?? meshdemo.m
字號:
40383860.31 3566212
40383731.5 3566125.75
40383553.56 3565973.5
40383425.21 3565709.543
40383371.94 3565600
40383371.84 3565318.25
40383274.28 3564910.026
40383245.78 3564790.75
40383273.06 3564571.75
40383335.34 3564413.428
40383428.94 3564175.5
40383531.16 3563776.25
40383642.44 3563321.75
40383810.19 3562821.75
40383928.86 3562532.133
40383993.25 3562375
40384073.5 3562158.25
40384227.84 3561709.25
40384321.22 3561416.25
40384372.13 3561191.5
40384462.22 3560927
40384494.16 3560711
40384531.3 3560487.548
40384541.53 3560426
40384596.53 3560224.5
40384634.59 3559944.5
40384634.2 3559831.205
40384634.1 3559802.336
40384633.85 3559730.603
40384633.85 3559703.137
40384633.85 3559667.332
40384633.85 3559448.881
40384633.85 3559389.062
40384618.86 3559231.416
40384557.12 3558952.631
40384561.23 3558714.283
40384585.89 3558586.889
40384709.17 3558525.248
40384873.55 3558471.825
40385009.16 3558492.372
];
n1 = size(p1,1);
n2 = size(p2,1);
c1 = [(1:n1-1)', (2:n1)'; n1, 1];
c2 = [(1:n2-1)', (2:n2)'; n2, 1];
node = [p1; p2];
cnect = [
c1
c2+n1
];
% Make mesh
[p,t] = mesh2d(node,cnect);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Lake Superior
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
answer = input(['The following is a mesh of Lake Superior and is a standard test of mesh algorithms. \n' ...
'\n' ...
'This example uses the automatic size function only' ...
'\n' ...
'Continue [y/n] \n'],'s');
if ~strcmp(answer,'y')
return
end
close all
% From:
% Computer Solutions Europe AB
% Bjornnasvagen 21
% S-113 47 Stockholm
% SWEDEN
% Tel: +46 8 15 30 22
% Fax: +46 8 15 76 35
% E-mail: info@comsol.se
% URL: http://www.comsol.se/
p1=[
-8.9154147 1.6615920
-8.8847064 1.5538653
-8.7270571 1.4396306
-8.6780329 1.3310253
-8.2763869 1.3642085
-7.7589437 1.5521208
-7.3399811 1.5866412
-7.2064877 1.7400111
-6.9871610 1.7838988
-6.9190874 1.6751018
-6.6594362 1.8237880
-6.4705078 2.0285109
-6.3982459 2.0257761
-6.1776033 2.1236043
-5.9683636 1.9041636
-6.0500631 1.6420917
-6.2751037 1.4382319
-6.2083449 1.2768143
-6.3593873 1.1233594
-6.4379782 0.9672913
-6.4389687 0.9408290
-6.3308569 0.9103191
-5.9216680 1.1606956
-5.8853530 1.1594465
-5.5306989 0.8827500
-5.4571118 0.9068911
-5.2776995 0.8218321
-4.6882658 1.0696109
-4.4325551 1.1157840
-3.9867787 1.5284986
-3.6232783 1.5733560
-3.5156848 1.5181578
-3.1151141 1.6162773
-2.6031886 1.9253444
-2.4201615 2.0814581
-2.0576784 2.1825510
-1.9469493 2.3929843
-1.6564457 2.6016249
-1.4385855 2.8113568
-1.1857180 2.9681802
-0.8965760 3.2839699
-0.4656316 3.4939341
-0.0715676 3.6520868
0.3221563 3.5994536
0.6089023 3.4943945
0.6092879 3.3885375
0.3942456 3.3878929
0.2866788 3.4141384
0.0717038 3.3345153
0.0896864 3.2286668
0.1076576 3.1757488
-0.1436793 3.0169900
-0.3235837 2.8584538
-0.4676923 2.7529346
-0.9391942 2.0668111
-1.0495193 1.7498742
-1.0882363 1.3531376
