Approximate the temperature of the plate at (1,0)

set(ax,'YTick',[ -1,... -0.90000000000000002,... -0.80000000000000004,... -0.69999999999999996,... -0.59999999999999998,... -0.5,... -0.39999999999999991,... -0.29999999999999993,... -0.19999999999999996,... -0.099999999999999978,... 0,... 0.099999999999999978,... 0.19999999999999996,... 0.29999999999999993,... 0.39999999999999991,... 0.5,... 0.59999999999999998,... 0.69999999999999996,... 0.80000000000000004,... 0.90000000000000002,... 1,...]);pdetool('gridon','on');

function pdemodel99[pde_fig,ax]=pdeinit;pdetool('appl_cb',1);pdetool('snapon','on');set(ax,'DataAspectRatio',[1 1.0499999999999998 1]);set(ax,'PlotBoxAspectRatio',[1.4285714285714286 0.95238095238095255 1.4285714285714286]);set(ax,'XLim',[-1 1]);set(ax,'YLim',[-1 1]);set(ax,'XTick',[ -1,... -0.90000000000000002,... -0.80000000000000004,... -0.69999999999999996,... -0.59999999999999998,... -0.5,... -0.39999999999999991,... -0.29999999999999993,... -0.19999999999999996,... -0.099999999999999978,... 0,... 0.099999999999999978,... 0.19999999999999996,... 0.29999999999999993,... 0.39999999999999991,... 0.5,... 0.59999999999999998,... 0.69999999999999996,... 0.80000000000000004,... 0.90000000000000002,... 1,...]);

pderect([0 1 0 1],'SQ1'); pdecirc(0,0,0.3,'C1');

pdepoly([ 0,0.5,0.5,0.2,0],[ 0,0,0.6,0.3,0.6],'P1');

function pdemodel[pde_fig,ax]=pdeinit;pdetool('appl_cb',1);pdetool('snapon','on');set(ax,'DataAspectRatio',[1 0.80000000000000004 1]);set(ax,'PlotBoxAspectRatio',[3.75 2.5 1]);set(ax,'XLim',[-1.5 6]);set(ax,'YLim',[-1 3]);set(ax,'XTickMode','auto');set(ax,'YTickMode','auto');pdetool('gridon','on'); % Geometry description:pdepoly([ 0,... 5, 4,1,],...[ 0,0, 1.7320508075688772, 1.7320508075688772,...],... 'P1');

% Mesh generation:setappdata(pde_fig,'trisize',1);setappdata(pde_fig,'Hgrad',1.3);setappdata(pde_fig,'refinemethod','regular');setappdata(pde_fig,'jiggle',char('on','mean',''));pdetool('initmesh')pdetool('refine')pdetool('refine')pdetool('refine')pdetool('refine') % PDE coefficients:pdeseteq(1,...'1.0',...'0.0',...'1.5/1.04',...'1.0',...'0:10',...'0.0',...'0.0',...'[0 100]')setappdata(pde_fig,'currparam',...['1.0 ';...'0.0 ';...'1.5/1.04';...'1.0 ']) % Solve parameters:setappdata(pde_fig,'solveparam',...str2mat('0','8064','10','pdeadworst',...'0.5','longest','0','1E-4','','fixed','Inf')) % Plotflags and user data strings:setappdata(pde_fig,'plotflags',[1 1 1 1 1 1 1 1 0 0 0 1 1 0 0 0 0 1]);setappdata(pde_fig,'colstring','');setappdata(pde_fig,'arrowstring','');setappdata(pde_fig,'deformstring','');setappdata(pde_fig,'heightstring',''); % Solve PDE:pdetool('solve')

set(findobj(get(pde_fig,'Children'),'Tag','PDEEval'),'String','P1') % Boundary conditions:pdetool('changemode',0)pdesetbd(4,...'neu',...1,...'0',...'4')pdesetbd(3,...'dir',...1,...'1',...'15')pdesetbd(2,...'neu',...1,...'0',...'4')pdesetbd(1,...'neu',...1,...'0',...'0')

Approximate the temperature of the plate at (1,0)

[pde_fig,ax]=pdeinit;pdecirc(-0.6,0,0.1,'C1'); % center then radiuspderect([-0.9 0.9 -0.5 0.5],'R1'); % x-values then y-valuesset(findobj(get(pde_fig,'Children'),'Tag','PDEEval'),'String','R1-C1')

function pdemodel[pde_fig,ax]=pdeinit;set(ax,'XLim',[-1.5 1.5]);set(ax,'YLim',[-1 1]);set(ax,'XTickMode','auto');set(ax,'YTickMode','auto');

% Geometry description:pderect([-0.8 0.9 0.6 -0.8],'R1');pdecirc(-0.7,0.5,0.1,'C1');pderect([-0.8 -0.7 0.6 0.5],'SQ1');set(findobj(get(pde_fig,'Children'),'Tag','PDEEval'),'String','R1-SQ1+C1')

When designing aircrafts it is very important to know the areodynamical properties of the wings

wing = Airfoil();[p,e,t]=initmesh(wing,'hmax',2);pdemesh(p,e,t)

function g=Airfoil()g=[2 17.7218 16.0116 1.5737 1.6675 1 02 16.0116 9.0610 1.6675 1.3668 1 02 9.0610 -0.5759 1.3668 -0.1102 1 02 -0.5759 -9.5198 -0.1102 -1.8942 1 02 -9.5198 -15.6511 -1.8942 -2.5938 1 02 -15.6511 -18.1571 -2.5938 -1.7234 1 02 -18.1571 -16.9459 -1.7234 0.2051 1 02 -16.9459 -12.4137 0.2051 2.2238 1 02 -12.4137 -5.4090 2.2238 3.4543 1 02 -5.4090 2.8155 3.4543 3.5046 1 02 2.8155 10.6777 3.5046 2.6664 1 02 10.6777 16.3037 2.6664 1.7834 1 02 16.3037 17.7218 1.7834 1.5737 1 02 -30.0000 30.0000 -15.0000 -15.0000 1 02 30.0000 30.0000 -15.0000 15.0000 1 02 30.0000 -30.0000 15.0000 15.0000 1 02 -30.0000 -30.0000 15.0000 -15.0000 1 0]'

Potential Flow Over a Wing

function r = rvect(p,e,gN)L1=[31,13,30]; %normal u =4L2=[4,29,12,28,11,27,10,26,2]; % u=15L3=[25,9,24]; %normal u =4L4=[1,19,5,20,6,21,7,22,8,23,2]; %normal u =0np = size(p,2);ne = size(e,2);r = zeros(np,1);for E = 1:ne loc2glb = e(1:2,E); x = p(1,loc2glb); y = p(2,loc2glb); len = sqrt((x(1)-x(2))ˆ2+(y(1)-y(2))ˆ2); xc = mean(x); yc = mean(y); tmp = gN(xc,yc); rK = tmp*[1; 1]*len/2; r(loc2glb) = r(loc2glb) + rK;end