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comparison diracDiscrCurve.m @ 1233:57df0bf741dc feature/dirac_discr

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Merge in curvilinear discr of dirac delta
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Tue, 19 Nov 2019 13:55:43 -0800
parents 8a456f6e54cc
children 1fbd93f24bed
comparison
equal deleted inserted replaced
1232:52d774e69b1f 1233:57df0bf741dc
1 function d = diracDiscrCurve(x_s, g, m_order, s_order, order, opSet)
2 % 2-dimensional delta function for single-block curvilinear grid
3 % x_s: source point coordinate vector, e.g. [x, y] or [x, y, z].
4 % g: single-block grid containing the source
5 % m_order: Number of moment conditions
6 % s_order: Number of smoothness conditions
7 % order: Order of SBP derivative approximations
8 % opSet: Cell array of function handle to opSet generator
9
10 default_arg('order', m_order);
11 default_arg('opSet', {@sbp.D2Variable, @sbp.D2Variable});
12
13 dim = length(x_s);
14 assert(dim == 2, 'diracDiscrCurve: Only implemented for 2d.');
15 assert(isa(g, 'grid.Curvilinear'));
16
17 m = g.size();
18 m_u = m(1);
19 m_v = m(2);
20 ops_u = opSet{1}(m_u, {0, 1}, order);
21 ops_v = opSet{2}(m_v, {0, 1}, order);
22 I_u = speye(m_u);
23 I_v = speye(m_v);
24
25 D1_u = ops_u.D1;
26 H_u = ops_u.H;
27
28 D1_v = ops_v.D1;
29 H_v = ops_v.H;
30
31 Du = kr(D1_u,I_v);
32 Dv = kr(I_u,D1_v);
33
34 u = ops_u.x;
35 v = ops_v.x;
36
37 % Compute Jacobian
38 coords = g.points();
39 x = coords(:,1);
40 y = coords(:,2);
41
42 x_u = Du*x;
43 x_v = Dv*x;
44 y_u = Du*y;
45 y_v = Dv*y;
46
47 J = x_u.*y_v - x_v.*y_u;
48
49 % Find approximate logical coordinates of point source
50 [U, V] = meshgrid(u, v);
51 U_interp = scatteredInterpolant(coords, U(:));
52 V_interp = scatteredInterpolant(coords, V(:));
53 uS = U_interp(x_s);
54 vS = V_interp(x_s);
55
56 d = (1./J).*diracDiscr([uS, vS], {u, v}, m_order, s_order, {H_u, H_v});
57
58 end