/[escript]/trunk/doc/user/finleyelements.tex
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Revision 1316 - (hide annotations)
Tue Sep 25 03:18:30 2007 UTC (12 years, 2 months ago) by ksteube
File MIME type: application/x-tex
File size: 10930 byte(s)
Quickly edited chapters 1 and 2 of the User Guide, but it needs more work.
Ran entire document through spell checker.

1 gross 625 %
2 ksteube 1316 % $Id$
3 gross 625 %
4 ksteube 1316 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
5     %
6     % Copyright 2003-2007 by ACceSS MNRF
7     % Copyright 2007 by University of Queensland
8     %
9     % http://esscc.uq.edu.au
10     % Primary Business: Queensland, Australia
11     % Licensed under the Open Software License version 3.0
12     % http://www.opensource.org/licenses/osl-3.0.php
13     %
14     %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
15     %
16    
17 jgs 102 \setlength{\unitlength}{1mm}
18    
19     \newsavebox{\HLa}
20     \savebox{\HLa}(0,0)
21     {\put(0,0){\circle*{2}}
22     \thicklines \put(1,0){\line(1,0){28}}
23     \put(30,0){\circle*{2}} }
24    
25     \newsavebox{\HLathin}
26     \savebox{\HLathin}(0,0)
27     {\put(0,0){\circle{2}}
28     \thinlines \put(1,0){\line(1,0){28}}
29     \put(30,0){\circle{2}} }
30    
31     \newsavebox{\VLa}
32     \savebox{\VLa}(0,30)
33     {\put(0,0){\circle*{2}}
34     \thicklines \put(0,1){\line(0,1){28}}
35     \put(0,30){\circle*{2}} }
36    
37     \newsavebox{\VLathin}
38     \savebox{\VLathin}(0,30)
39     {\put(0,0){\circle{2}}
40     \thinlines \put(0,1){\line(0,1){28}}
41     \put(0,30){\circle{2}} }
42    
43     \newsavebox{\SLax}
44     \savebox{\SLax}(0,30)
45     {\thicklines \put(0,0){\line(-1,1){30}}
46     \put(0,0){\circle*{2}}
47     \put(-30,30){\circle*{2}} }
48    
49     \newsavebox{\SLaa}
50     \savebox{\SLaa}(0,15)
51     {\thicklines \put(0,0){\line(-4,3){20}}
52     \put(0,0){\circle*{2}}
53     \put(-20,15){\circle*{2}} }
54    
55     \newsavebox{\SLab}
56     \savebox{\SLab}(0,-15)
57     {\thicklines \put(0,0){\line(-4,-3){20}}
58     \put(0,0){\circle*{2}}
59     \put(-20,-15){\circle*{2}} }
60    
61     \newsavebox{\SLabthin}
62     \savebox{\SLabthin}(0,-15)
63     {\thinlines \put(-0.7,-0.7){\line(-4,-3){18.7}}
64     \put(0,0){\circle{2}}
65     \put(-20,-15){\circle{2}} }
66    
67     \newsavebox{\SLac}
68     \savebox{\SLac}(0,15)
69     {\thicklines \put(0,0){\line(-2,3){10}}
70     \put(0,0){\circle*{2}}
71     \put(-10,15){\circle*{2}} }
72    
73     \newsavebox{\SLacthin}
74     \savebox{\SLacthin}(0,15)
75     {\thinlines \put(0,0){\line(-2,3){9.4}}
76     \put(0,0){\circle{2}}
77     \put(-10,15){\circle{2}} }
78    
79    
80     \newsavebox{\HLd}
81     \savebox{\HLd}(0,0)
82     {\put(0,0){\circle*{2}}
83     \put(10,0){\circle*{2}}
84     \thicklines \put(1,0){\line(1,0){28}}
