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Thu Sep 25 23:11:13 2008 UTC (11 years, 1 month ago) by ksteube
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1 ksteube 1811
2     %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3 gross 625 %
4 ksteube 1811 % Copyright (c) 2003-2008 by University of Queensland
5     % Earth Systems Science Computational Center (ESSCC)
6     % http://www.uq.edu.au/esscc
7 gross 625 %
8 ksteube 1811 % 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 ksteube 1316 %
12 ksteube 1811 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
13 ksteube 1316
14 ksteube 1811
15 jgs 102 \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} }
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} }
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}
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} }
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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