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1
2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3 %
4 % Copyright (c) 2003-2010 by University of Queensland
5 % Earth Systems Science Computational Center (ESSCC)
6 % http://www.uq.edu.au/esscc
7 %
8 % Primary Business: Queensland, Australia
9 % Licensed under the Open Software License version 3.0
10 % http://www.opensource.org/licenses/osl-3.0.php
11 %
12 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
13
14
15 \setlength{\unitlength}{1mm}
16
17 \newsavebox{\HLa}
18 \savebox{\HLa}(0,0)
19 {\put(0,0){\circle*{2}}
20 \thicklines \put(1,0){\line(1,0){28}}
21 \put(30,0){\circle*{2}} }
22
23 \newsavebox{\HLathin}
24 \savebox{\HLathin}(0,0)
25 {\put(0,0){\circle{2}}
26 \thinlines \put(1,0){\line(1,0){28}}
27 \put(30,0){\circle{2}} }
28
29 \newsavebox{\VLa}
30 \savebox{\VLa}(0,30)
31 {\put(0,0){\circle*{2}}
32 \thicklines \put(0,1){\line(0,1){28}}
33 \put(0,30){\circle*{2}} }
34
35 \newsavebox{\VLathin}
36 \savebox{\VLathin}(0,30)
37 {\put(0,0){\circle{2}}
38 \thinlines \put(0,1){\line(0,1){28}}
39 \put(0,30){\circle{2}} }
40
41 \newsavebox{\SLax}
42 \savebox{\SLax}(0,30)
43 {\thicklines \put(0,0){\line(-1,1){30}}
44 \put(0,0){\circle*{2}}
45 \put(-30,30){\circle*{2}} }
46
47 \newsavebox{\SLaa}
48 \savebox{\SLaa}(0,15)
49 {\thicklines \put(0,0){\line(-4,3){20}}
50 \put(0,0){\circle*{2}}
51 \put(-20,15){\circle*{2}} }
52
53 \newsavebox{\SLab}
54 \savebox{\SLab}(0,-15)
55 {\thicklines \put(0,0){\line(-4,-3){20}}
56 \put(0,0){\circle*{2}}
57 \put(-20,-15){\circle*{2}} }
58
59 \newsavebox{\SLabthin}
60 \savebox{\SLabthin}(0,-15)
61 {\thinlines \put(-0.7,-0.7){\line(-4,-3){18.7}}
62 \put(0,0){\circle{2}}
63 \put(-20,-15){\circle{2}} }
64
65 \newsavebox{\SLac}
66 \savebox{\SLac}(0,15)
67 {\thicklines \put(0,0){\line(-2,3){10}}
68 \put(0,0){\circle*{2}}
69 \put(-10,15){\circle*{2}} }
70
71 \newsavebox{\SLacthin}
72 \savebox{\SLacthin}(0,15)
73 {\thinlines \put(0,0){\line(-2,3){9.4}}
74 \put(0,0){\circle{2}}
75 \put(-10,15){\circle{2}} }
76
77
78 \newsavebox{\HLd}
79 \savebox{\HLd}(0,0)
80 {\put(0,0){\circle*{2}}
81 \put(10,0){\circle*{2}}
82 \thicklines \put(1,0){\line(1,0){28}}
83 \put(20,0){\circle*{2}}
84 \put(30,0){\circle*{2}} }
85
86 \newsavebox{\HLdthin}
87 \savebox{\HLdthin}(0,0)
88 {\put(0,0){\circle{2}}
89 \put(10,0){\circle{2}}
90 \thinlines \multiput(1,0)(10,0){3}{\line(1,0){8}}
91 \put(20,0){\circle{2}}
92 \put(30,0){\circle{2}} }
93
94 \newsavebox{\VLd}
95 \savebox{\VLd}(0,30)
96 {\put(0,0){\circle*{2}}
97 \put(0,10){\circle*{2}}
98 \thicklines \put(0,1){\line(0,1){28}}
99 \put(0,20){\circle*{2}}
100 \put(0,30){\circle*{2}} }
101
102 \newsavebox{\VLdthin}
103 \savebox{\VLdthin}(0,30)
104 {\put(0,0){\circle{2}}
105 \put(0,10){\circle{2}}
106 \thinlines \multiput(0,1)(0,10){3}{\line(0,1){8}}
107 \put(0,20){\circle{2}}
108 \put(0,30){\circle{2}} }
109
110 \newsavebox{\SLf}
111 \savebox{\SLf}(0,30)
112 {\thicklines \put(0,0){\line(-1,1){30}}
113 \put(0,0){\circle*{2}}
114 \put(-10,10){\circle*{2}}
115 \put(-20,20){\circle*{2}}
116 \put(-30,30){\circle*{2}} }