85     \put(20,0){\circle*{2}}
86     \put(30,0){\circle*{2}} }
87    
88     \newsavebox{\HLdthin}
89     \savebox{\HLdthin}(0,0)
90     {\put(0,0){\circle{2}}
91     \put(10,0){\circle{2}}
92     \thinlines \multiput(1,0)(10,0){3}{\line(1,0){8}}
93     \put(20,0){\circle{2}}
94     \put(30,0){\circle{2}} }
95    
96     \newsavebox{\VLd}
97     \savebox{\VLd}(0,30)
98     {\put(0,0){\circle*{2}}
99     \put(0,10){\circle*{2}}
100     \thicklines \put(0,1){\line(0,1){28}}
101     \put(0,20){\circle*{2}}
102     \put(0,30){\circle*{2}} }
103    
104     \newsavebox{\VLdthin}
105     \savebox{\VLdthin}(0,30)
106     {\put(0,0){\circle{2}}
107     \put(0,10){\circle{2}}
108     \thinlines \multiput(0,1)(0,10){3}{\line(0,1){8}}
109     \put(0,20){\circle{2}}
110     \put(0,30){\circle{2}} }
111    
112     \newsavebox{\SLf}
113     \savebox{\SLf}(0,30)
114     {\thicklines \put(0,0){\line(-1,1){30}}
115     \put(0,0){\circle*{2}}
116     \put(-10,10){\circle*{2}}
117     \put(-20,20){\circle*{2}}
118     \put(-30,30){\circle*{2}} }
119    
120     \newsavebox{\SLad}
121     \savebox{\SLad}(0,15)
122     {\thicklines \put(0,0){\line(-4,3){20}}
123     \put(0,0){\circle*{2}}
124     \put(-6.66,5){\circle*{2}}
125     \put(-13.33,10){\circle*{2}}
126     \put(-20,15){\circle*{2}} }
127    
128     \newsavebox{\SLbd}
129     \savebox{\SLbd}(0,-15)
130     {\thicklines \put(0,0){\line(-4,-3){20}}
131     \put(0,0){\circle*{2}}
132     \put(-6.66,-5){\circle*{2}}
133     \put(-13.33,-10){\circle*{2}}
134     \put(-20,-15){\circle*{2}} }
135    
136     \newsavebox{\SLbdthin}
137     \savebox{\SLbdthin}(0,-15)
138     {\thinlines \multiput(-0.7,-0.7)(-6.66,-5){3}{\line(-4,-3){5.1}}
139     \put(0,0){\circle{2}}
140     \put(-6.66,-5){\circle{2}}
141     \put(-13.33,-10){\circle{2}}
142     \put(-20,-15){\circle{2}} }
143    
144     \newsavebox{\SLcd}
145     \savebox{\SLcd}(0,15)
146     {\thicklines \put(0,0){\line(-2,3){10}}
147     \put(0,0){\circle*{2}}
148     \put(-3.33,5){\circle*{2}}
149     \put(-6.66,10){\circle*{2}}
150     \put(-10,15){\circle*{2}} }
151    
152     \newsavebox{\SLcdthin}
153     \savebox{\SLcdthin}(0,15)
154     {\thinlines \multiput(-0.6,0.8)(-3.33,5){3}{\line(-2,3){2.35}}
155     \put(0,0){\circle{2}}
156     \put(-3.33,5){\circle{2}}
157     \put(-6.66,10){\circle{2}}
158     \put(-10,15){\circle{2}} }
159    
160     \newsavebox{\HLe}
161     \savebox{\HLe}(0,0)
162     {\put(0,0){\circle*{2}}
163     \put(15,0){\circle*{2}}
164     \thicklines \put(1,0){\line(1,0){28}}
165     \put(30,0){\circle*{2}} }
166    
167     \newsavebox{\HLethin}
168     \savebox{\HLethin}(0,0)
169     {\put(0,0){\circle{2}}
170     \put(15,0){\circle{2}}
171     \thinlines \multiput(1,0)(15,0){2}{\line(1,0){13}}
172     \put(30,0){\circle{2}} }
173    
174     \newsavebox{\VLe}
175     \savebox{\VLe}(0,30)