-1.0158452 1.3262275
-0.9424102 1.4845979
-0.6152380 1.7477533
-0.5061946 1.9061816
-0.2890742 2.0115316
-0.5066670 1.7473959
-0.6160022 1.5360392
-0.3979720 1.8000363
-0.1808403 1.8525961
0.2894343 1.7998173
0.5431103 1.6681146
0.9058832 1.5373304
0.9432856 1.3258124
1.0534256 1.1147328
1.1641909 0.8507940
1.3109203 0.6930545
1.3117251 0.5871977
1.4214690 0.5351345
1.9317215 0.5400872
2.2226054 0.5965222
2.3340522 0.4391798
2.4073552 0.4137156
2.4449497 0.3348350
2.5909063 0.3369578
2.6249835 0.4962917
2.7343488 0.4979874
2.8454551 0.3938967
2.9366470 0.3954205
2.9201944 0.2892562
2.9931921 0.2905022
3.3135431 0.7199108
3.3863589 0.7213257
3.9960329 1.1315466
4.0705567 1.0538628
4.6490632 1.1744760
4.9039980 1.1550887
5.4495532 1.1450567
5.9850466 1.4278414
6.1653805 1.4607402
6.3476152 1.4409063
6.6355959 1.5048353
6.5309084 1.3948027
6.4623697 1.2862027
6.4803085 0.8098819
6.4094979 0.7542354
6.4100090 0.7012564
6.4882671 0.5981826
6.7068647 0.6065329
6.8546905 0.5593290
6.9296957 0.5093111
7.3625916 0.6332439
7.4195041 0.5826584
7.4810256 0.4262426
7.6622000 0.4606821
7.7339418 0.4903887
7.6927729 0.5946095
7.6199031 0.5913803
7.5788199 0.6956243
7.4649955 0.7967085
7.4604098 0.9025555
7.6668095 1.1767640
7.7709460 1.2875089
7.7298813 1.3917132
7.6707366 1.4951115
7.6356734 1.4670289
7.6246141 1.3074531
7.5532118 1.2777792
7.5280861 1.4357493
7.5345391 1.7011603
7.7131429 1.7621690
7.8603274 1.7158544
7.9228745 1.9308907
7.7348899 2.0813402
7.3713821 2.1182087
7.2698318 1.9547751
7.1885795 2.1633926
7.1152657 2.1868122
7.0441691 2.1573400
6.9336956 2.2058041
6.9676141 2.2602054
7.0648074 2.5292990
7.0897106 2.7954185
7.2917362 3.1221593
7.3230152 3.2295634
7.2074219 3.4101256
7.0987913 3.4319941
7.0562590 3.5892427
6.8349672 3.7390777
6.5426013 3.8863685
6.3538119 4.1440578
6.6493349 4.7917061
6.5385166 4.8932842
6.7052993 5.1650313
6.7009764 5.2708721
5.7441174 5.2345817
5.5686945 5.1755508
4.7886070 5.1509481
4.4636817 5.3536511
4.2075761 5.6646354
3.6075780 7.1858876
3.3873644 7.6576363
3.2804384 7.7613007
3.1762847 7.7327191
3.0381962 7.6506117
2.8286881 7.6467634
2.8598071 7.8590921
2.6845531 7.9089847
2.5468001 7.8008409
2.4437671 7.6933492
2.3390419 7.6917801
2.1983122 7.7691861
2.1616242 7.9010276
2.0918985 7.9000964
2.0235167 7.7933405
1.9540682 7.7660064
1.5705080 7.7353016
1.5002116 7.7875578
1.2547448 7.9442315
0.7309650 8.1526824
0.4522013 8.2575018
0.1738657 8.3098811
-0.0694533 8.5215153
-0.1737495 8.4157382
-0.2084645 8.4422444
-0.3476150 8.3630957
-0.4518238 8.3898231
-0.5558115 8.4695476
-0.5215963 8.3106439
-0.5221188 8.1518584
-0.4879606 7.9400337
-0.2092654 7.8335660
-0.2097517 7.4630660
-0.5257651 7.0403597
-0.5604465 7.1463352
-0.7716285 6.9354925
-0.9473082 6.8835005
-0.9833619 6.7249256
-1.1593398 6.6731632
-1.2287946 6.7795396
-1.1574372 6.9378046
-0.6994015 7.4115277
