Correction TP 5

Correction TP 5
//Schéma saute mouton pour l’eq des ondes sur un carré
// d2t(u)-c2.delta(u)=f
// u=0 au bord
function [z]=fonc_temps(t,a,t0)
z=exp(-a*(t-t0).*(t-t0));
endfunction
clear all;
c=1.;
//célérité du son
n=201;
//nombre de points en x et y
h=1./(n-1);
//pas de maillage
tf=5;
//temps final
lambda=0.99;
//cfl (1 limite de stabilité)
dt=lambda*h/(sqrt(2)*c);
//pas de temps calculé
//donnée de la gaussienne en temps
a=10000;
//rampe de la gaussienne
t0=0.04;
//centrage de la gaussienne en temps
cfl=c*dt/h
//CFL
cfl2=cfl*cfl;
dt2=dt*dt;
tcfl=[’\lambda = ’ string(lambda)];
th=[’h = 1/’ string(n-1)];
tdt=[’\Deltat = ’ msprintf(’%6.2g’,dt)]
uk=zeros(n,n);
ukm1=zeros(n,n);
ukp1=zeros(n,n);
v=zeros(n,n);
//vecteur
//vecteur
//vecteur
//vecteur
solution à l’instant tk
solution à l’instant tk-1
solution à l’instant tk+1
temporaire
//initialisation à l’instant 0 et dt
tk=2*dt;
//temps courant
k=2;
//source dirac au centre du carré (n impair !) (50000 pour f, 40 pour f")
f=zeros(n,n);
//f((n+1)/2,(n+1)/2)=80000.;
f(10,10)=900000;
//initialisation pour le graphique
scf(1);clf();hf=gcf();
hf.pixmap = "on";
hf.figure_size = [600 600];
hf.children.axes_visible=[’off’,’off’,’off’] ;
hf.children.isoview=’on’;
hf.children.tight_limits = "on"
hf.children.margins = [0,0,0,0];
hf.pixel_drawing_mode=’xor’
x=0:h:1;
xset("colormap",oceancolormap(128));
drawlater()
Sgrayplot(x’,x’,uk, strf="040")
drawnow()
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drawlater()
//boucle itérative en temps, schéma saute-mouton
while(tk<tf)
fk=f*fonc_temps(tk,a,t0);
v(2:n-1,2:n-1)=uk(3:n,2:n-1)+uk(1:n-2,2:n-1)+uk(2:n-1,3:n)+uk(2:n-1,1:n-2)-4*uk(2:n-1,2:n-1);
ukp1=2*uk-ukm1+cfl2*v+dt2*fk;
ukm1=uk;
uk=ukp1;
drawlater()
Sgrayplot(x’,x’,uk, strf="040")
tk=tk+dt;
drawnow()
drawlater()
end,
h.pixel_drawing_mode=’copy’
drawnow()
On illustre ci-après la façon dont on peut inclure cette simulation dans une interface utilisateur (gui).
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function [z]=fonc_temps(t,a,tau)
z=exp(-a*(t-tau).*(t-tau));
endfunction
function compute()
ht0 = findobj("tag", "t0");t0=evstr(ht0.string);
htf = findobj("tag", "tf"); tf=evstr(htf.string);
hn = findobj("tag", "n");n=evstr(hn.string);
hdt = findobj("tag", "dt");dt=evstr(hdt.string);
hc = findobj("tag", "c");c=evstr(hc.string);
htau = findobj("tag", "tau");tau=evstr(htau.string);
ha = findobj("tag", "a");a=evstr(ha.string);
hsi = findobj("tag", "source i");si=evstr(hsi.string);
hsj = findobj("tag", "source j");sj=evstr(hsj.string);
disp(t0,tf,n,dt,c,tau,a,si,sj)
ht = findobj("tag", "t");
hlt = findobj("tag", "lt");
hbtn = findobj("tag", "btn1");btn=hbtn.string;
if(btn=="Stop")
set(hbtn,’string’,’Calcul’);
set(ht,’visible’,’off’);
set(ht,’string’,’0’);
set(hlt,’visible’,’off’);
m_axes = gca();
m_axes.visible="off";
resume;
else
set(hbtn,’string’,’Stop’);
set(ht,’visible’,’on’);
set(hlt,’visible’,’on’);
end,
h=1./(n-1);
x=0:h:1;
lambda=0.9999;
dt=lambda*h/(sqrt(2)*c);
set(hdt,"string",string(dt));
cfl=c*dt/h;
//CFL
hcfl = findobj("tag", "cfl");
set(hcfl,"string",string(cfl))
cfl2=cfl*cfl;
dt2=dt*dt;
uk=zeros(n,n);
ukm1=zeros(n,n);
ukp1=zeros(n,n);
v=zeros(n,n);
//vecteur
//vecteur
//vecteur
//vecteur
//pas de maillage
//pas de temps calculé
solution à l’instant tk
solution à l’instant tk-1
solution à l’instant tk+1
temporaire
//initialisation à l’instant 0 et dt
tk=2*dt;
//temps courant
k=2;
//source dirac au centre du carré (n impair !) (50000 pour f, 40 pour f")
f=zeros(n,n);
//f((n+1)/2,(n+1)/2)=80000.;
f(si,sj)=900000;
m_axes = gca();
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m_axes.axes_bounds = [0.25,0.05,0.75,0.95];
m_axes.margins = [0.05 0.05 0.05 0.05];
m_axes.auto_scale="off";
m_axes.visible="on";
xset("colormap",oceancolormap(256));
drawlater()
Sgrayplot(x’,x’,uk, strf="040",zminmax=[-1,1])
drawnow()
drawlater()
//boucle itérative en temps, schéma saute-mouton
while(tk<tf)
set(ht,"string",string(tk));