176     {\put(0,0){\circle*{2}}
177     \put(0,15){\circle*{2}}
178     \thicklines \put(0,1){\line(0,1){28}}
179     \put(0,30){\circle*{2}} }
180    
181     \newsavebox{\VLethin}
182     \savebox{\VLethin}(0,30)
183     {\put(0,0){\circle{2}}
184     \put(0,15){\circle{2}}
185     \thinlines \multiput(0,1)(0,15){2}{\line(0,1){13}}
186     \put(0,30){\circle{2}} }
187    
188     \newsavebox{\SLe}
189     \savebox{\SLe}(0,30)
190     {\thicklines \put(0,0){\line(-1,1){30}}
191     \put(0,0){\circle*{2}}
192     \put(-15,15){\circle*{2}}
193     \put(-30,30){\circle*{2}} }
194    
195     \newsavebox{\SLae}
196     \savebox{\SLae}(0,15)
197     {\thicklines \put(0,0){\line(-4,3){20}}
198     \put(0,0){\circle*{2}}
199     \put(-10,7.5){\circle*{2}}
200     \put(-20,15){\circle*{2}} }
201    
202     \newsavebox{\SLbe}
203     \savebox{\SLbe}(0,-15)
204     {\thicklines \put(0,0){\line(-4,-3){20}}
205     \put(0,0){\circle*{2}}
206     \put(-10,-7.5){\circle*{2}}
207     \put(-20,-15){\circle*{2}} }
208    
209     \newsavebox{\SLbethin}
210     \savebox{\SLbethin}(0,-15)
211     {\thinlines \multiput(-0.7,-0.7)(-10,-7.5){2}{\line(-4,-3){8.4}}
212     \put(0,0){\circle{2}}
213     \put(-10,-7.5){\circle{2}}
214     \put(-20,-15){\circle{2}} }
215    
216     \newsavebox{\SLce}
217     \savebox{\SLce}(0,15)
218     {\thicklines \put(0,0){\line(-2,3){10}}
219     \put(0,0){\circle*{2}}
220     \put(-5,7.5){\circle*{2}}
221     \put(-10,15){\circle*{2}} }
222    
223     \newsavebox{\SLcethin}
224     \savebox{\SLcethin}(0,15)
225     {\thinlines \multiput(-0.6,0.8)(-5,7.5){2}{\line(-2,3){3.9}}
226     \put(0,0){\circle{2}}
227     \put(-5,7.5){\circle{2}}
228     \put(-10,15){\circle{2}} }
229    
230     %=====================================================================
231     %
232     % order 1
233     % -------
234     %
235    
236     \begin{figure}
237    
238    
239     \begin{picture}(170,210) \thicklines
240    
241    
242    
243     \put(20,205){\circle*{2}}
244     \put(10,195){\parbox[t]{45mm}
245     \finleyelement{Point1}}
246    
247     \put(90,205){\usebox{\HLa}}
248     \put(90,195){\parbox[t]{45mm}
249     \finleyelement{LINE2} }
250    
251     \put(10,145){\usebox{\HLa}}
252     \put(40,145){\usebox{\SLax}}
253     \put(10,145){\usebox{\VLa}}
254     \put(10,135){\parbox[t]{45mm}
255     \finleyelement{Tri3} }
256    
257     \put(90,145){\usebox{\HLa}}
258     \put(90,175){\usebox{\HLa}}
259     \put(90,145){\usebox{\VLa}}
260     \put(120,145){\usebox{\VLa}}
261     \put(90,135){\parbox[t]{45mm}
262     \finleyelement{Rec4} }
263    
264     \put(50,90){\usebox{\HLa}}
265     \put(80,90){\usebox{\SLax}}
266     \put(50,90){\usebox{\VLa}}
267     \put(80,90){\usebox{\SLac}}
268     \put(70,105){\usebox{\SLabthin}}
269     \put(70,105){\usebox{\SLaa}}
270     \put(50,80 ){\parbox[t]{45mm}