117
118 \newsavebox{\SLad}
119 \savebox{\SLad}(0,15)
120 {\thicklines \put(0,0){\line(-4,3){20}}
121 \put(0,0){\circle*{2}}
122 \put(-6.66,5){\circle*{2}}
123 \put(-13.33,10){\circle*{2}}
124 \put(-20,15){\circle*{2}} }
125
126 \newsavebox{\SLbd}
127 \savebox{\SLbd}(0,-15)
128 {\thicklines \put(0,0){\line(-4,-3){20}}
129 \put(0,0){\circle*{2}}
130 \put(-6.66,-5){\circle*{2}}
131 \put(-13.33,-10){\circle*{2}}
132 \put(-20,-15){\circle*{2}} }
133
134 \newsavebox{\SLbdthin}
135 \savebox{\SLbdthin}(0,-15)
136 {\thinlines \multiput(-0.7,-0.7)(-6.66,-5){3}{\line(-4,-3){5.1}}
137 \put(0,0){\circle{2}}
138 \put(-6.66,-5){\circle{2}}
139 \put(-13.33,-10){\circle{2}}
140 \put(-20,-15){\circle{2}} }
141
142 \newsavebox{\SLcd}
143 \savebox{\SLcd}(0,15)
144 {\thicklines \put(0,0){\line(-2,3){10}}
145 \put(0,0){\circle*{2}}
146 \put(-3.33,5){\circle*{2}}
147 \put(-6.66,10){\circle*{2}}
148 \put(-10,15){\circle*{2}} }
149
150 \newsavebox{\SLcdthin}
151 \savebox{\SLcdthin}(0,15)
152 {\thinlines \multiput(-0.6,0.8)(-3.33,5){3}{\line(-2,3){2.35}}
153 \put(0,0){\circle{2}}
154 \put(-3.33,5){\circle{2}}
155 \put(-6.66,10){\circle{2}}
156 \put(-10,15){\circle{2}} }
157
158 \newsavebox{\HLe}
159 \savebox{\HLe}(0,0)
160 {\put(0,0){\circle*{2}}
161 \put(15,0){\circle*{2}}
162 \thicklines \put(1,0){\line(1,0){28}}
163 \put(30,0){\circle*{2}} }
164
165 \newsavebox{\HLethin}
166 \savebox{\HLethin}(0,0)
167 {\put(0,0){\circle{2}}
168 \put(15,0){\circle{2}}
169 \thinlines \multiput(1,0)(15,0){2}{\line(1,0){13}}
170 \put(30,0){\circle{2}} }
171
172 \newsavebox{\VLe}
173 \savebox{\VLe}(0,30)
174 {\put(0,0){\circle*{2}}
175 \put(0,15){\circle*{2}}
176 \thicklines \put(0,1){\line(0,1){28}}
177 \put(0,30){\circle*{2}} }
178
179 \newsavebox{\VLethin}
180 \savebox{\VLethin}(0,30)
181 {\put(0,0){\circle{2}}
182 \put(0,15){\circle{2}}
183 \thinlines \multiput(0,1)(0,15){2}{\line(0,1){13}}
184 \put(0,30){\circle{2}} }
185
186 \newsavebox{\SLe}
187 \savebox{\SLe}(0,30)
188 {\thicklines \put(0,0){\line(-1,1){30}}
189 \put(0,0){\circle*{2}}
190 \put(-15,15){\circle*{2}}
191 \put(-30,30){\circle*{2}} }
192
193 \newsavebox{\SLae}
194 \savebox{\SLae}(0,15)
195 {\thicklines \put(0,0){\line(-4,3){20}}
196 \put(0,0){\circle*{2}}
197 \put(-10,7.5){\circle*{2}}
198 \put(-20,15){\circle*{2}} }
199
200 \newsavebox{\SLbe}
201 \savebox{\SLbe}(0,-15)
202 {\thicklines \put(0,0){\line(-4,-3){20}}
203 \put(0,0){\circle*{2}}
204 \put(-10,-7.5){\circle*{2}}
205 \put(-20,-15){\circle*{2}} }
206
207 \newsavebox{\SLbethin}
208 \savebox{\SLbethin}(0,-15)
209 {\thinlines \multiput(-0.7,-0.7)(-10,-7.5){2}{\line(-4,-3){8.4}}
210 \put(0,0){\circle{2}}
211 \put(-10,-7.5){\circle{2}}
212 \put(-20,-15){\circle{2}} }
213
214 \newsavebox{\SLce}
215 \savebox{\SLce}(0,15)
216 {\thicklines \put(0,0){\line(-2,3){10}}
217 \put(0,0){\circle*{2}}
218 \put(-5,7.5){\circle*{2}}
219 \put(-10,15){\circle*{2}} }
220
221 \newsavebox{\SLcethin}
222 \savebox{\SLcethin}(0,15)
223 {\thinlines \multiput(-0.6,0.8)(-5,7.5){2}{\line(-2,3){3.9}}
224 \put(0,0){\circle{2}}
225 \put(-5,7.5){\circle{2}}
