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annotate diracPrimDiscr1D.m @ 1138:afd06a84b69c feature/laplace_curvilinear_test

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Bugfixes in VirtaMin.interfaceStandard()
author Martin Almquist <malmquist@stanford.edu>
date Mon, 10 Jun 2019 14:39:14 +0200
parents 99fd66ffe714
children
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1130
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1 % Generates discretized derivative of delta function in 1D
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2 function ret = diracPrimDiscr1D(x_0in, x, m_order, s_order, H)
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3
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4 % diracPrim satisfies one more moment condition than dirac
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5 m_order = m_order + 1;
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6
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7 m = length(x);
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8
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9 % Return zeros if x0 is outside grid
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10 if(x_0in < x(1) || x_0in > x(end) )
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11
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12 ret = zeros(size(x));
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13
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14 else
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15
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16 fnorm = diag(H);
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17 eta = abs(x-x_0in);
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18 tot = m_order+s_order;
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19 S = [];
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20 M = [];
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21
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22 % Get interior grid spacing
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23 middle = floor(m/2);
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24 h = x(middle+1) - x(middle);
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25
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26 poss = find(tot*h/2 >= eta);
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27
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28 % Ensure that poss is not too long
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29 if length(poss) == (tot + 2)
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30 poss = poss(2:end-1);
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31 elseif length(poss) == (tot + 1)
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32 poss = poss(1:end-1);
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33 end
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34
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35 % Use first tot grid points
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36 if length(poss)<tot && x_0in < x(1) + ceil(tot/2)*h;
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37 index=1:tot;
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38 pol=(x(1:tot)-x(1))/(x(tot)-x(1));
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39 x_0=(x_0in-x(1))/(x(tot)-x(1));
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40 norm=fnorm(1:tot)/h;
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41
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42 % Use last tot grid points
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43 elseif length(poss)<tot && x_0in > x(end) - ceil(tot/2)*h;
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44 index = length(x)-tot+1:length(x);
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45 pol = (x(end-tot+1:end)-x(end-tot+1))/(x(end)-x(end-tot+1));
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46 norm = fnorm(end-tot+1:end)/h;
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47 x_0 = (x_0in-x(end-tot+1))/(x(end)-x(end-tot+1));
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48
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49 % Interior, compensate for round-off errors.
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50 elseif length(poss) < tot
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51 if poss(end)<m
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52 poss = [poss; poss(end)+1];
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53 else
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54 poss = [poss(1)-1; poss];
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55 end
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56 pol = (x(poss)-x(poss(1)))/(x(poss(end))-x(poss(1)));
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57 x_0 = (x_0in-x(poss(1)))/(x(poss(end))-x(poss(1)));
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58 norm = fnorm(poss)/h;
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59 index = poss;
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60
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61 % Interior
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62 else
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63 pol = (x(poss)-x(poss(1)))/(x(poss(end))-x(poss(1)));
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64 x_0 = (x_0in-x(poss(1)))/(x(poss(end))-x(poss(1)));
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65 norm = fnorm(poss)/h;
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66 index = poss;
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67 end
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68
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69 h_pol = pol(2)-pol(1);
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70 b = zeros(m_order+s_order,1);
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71
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72 b(1) = 0;
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73 for i = 2:m_order
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74 b(i) = -(i-1)*x_0^(i-2);
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75 end
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76
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77 for i = 1:(m_order+s_order)
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78 for j = 1:m_order
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79 M(j,i) = pol(i)^(j-1)*h_pol*norm(i);
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80 end
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81 end
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82
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83 for i = 1:(m_order+s_order)
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84 for j = 1:s_order
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85 S(j,i) = (-1)^(i-1)*pol(i)^(j-1);
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86 end
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87 end
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88
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89 A = [M;S];
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90
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91 d = A\b;
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92 ret = x*0;
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93 ret(index) = d*(h_pol/h)^2;
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94 end
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95
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96 end