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2 0 1 }{PSTYLE "Heading 2" -1 270 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 
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{SECT 0 {EXCHG {PARA 269 "" 0 "" {TEXT 259 15 "FINITE ELEMENTS" }}
{PARA 270 "" 0 "" {TEXT -1 29 "SYMBOLIC PROGRAMMING IN MAPLE" }}{PARA 
19 "" 0 "" {TEXT 260 16 "by Artur Portela" }{TEXT 261 0 "" }}{PARA 
271 "" 0 "" {TEXT 256 26 "Potential-Flow Example 4: " }{TEXT 284 19 "S
ymbolic Variables\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "rest
art:interface(verboseproc=3):printlevel:=3:" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 34 "libname := \"C:/mylib/fem\",libname:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "with(Plotter);" }}{PARA 12 "" 1 "" 
{XPPMATH 20 "6#7:%+draw_labelG%,draw_symbolG%*draw_textG%+draw_titleG%
)move_penG%*new_arrowG%)new_axesG%*new_colorG%.new_pen_styleG%1new_plo
t_shadingG%/new_plot_styleG%.new_thicknessG%)pen_downG%'pen_upG%-plot_
elementG%2show_2D_animationG%-show_2D_plotG%2show_3D_animationG%-show_
3D_plotG%3start_2D_animationG%.start_2D_plotG%3start_3D_animationG%.st
art_3D_plotG%/upgrade_framesG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 14 "with(Cgt_fem);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7&%(cgt_femG%/
compute_fluxesG%1element_geometryG%/read_save_dataG" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 16 "with(G_cgt_fem);" }}{PARA 12 "" 1 "" 
{XPPMATH 20 "6#7+%/animate_3D_defG%/animate_3D_rotG%3animate_velocitie
sG%3plot_contour_linesG%,plot_fluxesG%5plot_line_potentialsG%*plot_mes
hG%2plot_problem_dataG%0plot_velocitiesG" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 20 "" 0 "" {TEXT 262 17 " Data Prep
aration" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 31 "The best way to input d
ata for " }{TEXT 264 7 "Cgt_fem" }{TEXT -1 25 " is to use the procedur
e " }{TEXT 263 14 "read_save_data" }{TEXT -1 50 ", which reads a file \+
with the following structure:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 1 "*" }{TEXT 266 7 "control" }{TEXT -1 169 "*
             [title,point sources,element sources,boundary velocities]
\ntitle Potential Flow in a Rectangular Domain\npoint sources\nelement
 sources\nboundary velocities\n\n*" }{TEXT 267 9 "materials" }{TEXT 
-1 104 "*           [material,x-permeability,y-permeability,angle of t
he local x-direction]\n1 2 2 45\n2 8 8 45\n\n*" }{TEXT 268 5 "nodes" }
{TEXT -1 180 "*               [node,x,y]\n1  0   0\n2  0   1 \n3  0   \+
2 \n4  1   0 \n5  1   1 \n6  1   2\n7  2   0 \n8  2   1\n9  2   2\n10 \+
 3   0 \n11  3   1  \n12  3   2\n13  4   0 \n14  4   1\n15  4   2 \n\n
*" }{TEXT 269 8 "elements" }{TEXT -1 399 "*            [element,node1,
node2,node3,material]\n1  1   4   5   1       \n2  1   5   2   1      \+
\n3  2   5   3   1      \n4  3   5   6   1      \n5  4   7   8   1  \n
6  5   4   8   1\n7  5   8   6   1     \n8  6   8   9    1\n9  7   10 \+
  11    1  \n10  7   11   8    1   \n11  8   11   9    1\n12  11   12 \+
  9    1  \n13  10   13   14    1\n14  10   14   11    1 \n15  11   14
   12    1\n16  12   14   15    1 \n\n*" }{TEXT 270 11 "constraints" }
{TEXT -1 59 "*         [node,potential]\n1 10\n2 10\n3 10\n13 0\n14 0
\n15 0\n\n*" }{TEXT 271 19 "boundary velocities" }{TEXT -1 52 "* [node
1,node2,normal velocity]\n1 2 0\n2 3 0\n5 4 0\n\n*" }{TEXT 272 13 "poi
nt sources" }{TEXT -1 25 "*       [node,Q]\n1 -50\n\n*" }{TEXT 273 15 