226 \put(-10,15){\circle{2}} }
227
228 %=====================================================================
229 %
230 % order 1
231 % -------
232 %
233
234 \begin{figure}
235
236
237 \begin{picture}(170,210) \thicklines
238
239
240
241 \put(20,205){\circle*{2}}
242 \put(10,195){\parbox[t]{45mm}
243 \finleyelement{Point1}}
244
245 \put(90,205){\usebox{\HLa}}
246 \put(90,195){\parbox[t]{45mm}
247 \finleyelement{LINE2} }
248
249 \put(10,145){\usebox{\HLa}}
250 \put(40,145){\usebox{\SLax}}
251 \put(10,145){\usebox{\VLa}}
252 \put(10,135){\parbox[t]{45mm}
253 \finleyelement{Tri3} }
254
255 \put(90,145){\usebox{\HLa}}
256 \put(90,175){\usebox{\HLa}}
257 \put(90,145){\usebox{\VLa}}
258 \put(120,145){\usebox{\VLa}}
259 \put(90,135){\parbox[t]{45mm}
260 \finleyelement{Rec4} }
261
262 \put(50,90){\usebox{\HLa}}
263 \put(80,90){\usebox{\SLax}}
264 \put(50,90){\usebox{\VLa}}
265 \put(80,90){\usebox{\SLac}}
266 \put(70,105){\usebox{\SLabthin}}
267 \put(70,105){\usebox{\SLaa}}
268 \put(50,80 ){\parbox[t]{45mm}
269 \finleyelement{Tet4} }
270
271 \put(90,20){\usebox{\HLa}}
272 \put(90,50){\usebox{\HLa}}
273 \put(90,20){\usebox{\VLa}}
274 \put(120,20){\usebox{\VLa}}
275 \put(110,35){\usebox{\SLabthin}}
276 \put(140,35){\usebox{\SLab}}
277 \put(110,65){\usebox{\SLab}}
278 \put(140,65){\usebox{\SLab}}
279 \put(110,35){\usebox{\HLathin}}
280 \put(110,65){\usebox{\HLa}}
281 \put(110,35){\usebox{\VLathin}}
282 \put(140,35){\usebox{\VLa}}
283 \put(90,10 ){\parbox[t]{45mm}
284 \finleyelement{Hex8} }
285
286 % nummerierung der punkte:
287 \put(19,208){{\it 1}} % Point
288 \put(89,208){{\it 1}} % line
289 \put(119,208){{\it 2}}
290 \put(6,174){{\it 3}} % Triangle
291 \put(6,144){{\it 1}}
292 \put(43,144){{\it 2}}
293 \put(86,174){{\it 4}} % quadrilateral
294 \put(86,144){{\it 1}}
295 \put(123,174){{\it 3}}
296 \put(123,144){{\it 2}}
297 \put(46,119){{\it 4}} % Tetrahedron
298 \put(46,89){{\it 1}}
299 \put(83,89){{\it 2}}
300 \put(73,104){{\it 3}}
301 \put(86,49){{\it 5}} % Hexahedron
302 \put(86,19){{\it 1}}
303 \put(123,49){{\it 6}}
304 \put(123,19){{\it 2}}
305 \put(106,64){{\it 8}}
306 \put(106,34){{\it 4}}
307 \put(143,64){{\it 7}}
308 \put(143,34){{\it 3}}
309
310 \end{picture}
311 \caption{\label{FINLEY.FIG:1} Elements of order 1}
312 \end{figure}
313 %=====================================================================
314 %
315 %
316 % order 2
317 % -------
318 % (boxes in 'fesubelm')
319
320
321 \begin{figure}
322 \setlength{\unitlength}{1mm}
323
324
325
326 \begin{picture}(170,210) \thicklines
327
328 \put(20,205){\circle*{2}}
329 \put(10,195){\parbox[t]{45mm}
330 \finleyelement{Point1} }
331
332 \put(90,205){\usebox{\HLe}}
333 \put(90,195){\parbox[t]{45mm}
334 \finleyelement{Line3} and \finleyelement{Line3Macro} }
335
336 \put(10,145){\usebox{\HLe}}
337 \put(40,145){\usebox{\SLe}}
338 \put(10,145){\usebox{\VLe}}
339 \put(10,135){\parbox[t]{45mm}
340 \finleyelement{Tri6} }
341
342 \put(90,145){\usebox{\HLe}}
343 \put(90,175){\usebox{\HLe}}
344 \put(90,145){\usebox{\VLe}}
345 \put(120,145){\usebox{\VLe}}