271     \finleyelement{Tet4} }
272    
273     \put(90,20){\usebox{\HLa}}
274     \put(90,50){\usebox{\HLa}}
275     \put(90,20){\usebox{\VLa}}
276     \put(120,20){\usebox{\VLa}}
277     \put(110,35){\usebox{\SLabthin}}
278     \put(140,35){\usebox{\SLab}}
279     \put(110,65){\usebox{\SLab}}
280     \put(140,65){\usebox{\SLab}}
281     \put(110,35){\usebox{\HLathin}}
282     \put(110,65){\usebox{\HLa}}
283     \put(110,35){\usebox{\VLathin}}
284     \put(140,35){\usebox{\VLa}}
285     \put(90,10 ){\parbox[t]{45mm}
286     \finleyelement{Hex8} }
287    
288     % nummerierung der punkte:
289     \put(19,208){{\it 1}} % Point
290     \put(89,208){{\it 1}} % line
291     \put(119,208){{\it 2}}
292     \put(6,174){{\it 3}} % Triangle
293     \put(6,144){{\it 1}}
294     \put(43,144){{\it 2}}
295     \put(86,174){{\it 4}} % quadrilateral
296     \put(86,144){{\it 1}}
297     \put(123,174){{\it 3}}
298     \put(123,144){{\it 2}}
299     \put(46,119){{\it 4}} % Tetrahedron
300     \put(46,89){{\it 1}}
301     \put(83,89){{\it 2}}
302     \put(73,104){{\it 3}}
303     \put(86,49){{\it 5}} % Hexahedron
304     \put(86,19){{\it 1}}
305     \put(123,49){{\it 6}}
306     \put(123,19){{\it 2}}
307     \put(106,64){{\it 8}}
308     \put(106,34){{\it 4}}
309     \put(143,64){{\it 7}}
310     \put(143,34){{\it 3}}
311    
312     \end{picture}
313     \caption{\label{FINLEY.FIG:1} Elements of order 1}
314     \end{figure}
315     %=====================================================================
316     %
317     %
318     % order 2
319     % -------
320     % (boxes in 'fesubelm')
321    
322    
323     \begin{figure}
324     \setlength{\unitlength}{1mm}
325    
326    
327    
328     \begin{picture}(170,210) \thicklines
329    
330     \put(20,205){\circle*{2}}
331     \put(10,195){\parbox[t]{45mm}
332     \finleyelement{Point1} }
333    
334     \put(90,205){\usebox{\HLe}}
335     \put(90,195){\parbox[t]{45mm}
336     \finleyelement{LINE3} }
337    
338     \put(10,145){\usebox{\HLe}}
339     \put(40,145){\usebox{\SLe}}
340     \put(10,145){\usebox{\VLe}}
341     \put(10,135){\parbox[t]{45mm}
342     \finleyelement{Tri6} }
343    
344     \put(90,145){\usebox{\HLe}}
345     \put(90,175){\usebox{\HLe}}
346     \put(90,145){\usebox{\VLe}}
347     \put(120,145){\usebox{\VLe}}
348     \put(90,135){\parbox[t]{45mm}
349     \finleyelement{Rec8} }
350    
351     \put(50,90){\usebox{\HLe}}
352     \put(80,90){\usebox{\SLe}}
353     \put(50,90){\usebox{\VLe}}
354     \put(80,90){\usebox{\SLce}}
355     \put(70,105){\usebox{\SLbethin}}
356     \put(70,105){\usebox{\SLae}}
357     \put(50,80 ){\parbox[t]{45mm}
358     \finleyelement{Tet10} }
359    
360     \put(90,20){\usebox{\HLe}}
361     \put(90,50){\usebox{\HLe}}
362     \put(90,20){\usebox{\VLe}}
363     \put(120,20){\usebox{\VLe}}
364     \put(110,35){\usebox{\SLbethin}}
