/[escript]/trunk/doc/user/finleyelements.tex
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Revision 155 - (hide annotations)
Wed Nov 9 02:02:19 2005 UTC (14 years ago) by jgs
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File size: 10502 byte(s)
move all directories from trunk/esys2 into trunk and remove esys2

1 jgs 102 \setlength{\unitlength}{1mm}
2    
3     \newsavebox{\HLa}
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29     {\thicklines \put(0,0){\line(-1,1){30}}
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52     \savebox{\SLac}(0,15)
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74     {\put(0,0){\circle{2}}
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78     \put(30,0){\circle{2}} }
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104     \newsavebox{\SLad}
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110     \put(-20,15){\circle*{2}} }
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112     \newsavebox{\SLbd}
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152     \savebox{\HLethin}(0,0)
153     {\put(0,0){\circle{2}}
154     \put(15,0){\circle{2}}
155     \thinlines \multiput(1,0)(15,0){2}{\line(1,0){13}}
156     \put(30,0){\circle{2}} }
157    
158     \newsavebox{\VLe}
159     \savebox{\VLe}(0,30)
160     {\put(0,0){\circle*{2}}
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162     \thicklines \put(0,1){\line(0,1){28}}
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164    
165     \newsavebox{\VLethin}
166     \savebox{\VLethin}(0,30)
167     {\put(0,0){\circle{2}}
168     \put(0,15){\circle{2}}
169     \thinlines \multiput(0,1)(0,15){2}{\line(0,1){13}}
170     \put(0,30){\circle{2}} }
171    
172     \newsavebox{\SLe}
173     \savebox{\SLe}(0,30)
174     {\thicklines \put(0,0){\line(-1,1){30}}
175     \put(0,0){\circle*{2}}
176     \put(-15,15){\circle*{2}}
177     \put(-30,30){\circle*{2}} }
178    
179     \newsavebox{\SLae}
180     \savebox{\SLae}(0,15)
181     {\thicklines \put(0,0){\line(-4,3){20}}
182     \put(0,0){\circle*{2}}
183     \put(-10,7.5){\circle*{2}}
184     \put(-20,15){\circle*{2}} }
185    
186     \newsavebox{\SLbe}
187     \savebox{\SLbe}(0,-15)
188     {\thicklines \put(0,0){\line(-4,-3){20}}
189     \put(0,0){\circle*{2}}
190     \put(-10,-7.5){\circle*{2}}
191     \put(-20,-15){\circle*{2}} }
192    
193     \newsavebox{\SLbethin}
194     \savebox{\SLbethin}(0,-15)
195     {\thinlines \multiput(-0.7,-0.7)(-10,-7.5){2}{\line(-4,-3){8.4}}
196     \put(0,0){\circle{2}}
197     \put(-10,-7.5){\circle{2}}
198     \put(-20,-15){\circle{2}} }
199    
200     \newsavebox{\SLce}
201     \savebox{\SLce}(0,15)
202     {\thicklines \put(0,0){\line(-2,3){10}}
203     \put(0,0){\circle*{2}}
204     \put(-5,7.5){\circle*{2}}
205     \put(-10,15){\circle*{2}} }
206    
207     \newsavebox{\SLcethin}
208     \savebox{\SLcethin}(0,15)
209     {\thinlines \multiput(-0.6,0.8)(-5,7.5){2}{\line(-2,3){3.9}}
210     \put(0,0){\circle{2}}
211     \put(-5,7.5){\circle{2}}
212     \put(-10,15){\circle{2}} }
213    
214     %=====================================================================
215     %
216     % order 1
217     % -------
218     %
219    
220     \begin{figure}
221    
222    
223     \begin{picture}(170,210) \thicklines
224    
225    
226    