fk=f*fonc_temps(tk,a,tau);
v(2:n-1,2:n-1)=uk(3:n,2:n-1)+uk(1:n-2,2:n-1)+uk(2:n-1,3:n)+uk(2:n-1,1:n-2)-4*uk(2:n-1,2:n-1);
ukp1=2*uk-ukm1+cfl2*v+dt2*fk;
ukm1=uk;
uk=ukp1;
zmin=min(uk);zmax=max(uk);zmax=0.9*(zmax-zmin)/2;zmin=-zmax;
drawlater()
Sgrayplot(x’,x’,uk, strf="040",zminmax=[zmin,zmax])
tk=tk+dt;
drawnow()
end,
endfunction
// Window Parameters initialization
frame_w = 200; frame_h = 600;
plot_w = 600; plot_h = frame_h;
margin_x = 15; margin_y = 15;
defaultfont = "arial";
axes_w = 3*margin_x + frame_w + plot_w;
axes_h = 2*margin_y + frame_h;
gui_onde = scf(100001);
gui_onde.background = -2;
gui_onde.figure_position = [100 100];
gui_onde.figure_name = gettext("GUI Onde");
gui_onde.axes_size = [axes_w axes_h];
//
//
//
//
//
//
//
//
Frame width and height
Plot width and heigh
Horizontal and vertical margin for elements
Default Font
axes width
axes height (100 =>toolbar height)
Create window with id=100001 and make it the current one
Background and text
// Change dimensions of the figure
delmenu(gui_onde.figure_id,gettext("&File")); // Remove Scilab graphics menus & toolbar
delmenu(gui_onde.figure_id,gettext("&Tools"));
delmenu(gui_onde.figure_id,gettext("&Edit"));
delmenu(gui_onde.figure_id,gettext("&?"));
toolbar(gui_onde.figure_id,"off");
title = uicontrol("parent",gui_onde, "style","text", ...
"string","Simulation de l’’équation des ondes dans un carré", "units","pixels", ...
"position",[0 630 500 40],...
"fontname",defaultfont, "fontunits","points", ...
"fontsize",20, "horizontalalignment","center", ...
"background",[1 1 1], "tag","title_control");
// Frame parameters
my_frame = uicontrol("parent",gui_onde, "relief","groove", ...
"style","frame", "units","pixels", ...
"position",[ margin_x margin_y frame_w frame_h], ...
"horizontalalignment","center", "background",[1 1 1], ...
"tag","frame_control");
// Frame title parameter
my_frame_title = uicontrol("parent",gui_onde, "style","text", ...
"string","paramètres", "units","pixels", ...
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"position",[40+margin_x margin_y+frame_h-10 100 20],...
"fontname",defaultfont, "fontunits","points", ...
"fontsize",16, "horizontalalignment","center", ...
"background",[1 1 1], "tag","title_frame_control");
// Adding model parameters
h1 = frame_w;
h1o = 350;
// ordered list of labels
labels1 = ["c","t0", "tf", "n", "dt", "cfl","a","tau","source i", "source j"];
tips = ["vitesse du son","temps initial","temps final","découpage suivant x et y", ...
"pas de temps","cfl","rampe de la source gausienne","temps où la source gaussienne est maximale",...
"abcisse de la source (indice dans la grille)","ordonnée de la source (indice dans la grille)"];
// ordered list of default values
values1 = [1, 0, 5, 201, 0.01, 0, 10000, 0.04, 10, 10];
// positioning
l1 = 25; l2 = 100; l3 = 80;
drawlater
for k=1:size(labels1,2)
uicontrol("parent",gui_onde,"style","text",...
"string",labels1(k), "position",[l1,h1-k*20+h1o,l2,20], ...
"horizontalalignment","left", "fontsize",14, ...
"background",[1 1 1],’TooltipString’,tips(k));
guientry1(k) = uicontrol("parent",gui_onde, "style","edit",...
"string",string(values1(k)), "position",[l3,h1-k*20+h1o,120,20], ...
"horizontalalignment","left", "fontsize",14, ...
"background",[.9 .9 .9], "tag",labels1(k),’TooltipString’,tips(k));
end
uicontrol("parent",gui_onde,"style","text",...
"string",’t=’, "position",[55 60 80 20], ...
"horizontalalignment","left", "fontsize",14, ...
’visible’,’off’,’tag’,’lt’,"background",[1 1 1]);
uicontrol("parent",gui_onde, "style","edit",...
"string",’0’, "position",[70 60 80 20], ...
"horizontalalignment","left", "fontsize",14, ...
"background",[.9 .9 .9],’visible’,’off’, "tag",’t’);
// Adding button
huibutton = uicontrol(gui_onde, "style","pushbutton", ...
"Position",[70 100 80 20], "String","Calcul", ...
"BackgroundColor",[.9 .9 .9], "fontsize",14, ...
"tag","btn1","Callback","compute");
drawnow
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