346 \put(90,135){\parbox[t]{45mm}
347 \finleyelement{Rec8} }
348
349 \put(50,90){\usebox{\HLe}}
350 \put(80,90){\usebox{\SLe}}
351 \put(50,90){\usebox{\VLe}}
352 \put(80,90){\usebox{\SLce}}
353 \put(70,105){\usebox{\SLbethin}}
354 \put(70,105){\usebox{\SLae}}
355 \put(50,80 ){\parbox[t]{45mm}
356 \finleyelement{Tet10} and \finleyelement{Tet10Macro}}
357
358 \put(90,20){\usebox{\HLe}}
359 \put(90,50){\usebox{\HLe}}
360 \put(90,20){\usebox{\VLe}}
361 \put(120,20){\usebox{\VLe}}
362 \put(110,35){\usebox{\SLbethin}}
363 \put(140,35){\usebox{\SLbe}}
364 \put(110,65){\usebox{\SLbe}}
365 \put(140,65){\usebox{\SLbe}}
366 \put(110,35){\usebox{\HLethin}}
367 \put(110,65){\usebox{\HLe}}
368 \put(110,35){\usebox{\VLethin}}
369 \put(140,35){\usebox{\VLe}}
370 \put(90,10 ){\parbox[t]{45mm}
371 \finleyelement{Hex20} }
372
373
374 % nummerierung der punkte:
375 \put(19,208){{\it 1}} % Point
376 \put(89,208){{\it 1}} % line
377 \put(104,208){{\it 3}}
378 \put(119,208){{\it 2}}
379 \put(6,174){{\it 3}} % Triangle
380 \put(6,159){{\it 6}}
381 \put(6,144){{\it 1}}
382 \put(28,159){{\it 5}}
383 \put(43,144){{\it 2}}
384 \put(24,140){{\it 4}}
385 \put(104,140){{\it 5}} % quaTrilateral
386 \put(86,174){{\it 4}}
387 \put(86,159){{\it 8}}
388 \put(86,144){{\it 1}}
389 \put(104,178){{\it 7}}
390 \put(123,174){{\it 3}}
391 \put(123,159){{\it 6}}
392 \put(123,144){{\it 2}}
393 \put(64,85){{\it 5}} % Tetrahedron
394 \put(46,119){{\it 4}}
395 \put(46,104){{\it 8}}
396 \put(46,89){{\it 1}}
397 \put(61,104){{\it 9}}
398 \put(83,89){{\it 2}}
399 \put(56,96.5){{\it 7}}
400 \put(78,96.5){{\it 6}}
401 \put(73,104){{\it 3}}
402 \put(62.5,111.5){{\it 10}}
403 \put(104,15){{\it 9}} % Hexahedron
404 \put(86,49){{\it 5}}
405 \put(85,34){{\it 13}}
406 \put(86,19){{\it 1}}
407 \put(104,52){{\it 17}}
408 \put(123,49){{\it 6}}
409 \put(115,37){{\it 14}}
410 \put(123,19){{\it 2}}
411 \put(125,37){{\it 11}}
412 \put(106,64){{\it 8}}
413 \put(112,46){{\it 16}}
414 \put(106,34){{\it 4}}
415 \put(124,68){{\it 19}}
416 \put(143,64){{\it 7}}
417 \put(142,49){{\it 15}}
418 \put(143,34){{\it 3}}
419 \put(94.5,26.5){{\it 12}}
420 \put(132.5,26.5){{\it 10}}
421 \put(94.5,56.5){{\it 20}}
422 \put(132.5,56.5){{\it 18}}
423
424 \end{picture}
425 \caption{\label{FINLEY.FIG:2} Elements of order 2 and macro elements}
426 \end{figure}
427
428 %
429 % additional elements
430 %
431 \begin{figure}
432 \begin{picture}(170,210) \thicklines
433
434 \put(50,095){\usebox{\HLe}}
435 \put(50,125){\usebox{\HLe}}
436 \put(50,095){\usebox{\VLe}}
437 \put(80,095){\usebox{\VLe}}
438 \put(65,110){\circle*{2}}
439 \put(50,085){\parbox[t]{45mm}
440 \finleyelement{Rec9} and \finleyelement{Rec9Macro}}
441
442
443 \put(64,090){{\it 5}}
444 \put(46,124){{\it 4}}
445 \put(46,109){{\it 8}}
446 \put(46,094){{\it 1}}
447 \put(64,128){{\it 7}}
448 \put(83,124){{\it 3}}
449 \put(83,109){{\it 6}}
450 \put(83,094){{\it 2}}
451 \put(64,105){{\it 9}}
452
453
454 \end{picture}
455 \caption{\label{FINLEY.FIG:4} Additional shape functions}
456 \end{figure}

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