227     \put(20,205){\circle*{2}}
228     \put(10,195){\parbox[t]{45mm}
229     \finleyelement{Point1}}
230    
231     \put(90,205){\usebox{\HLa}}
232     \put(90,195){\parbox[t]{45mm}
233     \finleyelement{LINE2} }
234    
235     \put(10,145){\usebox{\HLa}}
236     \put(40,145){\usebox{\SLax}}
237     \put(10,145){\usebox{\VLa}}
238     \put(10,135){\parbox[t]{45mm}
239     \finleyelement{Tri3} }
240    
241     \put(90,145){\usebox{\HLa}}
242     \put(90,175){\usebox{\HLa}}
243     \put(90,145){\usebox{\VLa}}
244     \put(120,145){\usebox{\VLa}}
245     \put(90,135){\parbox[t]{45mm}
246     \finleyelement{Rec4} }
247    
248     \put(50,90){\usebox{\HLa}}
249     \put(80,90){\usebox{\SLax}}
250     \put(50,90){\usebox{\VLa}}
251     \put(80,90){\usebox{\SLac}}
252     \put(70,105){\usebox{\SLabthin}}
253     \put(70,105){\usebox{\SLaa}}
254     \put(50,80 ){\parbox[t]{45mm}
255     \finleyelement{Tet4} }
256    
257     \put(90,20){\usebox{\HLa}}
258     \put(90,50){\usebox{\HLa}}
259     \put(90,20){\usebox{\VLa}}
260     \put(120,20){\usebox{\VLa}}
261     \put(110,35){\usebox{\SLabthin}}
262     \put(140,35){\usebox{\SLab}}
263     \put(110,65){\usebox{\SLab}}
264     \put(140,65){\usebox{\SLab}}
265     \put(110,35){\usebox{\HLathin}}
266     \put(110,65){\usebox{\HLa}}
267     \put(110,35){\usebox{\VLathin}}
268     \put(140,35){\usebox{\VLa}}
269     \put(90,10 ){\parbox[t]{45mm}
270     \finleyelement{Hex8} }
271    
272     % nummerierung der punkte:
273     \put(19,208){{\it 1}} % Point
274     \put(89,208){{\it 1}} % line
275     \put(119,208){{\it 2}}
276     \put(6,174){{\it 3}} % Triangle
277     \put(6,144){{\it 1}}
278     \put(43,144){{\it 2}}
279     \put(86,174){{\it 4}} % quadrilateral
280     \put(86,144){{\it 1}}
281     \put(123,174){{\it 3}}
282     \put(123,144){{\it 2}}
283     \put(46,119){{\it 4}} % Tetrahedron
284     \put(46,89){{\it 1}}
285     \put(83,89){{\it 2}}
286     \put(73,104){{\it 3}}
287     \put(86,49){{\it 5}} % Hexahedron
288     \put(86,19){{\it 1}}
289     \put(123,49){{\it 6}}
290     \put(123,19){{\it 2}}
291     \put(106,64){{\it 8}}
292     \put(106,34){{\it 4}}
293     \put(143,64){{\it 7}}
294     \put(143,34){{\it 3}}
295    
296     \end{picture}
297     \caption{\label{FINLEY.FIG:1} Elements of order 1}
298     \end{figure}
299     %=====================================================================
300     %
301     %
302     % order 2
303     % -------
304     % (boxes in 'fesubelm')
305    
306    
307     \begin{figure}
308     \setlength{\unitlength}{1mm}
309    
310    
311    
312     \begin{picture}(170,210) \thicklines
313    
314     \put(20,205){\circle*{2}}
315     \put(10,195){\parbox[t]{45mm}
316     \finleyelement{Point1} }
317    
318     \put(90,205){\usebox{\HLe}}
319     \put(90,195){\parbox[t]{45mm}
320     \finleyelement{LINE3} }
321    
322     \put(10,145){\usebox{\HLe}}
323     \put(40,145){\usebox{\SLe}}
324     \put(10,145){\usebox{\VLe}}
325     \put(10,135){\parbox[t]{45mm}
326     \finleyelement{Tri6} }
327    
328     \put(90,145){\usebox{\HLe}}
329     \put(90,175){\usebox{\HLe}}
330     \put(90,145){\usebox{\VLe}}
331     \put(120,145){\usebox{\VLe}}
332     \put(90,135){\parbox[t]{45mm}
333     \finleyelement{Rec8} }
334    
335     \put(50,90){\usebox{\HLe}}