-0.5933112 7.7286747
-0.6973173 7.8878837
-0.9759166 7.9422776
-1.1175557 7.6256239
-1.1194069 7.3609825
-1.2951661 7.2564438
-1.5483098 6.4117610
-1.9366363 6.3100700
-1.8637764 6.5209552
-1.7582839 6.5197737
-1.7202965 6.7840348
-1.5427314 6.9939696
-1.5417155 7.0998256
-1.5762336 7.1530937
-1.9985176 6.9989869
-2.3506579 6.8978706
-2.5645144 6.6893724
-2.5351899 6.3183276
-2.7562921 5.7395724
-3.7980607 5.0191439
-4.3373509 4.7676755
-4.9834948 4.5740477
-5.9256532 4.1282314
-7.0382285 3.1643631
-7.4517045 2.7580044
-8.2033903 2.1245258
-8.7235361 1.8639192
];
p2=[
-6.0222359 1.4026510
-5.9152018 1.5578835
-5.8726343 1.5299217
-5.7920161 1.5536639
-5.8345898 1.5816055
-5.8318773 1.6609928
-5.6635570 1.7083083
-5.5966615 1.7590827
-5.6808641 1.8413432
-5.7929717 1.7391469
-6.0818599 1.5637339
-6.0865686 1.4314222
];
p3=[
-5.7324455 1.9225485
-5.5683675 1.9594866
-5.5335991 1.9159672
-5.5318777 1.9688923
-5.4498160 2.0457126
-5.4914569 2.1000333
-5.7297704 2.0019357
-5.7677013 1.9502324
];
p4=[
-5.2706487 2.2254789
-5.2257103 2.2770640
-5.2196558 2.3563407
-5.1911650 2.4614151
-5.2924029 2.4539566
-5.3166868 2.3699543
-5.3193455 2.2852741
-5.3444930 2.1748120
];
p5=[
-2.6285090 4.8904087
-2.5231726 4.8093509
-2.4524965 4.7818143
-2.1664250 4.9101487
-1.8814086 4.9860466
-2.0588911 4.9881727
-2.0937130 5.0415487
-1.9150532 5.1452403
-1.7011793 5.2487523
-1.5239785 5.2470098
-1.1676824 5.5087407
-1.2022868 5.6148538
-0.9185046 5.7718016
-0.8828910 5.8245348
-0.9532116 5.8778612
-1.3075201 5.7215257
-1.5563954 5.5649116
-1.6276655 5.5126727
-1.7340945 5.4872998
-1.8405570 5.4619959
-2.0900008 5.3326514
-2.3756722 5.1777288
-2.5904890 5.0486276
];
p6=[
-0.1745905 7.6482740
-0.1048759 7.4629629
-0.0174793 7.4629295
-0.0349355 7.5687895
0.0349007 7.7275752
0.2267794 7.7806613
0.3839078 7.7280333
0.5583180 7.7550129
0.6632222 7.7024853
0.8201638 7.7296796
0.7325480 7.8086476
0.6273773 7.9405222
0.4880418 7.9135694
0.1393711 7.9922753
0.0348428 7.9922181
-0.1743299 7.8864526
];
p7=[
4.5964504 4.4039327
4.8814214 4.4120893
4.9866866 4.4681990
5.1274771 4.5254771
5.1614199 4.5795088
5.0886198 4.6302255
4.9818982 4.6269721
4.8364965 4.7285905
4.5535316 4.6675729
4.3785074 4.5569131
4.3813116 4.4510625
];
n1 = size(p1,1);
n2 = size(p2,1);
n3 = size(p3,1);
n4 = size(p4,1);
n5 = size(p5,1);
n6 = size(p6,1);
n7 = size(p7,1);
c1 = [(1:n1-1)', (2:n1)'; n1, 1];
c2 = [(1:n2-1)', (2:n2)'; n2, 1];
c3 = [(1:n3-1)', (2:n3)'; n3, 1];
c4 = [(1:n4-1)', (2:n4)'; n4, 1];
c5 = [(1:n5-1)', (2:n5)'; n5, 1];
c6 = [(1:n6-1)', (2:n6)'; n6, 1];
c7 = [(1:n7-1)', (2:n7)'; n7, 1];
node = [p1; p2; p3; p4; p5; p6; p7];
cnect = [
c1
c2+n1
c3+n2+n1
c4+n3+n2+n1
c5+n4+n3+n2+n1
c6+n5+n4+n3+n2+n1
c7+n6+n5+n4+n3+n2+n1
];
% Make mesh
[p,t] = mesh2d(node,cnect);
answer = input(['The following shows the influence of gradient limiting on the size function. \n' ...
