>
<b>WEDG_UNIT_RULE</b> returns a quadrature rule for the unit wedge.
</li>
<li>
<b>WEDG_UNIT_VOLUME:</b> volume of a unit wedge.
</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 16 July 2009.
</i>
<!-- John Burkardt -->
</body>
<!-- Initial HTML skeleton created by HTMLINDEX. -->
</html>