336     \put(80,90){\usebox{\SLe}}
337     \put(50,90){\usebox{\VLe}}
338     \put(80,90){\usebox{\SLce}}
339     \put(70,105){\usebox{\SLbethin}}
340     \put(70,105){\usebox{\SLae}}
341     \put(50,80 ){\parbox[t]{45mm}
342     \finleyelement{Tet10} }
343    
344     \put(90,20){\usebox{\HLe}}
345     \put(90,50){\usebox{\HLe}}
346     \put(90,20){\usebox{\VLe}}
347     \put(120,20){\usebox{\VLe}}
348     \put(110,35){\usebox{\SLbethin}}
349     \put(140,35){\usebox{\SLbe}}
350     \put(110,65){\usebox{\SLbe}}
351     \put(140,65){\usebox{\SLbe}}
352     \put(110,35){\usebox{\HLethin}}
353     \put(110,65){\usebox{\HLe}}
354     \put(110,35){\usebox{\VLethin}}
355     \put(140,35){\usebox{\VLe}}
356     \put(90,10 ){\parbox[t]{45mm}
357     \finleyelement{Hex20} }
358    
359    
360     % nummerierung der punkte:
361     \put(19,208){{\it 1}} % Point
362     \put(89,208){{\it 1}} % line
363     \put(104,208){{\it 3}}
364     \put(119,208){{\it 2}}
365     \put(6,174){{\it 3}} % Triangle
366     \put(6,159){{\it 6}}
367     \put(6,144){{\it 1}}
368     \put(28,159){{\it 5}}
369     \put(43,144){{\it 2}}
370     \put(24,140){{\it 4}}
371     \put(104,140){{\it 5}} % quaTrilateral
372     \put(86,174){{\it 4}}
373     \put(86,159){{\it 8}}
374     \put(86,144){{\it 1}}
375     \put(104,178){{\it 7}}
376     \put(123,174){{\it 3}}
377     \put(123,159){{\it 6}}
378     \put(123,144){{\it 2}}
379     \put(64,85){{\it 5}} % Tetrahedron
380     \put(46,119){{\it 4}}
381     \put(46,104){{\it 8}}
382     \put(46,89){{\it 1}}
383     \put(61,104){{\it 9}}
384     \put(83,89){{\it 2}}
385     \put(56,96.5){{\it 7}}
386     \put(78,96.5){{\it 6}}
387     \put(73,104){{\it 3}}
388     \put(62.5,111.5){{\it 10}}
389     \put(104,15){{\it 9}} % Hexahedron
390     \put(86,49){{\it 5}}
391     \put(85,34){{\it 13}}
392     \put(86,19){{\it 1}}
393     \put(104,52){{\it 17}}
394     \put(123,49){{\it 6}}
395     \put(115,37){{\it 14}}
396     \put(123,19){{\it 2}}
397     \put(125,37){{\it 11}}
398     \put(106,64){{\it 8}}
399     \put(112,46){{\it 16}}
400     \put(106,34){{\it 4}}
401     \put(124,68){{\it 19}}
402     \put(143,64){{\it 7}}
403     \put(142,49){{\it 15}}
404     \put(143,34){{\it 3}}
405     \put(94.5,26.5){{\it 12}}
406     \put(132.5,26.5){{\it 10}}
407     \put(94.5,56.5){{\it 20}}
408     \put(132.5,56.5){{\it 18}}
409    
410     \end{picture}
411     \caption{\label{FINLEY.FIG:2} Elements of order 2}
412     \end{figure}
413    
414     %
415     % additional elements
416     %
417     \begin{figure}
418     \begin{picture}(170,210) \thicklines
419    
420     \put(50,095){\usebox{\HLe}}
421     \put(50,125){\usebox{\HLe}}
422     \put(50,095){\usebox{\VLe}}
423     \put(80,095){\usebox{\VLe}}
424     \put(65,110){\circle*{2}}
425     \put(50,085){\parbox[t]{45mm}
426     \finleyelement{Rec9} }
427    
428    
429     \put(64,090){{\it 5}}
430     \put(46,124){{\it 4}}
431     \put(46,109){{\it 8}}
432     \put(46,094){{\it 1}}
433     \put(64,128){{\it 7}}
434     \put(83,124){{\it 3}}
435     \put(83,109){{\it 6}}
436     \put(83,094){{\it 2}}
437     \put(64,105){{\it 9}}
438    
439    
440     \end{picture}
441     \caption{\label{FINLEY.FIG:4} Additional shape functions}
442     \end{figure}

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