'The value dhmax is reduced to 0.1 \n' ...
'\n' ...
'Continue [y/n] \n'],'s');
if ~strcmp(answer,'y')
return
end
close all
% Solver options
options.dhmax = 0.1;
% Make mesh
[p,t] = mesh2d(node,cnect,[],options);
%save('D:\1.mat','p','t');
% User defined size functions
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
answer = input(['The following example shows how the element size can be controlled using the \n' ...
'various settings in HDATA. \n' ...
'\n' ...
'Continue [y/n] \n'],'s');
if ~strcmp(answer,'y')
return
end
close all
hdata = [];
options.output = false;
node = [0 0; 1 0; 1 1; 0 1]; % Simple square example
[p,t] = mesh2d(node,[],[],options); % Auto size fun only
figure
subplot(2,2,1)
patch('faces',t,'vertices',p,'facecolor','none','edgecolor','b');
axis equal off;
title('Automatic size fun only')
hdata.hmax = 0.1; % Global size of 0.1
[p,t] = mesh2d(node,[],hdata,options);
subplot(2,2,3)
patch('faces',t,'vertices',p,'facecolor','none','edgecolor','b');
axis equal off;
title('Global size fun with h0=0.1')
hdata.hmax = 0.1; % Global size of 0.1
hdata.edgeh = [1,0.05]; % Boundary layer on bottom edge
[p,t] = mesh2d(node,[],hdata,options);
subplot(2,2,2)
patch('faces',t,'vertices',p,'facecolor','none','edgecolor','b');
axis equal off;
title('Additional boundary layer function on bottom edge')
hdata = [];
hdata.fun = @hfun1;
[p,t] = mesh2d(node,[],hdata,options);
subplot(2,2,4)
patch('faces',t,'vertices',p,'facecolor','none','edgecolor','b');
axis equal off; hold on;
title('User defined funcion centred at [0.25,0.75]')
% Refinement
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
answer = input(['The following example shows how an existing mesh can be refined using the \n' ...
'REFINE function. This avoids doing expensive retriangulation. \n' ...
'\n' ...
'Continue [y/n] \n'],'s');
if ~strcmp(answer,'y')
return
end
close all
hdata = [];
options.output = false;
hdata.hmax = 0.1;
node = [0 0; 1 0; 1 1; 0 1]; % Simple square example
[p,t] = mesh2d(node,[],hdata,options); % Auto size fun only
figure
subplot(2,2,1)
patch('faces',t,'vertices',p,'facecolor','none','edgecolor','b');
axis equal off; hold on;
title('Uniform mesh from MESH2D')
node = [0.3,0.3; 0.7,0.3; 0.7,0.7; 0.3,0.7];
in = inpoly(p,node);
ti = sum(in(t),2)>0;
[p,t] = refine(p,t,ti);
subplot(2,2,2)
patch('faces',t,'vertices',p,'facecolor','none','edgecolor','b');
axis equal off; hold on;
title('Mesh refined in centre region using REFINE')
[p,t] = smoothmesh(p,t);
subplot(2,2,3)
patch('faces',t,'vertices',p,'facecolor','none','edgecolor','b');
axis equal off; hold on;
title('Smoothed mesh using SMOOTHMESH')
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function p = move(p,xm,ym)
% Move a node set p by [xm,ym]
n = size(p,1);
p = p + [xm*ones(n,1), ym*ones(n,1)];
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function p = rotate(p,A)
% Rotate a node set p by A degrees.
A = A*pi/180;
T = [ cos(A), sin(A)
-sin(A), cos(A)];
p = (T*p')';
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function h = hfun1(x,y)
% User defined size function for square
h = 0.01 + 0.1*sqrt( (x-0.5).^2+(y-0.5).^2 );
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function h = hfun2(x,y)
% User defined size function for cylinder
h1 = inf*ones(size(x));
in = (x>=0)&(x<=25)&(y>=-3)&(y<=3);
h1(in) = 0.2;
r = sqrt(x.^2+y.^2);
h2 = inf*h1;
h2(r<=3) = 0.02 + 0.05*r(r<=3);
h = min(h1,h2);
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