"element sources" }{TEXT -1 25 "*     [element,q]\n2 30\n\n*" }{TEXT 
274 3 "end" }{TEXT -1 1 "*" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 
"" 0 "" {TEXT -1 85 "The data blocks, with the respective keyword on t
he top, can be defined in any order." }}{PARA 0 "" 0 "" {TEXT -1 0 "" 
}}{PARA 0 "" 0 "" {TEXT -1 83 "Alternatively, data can be given manual
ly through the definition of the variables: " }{TEXT 275 5 "tcase" }
{TEXT -1 2 ", " }{TEXT 276 7 "control" }{TEXT -1 2 ", " }{TEXT 277 4 "
nods" }{TEXT -1 2 ", " }{TEXT 278 5 "elems" }{TEXT -1 2 ", " }{TEXT 
279 9 "mat_props" }{TEXT -1 2 ", " }{TEXT 280 9 "bdr_conds" }{TEXT -1 
2 ", " }{TEXT 281 7 "b_velts" }{TEXT -1 2 ", " }{TEXT 282 6 "p_srcs" }
{TEXT -1 5 " and " }{TEXT 283 6 "e_srcs" }{TEXT -1 46 ". See bellow th
e structure of these variables." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 0 "" }}}}{SECT 0 {PARA 20 "" 0 "" {TEXT 265 19 " Symbolic Variable
s" }{TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 63 "For the sake o
f simplicity, start reading the data of example 1" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 17 "read_save_data();" }}}{EXCHG {PARA 0 "read d
ata from a file (y/n) ? " 0 "" {MPLTEXT 1 0 2 "y;" }}}{EXCHG {PARA 0 "
file name: " 0 "" {MPLTEXT 1 0 16 "\"dat_test1.txt\";" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#Q**control*6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
Q,*materials*6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#Q(*nodes*6\"" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#Q+*elements*6\"" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#Q.*constraints*6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#Q
6*boundary~velocities*6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#Q0*point~
sources*6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#Q2*element~sources*6\"
" }}}{EXCHG {PARA 0 "save data into a file (y/n) ? " 0 "" {MPLTEXT 1 
0 2 "n;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "tcase;control;no
ds;elems;mat_props;bdr_conds;b_velts;p_srcs;e_srcs;" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#QH~Potential~Flow~in~a~Rectangular~Domain6\"" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#7%Q.point~sources6\"Q0element~sourcesF
%Q4boundary~velocitiesF%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#717$\"\"!F
%7$F%\"\"\"7$F%\"\"#7$F'F%7$F'F'7$F'F)7$F)F%7$F)F'7$F)F)7$\"\"$F%7$F1F
'7$F1F)7$\"\"%F%7$F5F'7$F5F)" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#727&\"
\"\"\"\"%\"\"&F%7&F%F'\"\"#F%7&F)F'\"\"$F%7&F+F'\"\"'F%7&F&\"\"(\"\")F
%7&F'F&F0F%7&F'F0F-F%7&F-F0\"\"*F%7&F/\"#5\"#6F%7&F/F7F0F%7&F0F7F4F%7&
F7\"#7F4F%7&F6\"#8\"#9F%7&F6F>F7F%7&F7F>F;F%7&F;F>\"#:F%" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#7$7%\"\"#F%\"#X7%\"\")F(F&" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#7(7$\"\"\"\"#57$\"\"#F&7$\"\"$F&7$\"#8\"\"!7$\"#9F-7$\"
#:F-" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%7%\"\"\"\"\"#\"\"!7%F&\"\"$F
'7%\"\"&\"\"%F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7#7$\"\"\"!#]" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#7#7$\"\"#\"#I" }}}{EXCHG {PARA 0 "" 0 
"" {TEXT -1 44 "Redefine this data with symbolic variables :" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 214 "mat_props:=[[kx,ky,alpha]]:
elems:=[[1,4,5,1],[1,5,2,1],[2,5,3,1],[3,5,6,1],[4,7,8,1],[5,4,8,1],[5
