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comparison diracDiscrCurve.m @ 1251:6424745e1b58 feature/volcano

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Merge in latest changes from default
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Wed, 20 Nov 2019 14:26:57 -0800
parents 25efceb0c392
children 663eb90a4559
comparison
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1248:10881b234f77 1251:6424745e1b58
1 % 2-dimensional delta function for single-block curvilinear grid
2 % x_s: source point coordinate vector, e.g. [x; y] or [x; y; z].
3 % g: single-block grid containing the source
4 % m_order: Number of moment conditions
5 % s_order: Number of smoothness conditions
6 % order: Order of SBP derivative approximations
7 % opSet: Cell array of function handle to opSet generator
8 function d = diracDiscrCurve(x_s, g, m_order, s_order, order, opSet)
9 default_arg('order', m_order);
10 default_arg('opSet', {@sbp.D2Variable, @sbp.D2Variable});
11
12 dim = length(x_s);
13 assert(dim == 2, 'diracDiscrCurve: Only implemented for 2d.');
14 assertType(g, 'grid.Curvilinear');
15
16 % Compute Jacobian
17 J = jacobian(g, opSet, order);
18
19 % Find approximate logical coordinates of point source
20 X = g.points();
21 U = g.logic.points();
22 U_interp = scatteredInterpolant(X, U(:,1));
23 V_interp = scatteredInterpolant(X, U(:,2));
24 uS = U_interp(x_s);
25 vS = V_interp(x_s);
26
27 % Get quadrature matrices for moment conditions
28 m = g.size();
29 ops_u = opSet{1}(m(1), {0, 1}, order);
30 ops_v = opSet{2}(m(2), {0, 1}, order);
31 H_u = ops_u.H;
32 H_v = ops_v.H;
33
34 % Get delta function for logical grid and scale by Jacobian
35 d = (1./J).*diracDiscr(g, [uS; vS], m_order, s_order, {H_u, H_v});
36 end
37
38 function J = jacobian(g, opSet, order)
39 m = g.size();
40 m_u = m(1);
41 m_v = m(2);
42 ops_u = opSet{1}(m_u, {0, 1}, order);
43 ops_v = opSet{2}(m_v, {0, 1}, order);
44 I_u = speye(m_u);
45 I_v = speye(m_v);
46
47 D1_u = ops_u.D1;
48 D1_v = ops_v.D1;
49
50 Du = kr(D1_u,I_v);
51 Dv = kr(I_u,D1_v);
52
53 coords = g.points();
54 x = coords(:,1);
55 y = coords(:,2);
56
57 x_u = Du*x;
58 x_v = Dv*x;
59 y_u = Du*y;
60 y_v = Dv*y;
61
62 J = x_u.*y_v - x_v.*y_u;
63 end