365     \put(140,35){\usebox{\SLbe}}
366     \put(110,65){\usebox{\SLbe}}
367     \put(140,65){\usebox{\SLbe}}
368     \put(110,35){\usebox{\HLethin}}
369     \put(110,65){\usebox{\HLe}}
370     \put(110,35){\usebox{\VLethin}}
371     \put(140,35){\usebox{\VLe}}
372     \put(90,10 ){\parbox[t]{45mm}
373     \finleyelement{Hex20} }
374    
375    
376     % nummerierung der punkte:
377     \put(19,208){{\it 1}} % Point
378     \put(89,208){{\it 1}} % line
379     \put(104,208){{\it 3}}
380     \put(119,208){{\it 2}}
381     \put(6,174){{\it 3}} % Triangle
382     \put(6,159){{\it 6}}
383     \put(6,144){{\it 1}}
384     \put(28,159){{\it 5}}
385     \put(43,144){{\it 2}}
386     \put(24,140){{\it 4}}
387     \put(104,140){{\it 5}} % quaTrilateral
388     \put(86,174){{\it 4}}
389     \put(86,159){{\it 8}}
390     \put(86,144){{\it 1}}
391     \put(104,178){{\it 7}}
392     \put(123,174){{\it 3}}
393     \put(123,159){{\it 6}}
394     \put(123,144){{\it 2}}
395     \put(64,85){{\it 5}} % Tetrahedron
396     \put(46,119){{\it 4}}
397     \put(46,104){{\it 8}}
398     \put(46,89){{\it 1}}
399     \put(61,104){{\it 9}}
400     \put(83,89){{\it 2}}
401     \put(56,96.5){{\it 7}}
402     \put(78,96.5){{\it 6}}
403     \put(73,104){{\it 3}}
404     \put(62.5,111.5){{\it 10}}
405     \put(104,15){{\it 9}} % Hexahedron
406     \put(86,49){{\it 5}}
407     \put(85,34){{\it 13}}
408     \put(86,19){{\it 1}}
409     \put(104,52){{\it 17}}
410     \put(123,49){{\it 6}}
411     \put(115,37){{\it 14}}
412     \put(123,19){{\it 2}}
413     \put(125,37){{\it 11}}
414     \put(106,64){{\it 8}}
415     \put(112,46){{\it 16}}
416     \put(106,34){{\it 4}}
417     \put(124,68){{\it 19}}
418     \put(143,64){{\it 7}}
419     \put(142,49){{\it 15}}
420     \put(143,34){{\it 3}}
421     \put(94.5,26.5){{\it 12}}
422     \put(132.5,26.5){{\it 10}}
423     \put(94.5,56.5){{\it 20}}
424     \put(132.5,56.5){{\it 18}}
425    
426     \end{picture}
427     \caption{\label{FINLEY.FIG:2} Elements of order 2}
428     \end{figure}
429    
430     %
431     % additional elements
432     %
433     \begin{figure}
434     \begin{picture}(170,210) \thicklines
435    
436     \put(50,095){\usebox{\HLe}}
437     \put(50,125){\usebox{\HLe}}
438     \put(50,095){\usebox{\VLe}}
439     \put(80,095){\usebox{\VLe}}
440     \put(65,110){\circle*{2}}
441     \put(50,085){\parbox[t]{45mm}
442     \finleyelement{Rec9} }
443    
444    
445     \put(64,090){{\it 5}}
446     \put(46,124){{\it 4}}
447     \put(46,109){{\it 8}}
448     \put(46,094){{\it 1}}
449     \put(64,128){{\it 7}}
450     \put(83,124){{\it 3}}
451     \put(83,109){{\it 6}}
452     \put(83,094){{\it 2}}
453     \put(64,105){{\it 9}}
454    
455    
456     \end{picture}
457     \caption{\label{FINLEY.FIG:4} Additional shape functions}
458     \end{figure}

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