,8,6,1],[6,8,9,1],[7,10,11,1],[7,11,8,1],[8,11,9,1],[11,12,9,1],[10,13
,14,1],[10,14,11,1],[11,14,12,1],[12,14,15,1]]:" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 67 "tcase;control;nods;elems;mat_props;bdr_conds;b
_velts;p_srcs;e_srcs;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#QH~Potential~
Flow~in~a~Rectangular~Domain6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%Q
.point~sources6\"Q0element~sourcesF%Q4boundary~velocitiesF%" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#717$\"\"!F%7$F%\"\"\"7$F%\"\"#7$F'F%7$F'F'7$
F'F)7$F)F%7$F)F'7$F)F)7$\"\"$F%7$F1F'7$F1F)7$\"\"%F%7$F5F'7$F5F)" }}
{PARA 12 "" 1 "" {XPPMATH 20 "6#727&\"\"\"\"\"%\"\"&F%7&F%F'\"\"#F%7&F
)F'\"\"$F%7&F+F'\"\"'F%7&F&\"\"(\"\")F%7&F'F&F0F%7&F'F0F-F%7&F-F0\"\"*
F%7&F/\"#5\"#6F%7&F/F7F0F%7&F0F7F4F%7&F7\"#7F4F%7&F6\"#8\"#9F%7&F6F>F7
F%7&F7F>F;F%7&F;F>\"#:F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7#7%%#kxG%
#kyG%&alphaG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7(7$\"\"\"\"#57$\"\"#F
&7$\"\"$F&7$\"#8\"\"!7$\"#9F-7$\"#:F-" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#7%7%\"\"\"\"\"#\"\"!7%F&\"\"$F'7%\"\"&\"\"%F'" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#7#7$\"\"\"!#]" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7#7$\"
\"#\"#I" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "cgt_fem(yes);" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#%>Initializing~global~matrices:G" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6$-%'matrixG6#7171\"\"!F(F(F(F(F(F(F(F(F
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1 "" {XPPMATH 20 "6#*(%3Assembling~elementG\"\"\"7&F%\"\"%\"\"&F%F%%\"
:GF%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7171,$%#kxG#!\"\"
\"\"#\"\"!F-,$F)#\"\"\"F,F-F-F-F-F-F-F-F-F-F-F-71F-F-F-F-F-F-F-F-F-F-F
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" 1 "" {XPPMATH 20 "6#*(%3Assembling~elementG\"\"\"7&F%\"\"&\"\"#F%F%%
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\"\"\"#*&#\"\"\"F,F/%#kyGF/F+,$F0#F/F,\"\"!,$F)F2F3F3F3F3F3F3F3F3F3F3F
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6F6F6F6F6" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*(%3Assembling~elementG\"
\"\"7&\"\"#\"\"&\"\"$F%F%%\":GF%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%
'matrixG6#7171,&%#kxG#!\"\"\"\"#*&#\"\"\"F,F/%#kyGF/F+,$F0#F/F,\"\"!,$
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{XPPMATH 20 "6#-%'matrixG6#7171,&%#kxG#!\"\"\"\"#*&#\"\"\"F,F/%#kyGF/F
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3F3F3F371F3F)F3F1F6F1F3F3F3F3F3F3F3F3F371F3F3F4F3F1F(F3F3F3F3F3F3F3F3F
371F3F3F3F3F3F3F3F3F3F3F3F3F3F3F3F;F;F;F;F;F;F;F;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#*(%3Assembling~elementG\"\"\"7&\"\"%\"\"(\"\")F%F%%\":G
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\"#*&#\"\"\"F,F/%#kyGF/F+,$F0#F/F,\"\"!,$F)F2F3F3F3F3F3F3F3F3F3F3F371F
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20 "6#-%'matrixG6#7171,&%#kxG#!\"\"\"\"#*&#\"\"\"F,F/%#kyGF/F+,$F0#F/F
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"" 1 "" {XPPMATH 20 "6#*(%3Assembling~elementG\"\"\"7&\"\"&\"\")\"\"'F
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11 "" 1 "" {XPPMATH 20 "6#*(%3Assembling~elementG\"\"\"7&\"\")\"#6\"\"
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G#!\"\"\"\"#*&#\"\"\"F,F/%#kyGF/F+,$F0#F/F,\"\"!,$F)F2F3F3F3F3F3F3F3F3
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