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}{PSTYLE "Heading 1" -1 269 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }3 1 0 0 8 4 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 2" -1 270 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }3 1 0 0 8 2 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 3" -1 271 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 1 1 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 269 "" 0 "" {TEXT 258 15 "FINITE ELEMENTS" }} {PARA 270 "" 0 "" {TEXT -1 29 "SYMBOLIC PROGRAMMING IN MAPLE" }}{PARA 19 "" 0 "" {TEXT 259 16 "by Artur Portela" }{TEXT 260 0 "" }}{PARA 271 "" 0 "" {TEXT 256 26 "Potential-Flow Example 3: " }{TEXT 283 47 "F low with Specified Normal-Boundary Velocities\n" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 47 "restart: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(Plot ter);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7:%+draw_labelG%,draw_symbolG %*draw_textG%+draw_titleG%)move_penG%*new_arrowG%)new_axesG%*new_color G%.new_pen_styleG%1new_plot_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_plot G%3start_3D_animationG%.start_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_fe m);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7+%/animate_3D_defG%/animate_3D _rotG%3animate_velocitiesG%3plot_contour_linesG%,plot_fluxesG%5plot_li ne_potentialsG%*plot_meshG%2plot_problem_dataG%0plot_velocitiesG" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 20 "" 0 " " {TEXT 261 17 " Data Preparation" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 31 "The best way to input data for " }{TEXT 263 7 "Cgt_fem" }{TEXT -1 25 " is to use the procedure " }{TEXT 262 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 264 7 "co ntrol" }{TEXT -1 169 "* [title,point sources,element sourc es,boundary velocities]\ntitle Potential Flow in a Rectangular Domain \npoint sources\nelement sources\nboundary velocities\n\n*" }{TEXT 265 9 "materials" }{TEXT -1 104 "* [material,x-permeability, y-permeability,angle of the local x-direction]\n1 2 2 45\n2 8 8 45\n\n *" }{TEXT 266 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 \n 14 4 1\n15 4 2 \n\n*" }{TEXT 267 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 \n6 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 1 4 11 1 \n15 11 14 12 1\n16 12 14 15 1 \n\n*" } {TEXT 268 11 "constraints" }{TEXT -1 59 "* [node,potential]\n1 10\n2 10\n3 10\n13 0\n14 0\n15 0\n\n*" }{TEXT 269 19 "boundary veloci ties" }{TEXT -1 52 "* [node1,node2,normal velocity]\n1 2 0\n2 3 0\n5 4 0\n\n*" }{TEXT 270 13 "point sources" }{TEXT -1 25 "* [node,Q] \n1 -50\n\n*" }{TEXT 271 15 "element sources" }{TEXT -1 25 "* [ele ment,q]\n2 30\n\n*" }{TEXT 272 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 the top, can be defined in any order." }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 83 "Alternati vely, data can be given manually through the definition of the variabl es: " }{TEXT 273 5 "tcase" }{TEXT -1 2 ", " }{TEXT 274 7 "control" } {TEXT -1 2 ", " }{TEXT 275 4 "nods" }{TEXT -1 2 ", " }{TEXT 276 5 "ele ms" }{TEXT -1 2 ", " }{TEXT 277 9 "mat_props" }{TEXT -1 2 ", " }{TEXT 278 9 "bdr_conds" }{TEXT -1 2 ", " }{TEXT 279 7 "b_velts" }{TEXT -1 2 ", " }{TEXT 280 6 "p_srcs" }{TEXT -1 5 " and " }{TEXT 281 6 "e_srcs" } {TEXT -1 46 ". See bellow the structure of these variables." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 20 "" 0 " " {TEXT 282 47 " Flow with Specified Normal-Boundary Velocities" } {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 258 "As another proble m, consider the same case of a uniform flow in a rectangular domain. D efine flow potentials, uniformly distributed on side, and, uniform vel ocities normal to the boundary, on the opposite side. Consider the hyd raulic conductivity parameters." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "read_save_data();" }}}{EXCHG {PARA 0 "read data from a file (y /n) ? " 0 "" {MPLTEXT 1 0 2 "y;" }}}{EXCHG {PARA 0 "file name: " 0 "" {MPLTEXT 1 0 16 "\"dat_test3.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.*c onstraints*6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#Q6*boundary~velociti es*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) ? 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