OptFEM3DP1 Toolbox: valid/validMass3DP1.m Source File

| OptFEM3DP1 Toolbox 20130618_070730 Matlab/Octave Optimized P1-Lagrange Finite Element Method in 3D

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validMass3DP1.m
Go to the documentation of this file.
1 function validMass3DP1()
2 % Copyright:
3 % See \ref license
4
5 Th=CubeMesh(3);
6 %M=MassAssembling3DP1base(Th.nq,Th.nme,Th.me,Th.volumes);
7
8
9 disp('-----------------------------------------')
10 disp(' Test 1: Matrices errors and CPU times ')
11 disp('-----------------------------------------')
12 tic();
13 Mbase=MassAssembling3DP1base(Th.nq,Th.nme,Th.me,Th.volumes);
14 T(1)=toc();
15 tic();
16 MOptV0=MassAssembling3DP1OptV0(Th.nq,Th.nme,Th.me,Th.volumes);
17 T(2)=toc();
18 Test1.error(1)=norm(Mbase-MOptV0,Inf);
19 Test1.name{1}='MassAssembling3DP1OptV0';
20 fprintf(' Error P1base vs OptV0 : %e\n',Test1.error(1))
21 tic();
22 MOptV1=MassAssembling3DP1OptV1(Th.nq,Th.nme,Th.me,Th.volumes);
23 T(3)=toc();
24 Test1.error(2)=norm(Mbase-MOptV1,Inf);
25 Test1.name{2}='MassAssembling3DP1OptV1';
26 fprintf(' Error P1base vs OptV1 : %e\n',Test1.error(2))
27 tic();
28 MOptV2=MassAssembling3DP1OptV2(Th.nq,Th.nme,Th.me,Th.volumes);
29 T(4)=toc();
30 Test1.error(3)=norm(Mbase-MOptV2,Inf);
31 Test1.name{3}='MassAssembling3DP1OptV2';
32 fprintf(' Error P1base vs OptV2 : %e\n',Test1.error(3))
33
34 fprintf(' CPU times base (ref) : %3.4f (s)\n',T(1))
35 fprintf(' CPU times OptV0 : %3.4f (s) - Speed Up X%3.3f\n',T(2),T(1)/T(2))
36 fprintf(' CPU times OptV1 : %3.4f (s) - Speed Up X%3.3f\n',T(3),T(1)/T(3))
37 fprintf(' CPU times OptV2 : %3.4f (s) - Speed Up X%3.3f\n',T(4),T(1)/T(4))
38 checkTest1(Test1)
39
40 % TEST 2
41 disp('-----------------------------------------------------------')
42 disp(' Test 2: Validations by integration on [0,1]x[0,1]x[0,1] ')
43 disp('-----------------------------------------------------------')
44 Test=valid_FEMmatrices();
45 M=Mbase;
46 for kk=1:length(Test)
47 U=Test(kk).u(Th.q(1,:),Th.q(2,:),Th.q(3,:));
48 V=Test(kk).v(Th.q(1,:),Th.q(2,:),Th.q(3,:));
49 Test(kk).error=abs(Test(kk).Mass-U*M*V');
50 fprintf(' function %d : u(x,y,z)=%s, v(x,y,z)=%s,\n -> Mass error=%e\n',kk,Test(kk).cu,Test(kk).cv,abs(Test(kk).Mass-U*M*V'));
51 end
52 checkTest2(Test)
53
54 % TEST 3
55 disp('--------------------------------')
56 disp(' Test 3: Validations by order ')
57 disp('--------------------------------')
58 n=length(Test);
59 u=Test(n).u;
60 v=Test(n).v;
61 ExSol=Test(n).Mass;
62 fprintf(' functions %d : u(x,y,z)=%s, v(x,y,z)=%s,\n',n, ...
63 Test(n).cu,Test(n).cv);
64 fprintf(' Integral of u(x,y,z)v(x,y,z) over unit cube : %.16f\n',ExSol);
65 N=10;
66 for k=1:10
67 Th=CubeMesh(5+k*3);
68 fprintf('(%d/%d) Matrix size : %d\n',k,N,Th.nq);
69 h(k)=GetMaxLengthEdges(Th.q,Th.me);
70 tic();
71 M=MassAssembling3DP1OptV2(Th.nq,Th.nme,Th.me,Th.volumes);
72 TT(k)=toc();
73 U=u(Th.q(1,:),Th.q(2,:),Th.q(3,:));
74 V=v(Th.q(1,:),Th.q(2,:),Th.q(3,:));
75 Error(k)=abs(ExSol-U*M*V');
76 fprintf(' MassAssembling3DP1OptV2 CPU times : %3.3f(s)\n',TT(k));
77 fprintf(' Error : %e\n',Error(k));
78 end
79
80 loglog(h,Error,'+-r',h,h*1.1*Error(1)/h(1),'-sm',h,1.1*Error(1)*(h/h(1)).^2,'-db')
81 legend('Error','O(h)','O(h^2)')
82 xlabel('h')
83 title('Test 3 : Mass Matrix')
84 checkTest3(h,Error)
85 end
86
87
88 function checkTest1(Test)
89 I=find(Test.error>1e-14);
90 if isempty(I)
91 disp('------------------------')
92 disp(' Test 1 (results): OK')
93 disp('------------------------')
94 else
95 disp('----------------------------')
96 disp(' Test 1 (results): FAILED')
97 disp('----------------------------')
98 end
99 end
100
101 function checkTest2(Test)
102 N=length(Test);
103 cntFalse=0;
104 for k=1:N
105 if (ismember(Test(k).degree,[0 1]))
106 if (Test(k).error>1e-14)
107 cntFalse=cntFalse+1;
108 end
109 end
110 end
111 if (cntFalse==0)
112 disp('------------------------')
113 disp(' Test 2 (results): OK')
114 disp('------------------------')
115 else
116 disp('----------------------------')
117 disp(' Test 2 (results): FAILED')
118 disp('----------------------------')
119 end
120 end
121
122 function checkTest3(h,error)
123 % order 2
124 P=polyfit(log(h),log(error),1);
125 if abs(P(1)-2)< 0.1
126 disp('------------------------')
127 disp(' Test 3 (results): OK')
128 fprintf(' -> found numerical order %f. Must be 2\n',P(1))
129 disp('------------------------')
130 else
131 disp('----------------------------')
132 disp(' Test 3 (results): FAILED')
133 fprintf(' -> found numerical order %f. Must be 2\n',P(1))
134 disp('----------------------------')
135 end
136 end
137