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comparison diracDiscr.m @ 1128:3a9262c045d0 feature/laplace_curvilinear_test

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Copy diracDiscr.m from feature/poroelastic
author Martin Almquist <malmquist@stanford.edu>
date Tue, 21 May 2019 17:59:30 -0700
parents
children b29892853daf 52d774e69b1f
comparison
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1127:0aed89043ad6 1128:3a9262c045d0
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2 function d = diracDiscr(x_s, x, m_order, s_order, H)
3 % n-dimensional delta function
4 % x_s: source point coordinate vector, e.g. [x, y] or [x, y, z].
5 % x: cell array of grid point column vectors for each dimension.
6 % m_order: Number of moment conditions
7 % s_order: Number of smoothness conditions
8 % H: cell array of 1D norm matrices
9
10 dim = length(x_s);
11 d_1D = cell(dim,1);
12
13 % If 1D, non-cell input is accepted
14 if dim == 1 && ~iscell(x)
15 d = diracDiscr1D(x_s, x, m_order, s_order, H);
16
17 else
18 for i = 1:dim
19 d_1D{i} = diracDiscr1D(x_s(i), x{i}, m_order, s_order, H{i});
20 end
21
22 d = d_1D{dim};
23 for i = dim-1: -1: 1
24 % Perform outer product, transpose, and then turn into column vector
25 d = (d_1D{i}*d')';
26 d = d(:);
27 end
28 end
29
30 end
31
32
33 % Helper function for 1D delta functions
34 function ret = diracDiscr1D(x_0in , x , m_order, s_order, H)
35
36 m = length(x);
37
38 % Return zeros if x0 is outside grid
39 if(x_0in < x(1) || x_0in > x(end) )
40
41 ret = zeros(size(x));
42
43 else
44
45 fnorm = diag(H);
46 eta = abs(x-x_0in);
47 tot = m_order+s_order;
48 S = [];
49 M = [];
50
51 % Get interior grid spacing
52 middle = floor(m/2);
53 h = x(middle+1) - x(middle);
54
55 poss = find(tot*h/2 >= eta);
56
57 % Ensure that poss is not too long
58 if length(poss) == (tot + 2)
59 poss = poss(2:end-1);
60 elseif length(poss) == (tot + 1)
61 poss = poss(1:end-1);
62 end
63
64 % Use first tot grid points
65 if length(poss)<tot && x_0in < x(1) + ceil(tot/2)*h;
66 index=1:tot;
67 pol=(x(1:tot)-x(1))/(x(tot)-x(1));
68 x_0=(x_0in-x(1))/(x(tot)-x(1));
69 norm=fnorm(1:tot)/h;
70
71 % Use last tot grid points
72 elseif length(poss)<tot && x_0in > x(end) - ceil(tot/2)*h;
73 index = length(x)-tot+1:length(x);
74 pol = (x(end-tot+1:end)-x(end-tot+1))/(x(end)-x(end-tot+1));
75 norm = fnorm(end-tot+1:end)/h;
76 x_0 = (x_0in-x(end-tot+1))/(x(end)-x(end-tot+1));
77
78 % Interior, compensate for round-off errors.
79 elseif length(poss) < tot
80 if poss(end)<m
81 poss = [poss; poss(end)+1];
82 else
83 poss = [poss(1)-1; poss];
84 end
85 pol = (x(poss)-x(poss(1)))/(x(poss(end))-x(poss(1)));
86 x_0 = (x_0in-x(poss(1)))/(x(poss(end))-x(poss(1)));
87 norm = fnorm(poss)/h;
88 index = poss;
89
90 % Interior
91 else
92 pol = (x(poss)-x(poss(1)))/(x(poss(end))-x(poss(1)));
93 x_0 = (x_0in-x(poss(1)))/(x(poss(end))-x(poss(1)));
94 norm = fnorm(poss)/h;
95 index = poss;
96 end
97
98 h_pol = pol(2)-pol(1);
99 b = zeros(m_order+s_order,1);
100
101 for i = 1:m_order
102 b(i,1) = x_0^(i-1);
103 end
104
105 for i = 1:(m_order+s_order)
106 for j = 1:m_order
107 M(j,i) = pol(i)^(j-1)*h_pol*norm(i);
108 end
109 end
110
111 for i = 1:(m_order+s_order)
112 for j = 1:s_order
113 S(j,i) = (-1)^(i-1)*pol(i)^(j-1);
114 end
115 end
116
117 A = [M;S];
118
119 d = A\b;
120 ret = x*0;
121 ret(index) = d/h*h_pol;
122 end
123
124 end
125
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