/[escript]/trunk/doc/user/finleyelements.tex
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Contents of /trunk/doc/user/finleyelements.tex

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Revision 155 - (show annotations)
Wed Nov 9 02:02:19 2005 UTC (14 years, 1 month ago) by jgs
File MIME type: application/x-tex
File size: 10502 byte(s)
move all directories from trunk/esys2 into trunk and remove esys2

1 \setlength{\unitlength}{1mm}
2
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17 {\put(0,0){\circle*{2}}
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171
172 \newsavebox{\SLe}
173 \savebox{\SLe}(0,30)
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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}}
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183 \put(-10,7.5){\circle*{2}}
184 \put(-20,15){\circle*{2}} }
185
186 \newsavebox{\SLbe}
187 \savebox{\SLbe}(0,-15)
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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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