1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153 | function [phi,dphix,dphiy]=CreateNURBSBasis2D(mesh_file,p,yi,xi,type_nurbs,isclosed,nband,sizeim)
if nargin < 5 , type_nurbs=1;end
if nargin < 6 , isclosed=[0,0];end
if nargin < 7 , nband=[];end
load(mesh_file,'xo','yo','uo','vo');
if ~isempty(nband)
assert(nargin==8);
yi=yi(nband);
xi=xi(nband);
end
if numel(p)==1
p=[p,p];
end
npt=length(yi(:));
indp=zeros((p(1)+1)*npt,1);
indn=zeros((p(1)+1)*npt,1);
val=zeros((p(1)+1)*npt,1);
dval=zeros((p(1)+1)*npt,1);
if type_nurbs
Nny=length(yo)+p(1)-1;
else
Nny=length(yo)*p(1)-(p(1)-1);
end
nel=0;
toto=1;
Nelems=length(yo)-1;
for iy=1:Nelems
if iy==Nelems
found=find((yi(:)>=yo(iy))&(yi(:)<=yo(iy+1)));
else
found=find((yi(:)>=yo(iy))&(yi(:)<yo(iy+1)));
end
yp=yi(found);
if type_nurbs
[N]=NURBSBasisFunc(iy+p(1),p(1),yp',vo,2);
else
toto=toto+p;
[N]=NURBSBasisFunc(toto,p(1),yp',vo,2);
end
Sel=length(yp);
for ip=1:(p(1)+1)
if type_nurbs
indn(nel+(1:Sel))=iy+ip-1;
else
indn(nel+(1:Sel))=iy*p(1)-p+ip;
end
indp(nel+(1:Sel))=found;
val(nel+(1:Sel))=N(:,ip,1);
dval(nel+(1:Sel))=N(:,ip,2);
nel=nel+Sel;
end
end
found=find(indp);
indp=indp(found);
indn=indn(found);
val=val(found);
dval=dval(found);
if isclosed(1)
for ip=1:p(1)
found=find(indn==Nny-ip+1);
indn(found)=p(1)-ip+1;
end
Nny=Nny-p(1);
end
if isempty(nband)
size1=npt;
else
indp=nband(indp);
size1=prod(sizeim);
end
phiy=sparse(indp,indn,val,size1,Nny);
dphiy1=sparse(indp,indn,dval,size1,Nny);
npt=length(xi(:));
indp=zeros((p(2)+1)*npt,1);
indn=zeros((p(2)+1)*npt,1);
val=zeros((p(2)+1)*npt,1);
dval=zeros((p(2)+1)*npt,1);
if type_nurbs
Nny=length(xo)+p(2)-1;
else
Nny=length(xo)*p(2)-(p(2)-1);
end
nel=0;
toto=1;
Nelems=length(xo)-1;
for iy=1:Nelems
if iy==Nelems
found=find((xi(:)>=xo(iy))&(xi(:)<=xo(iy+1)));
else
found=find((xi(:)>=xo(iy))&(xi(:)<xo(iy+1)));
end
xp=xi(found);
if type_nurbs
[N]=NURBSBasisFunc(iy+p(2),p(2),xp',uo,2);
else
toto=toto+p;
[N]=NURBSBasisFunc(toto,p(2),xp',uo,2);
end
Sel=length(xp);
for ip=1:(p(2)+1)
if type_nurbs
indn(nel+(1:Sel))=iy+ip-1;
else
indn(nel+(1:Sel))=iy*p(2)-p(2)+ip;
end
indp(nel+(1:Sel))=found;
val(nel+(1:Sel))=N(:,ip,1);
dval(nel+(1:Sel))=N(:,ip,2);
nel=nel+Sel;
end
end
indp((nel+1):end)=[];
indn((nel+1):end)=[];
val((nel+1):end)=[];
dval((nel+1):end)=[];
if isclosed(2)
for ip=1:p(2)
found=find(indn==Nny-ip+1);
indn(found)=p(2)-ip+1;
end
Nny=Nny-p(2);
end
if isempty(nband)
size1=npt;
else
indp=nband(indp);
size1=prod(sizeim);
end
phix=sparse(indp,indn,val,size1,Nny);
dphix1=sparse(indp,indn,dval,size1,Nny);
[indj,indi]=meshgrid(1:size(phix,2),1:size(phiy,2));
phi=phix(:,indj).*phiy(:,indi);
dphix=dphix1(:,indj).*phiy(:,indi);
dphiy=phix(:,indj).*dphiy1(:,indi);
% phi=phix(:)*(phiy(:)');
%
% [indx,indy,val]=find(phi);
% indp=mod(indx,sizeim(1))+sizeim(1)*(mod(indy,sizeim(2))-1)+sizeim(1)*sizeim(2)*(mod(indy,sizeim(2))-1);
% indn=ceil(indx/(sizeim(1)))+Nnx*(ceil(indy/(sizeim(2)))-1);
% phi=sparse(indp,indn,val,prod(sizeim),Nnx*Nny);
end
|