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annotate diracDiscr.m @ 652:be941bb0a11a feature/d1_staggered

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Add staggered 1D variable coefficient. Convergence study working.
author Martin Almquist <malmquist@stanford.edu>
date Mon, 04 Dec 2017 11:11:03 -0800
parents 4ee7d15bd8e6
children 5264ce57b573
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a5307adc6177 Add diracDiscr.m. Noticed bug if source is on grid point.
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1 function ret = diracDiscr(x_0in , x , m_order, s_order, H)
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3 m = length(x);
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5 % Return zeros if x0 is outside grid
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6 if(x_0in < x(1) || x_0in > x(end) )
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7
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8 ret = zeros(size(x));
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9
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10 else
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11
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12 fnorm = diag(H);
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13 eta = abs(x-x_0in);
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14 h = x(2)-x(1);
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15 tot = m_order+s_order;
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16 S = [];
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17 M = [];
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18 poss = find(tot*h/2 >= eta);
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19
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20 % Ensure that poss is not too long
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21 if length(poss) == (tot + 2)
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22 poss = poss(2:end-1);
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23 elseif length(poss) == (tot + 1)
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24 poss = poss(1:end-1);
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25 end
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26
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27 % Use first tot grid points
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28 if length(poss)<tot && x_0in < x(1) + ceil(tot/2)*h;
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29 index=1:tot;
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30 pol=(x(1:tot)-x(1))/(x(tot)-x(1));
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31 x_0=(x_0in-x(1))/(x(tot)-x(1));
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32 norm=fnorm(1:tot)/h;
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33
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34 % Use last tot grid points
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35 elseif length(poss)<tot && x_0in > x(end) - ceil(tot/2)*h;
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36 index = length(x)-tot+1:length(x);
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37 pol = (x(end-tot+1:end)-x(end-tot+1))/(x(end)-x(end-tot+1));
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38 norm = fnorm(end-tot+1:end)/h;
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39 x_0 = (x_0in-x(end-tot+1))/(x(end)-x(end-tot+1));
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40
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41 % Interior, compensate for round-off errors.
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42 elseif length(poss) < tot
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43 if poss(end)<m
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44 poss = [poss; poss(end)+1];
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45 else
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46 poss = [poss(1)-1; poss];
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47 end
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48 pol = (x(poss)-x(poss(1)))/(x(poss(end))-x(poss(1)));
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49 x_0 = (x_0in-x(poss(1)))/(x(poss(end))-x(poss(1)));
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50 norm = fnorm(poss)/h;
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51 index = poss;
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53 % Interior
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54 else
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55 pol = (x(poss)-x(poss(1)))/(x(poss(end))-x(poss(1)));
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56 x_0 = (x_0in-x(poss(1)))/(x(poss(end))-x(poss(1)));
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57 norm = fnorm(poss)/h;
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58 index = poss;
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59 end
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60
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61 h_pol = pol(2)-pol(1);
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62 b = zeros(m_order+s_order,1);
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63
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64 for i = 1:m_order
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65 b(i,1) = x_0^(i-1);
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66 end
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67
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68 for i = 1:(m_order+s_order)
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69 for j = 1:m_order
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70 M(j,i) = pol(i)^(j-1)*h_pol*norm(i);
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71 end
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72 end
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74 for i = 1:(m_order+s_order)
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75 for j = 1:s_order
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76 S(j,i) = (-1)^(i-1)*pol(i)^(j-1);
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77 end
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78 end
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79
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80 A = [M;S];
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81
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82 d = A\b;
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83 ret = x*0;
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84 ret(index) = d/h*h_pol;
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85 end
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87 end
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