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annotate diracDiscr1D.m @ 1136:eee71789f13b feature/laplace_curvilinear_test

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Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only.
author Martin Almquist <malmquist@stanford.edu>
date Mon, 10 Jun 2019 10:43:12 +0200
parents b29892853daf
children
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b29892853daf Refactor diracDiscr.m by moving the helper function diracDiscr1D to a separate file.
Martin Almquist <malmquist@stanford.edu>
parents:
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1 % Generates discrete 1D delta function
b29892853daf Refactor diracDiscr.m by moving the helper function diracDiscr1D to a separate file.
Martin Almquist <malmquist@stanford.edu>
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2 function ret = diracDiscr1D(x_0in , x , m_order, s_order, H)
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3
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4 m = length(x);
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5
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6 % Return zeros if x0 is outside grid
b29892853daf Refactor diracDiscr.m by moving the helper function diracDiscr1D to a separate file.
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7 if(x_0in < x(1) || x_0in > x(end) )
b29892853daf Refactor diracDiscr.m by moving the helper function diracDiscr1D to a separate file.
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8
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9 ret = zeros(size(x));
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10
b29892853daf Refactor diracDiscr.m by moving the helper function diracDiscr1D to a separate file.
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11 else
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12
b29892853daf Refactor diracDiscr.m by moving the helper function diracDiscr1D to a separate file.
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13 fnorm = diag(H);
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14 eta = abs(x-x_0in);
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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
b29892853daf Refactor diracDiscr.m by moving the helper function diracDiscr1D to a separate file.
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19 % Get interior grid spacing
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Martin Almquist <malmquist@stanford.edu>
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20 middle = floor(m/2);
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21 h = x(middle+1) - x(middle);
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22
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23 poss = find(tot*h/2 >= eta);
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24
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25 % Ensure that poss is not too long
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26 if length(poss) == (tot + 2)
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27 poss = poss(2:end-1);
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28 elseif length(poss) == (tot + 1)
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29 poss = poss(1:end-1);
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30 end
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31
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32 % Use first tot grid points
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33 if length(poss)<tot && x_0in < x(1) + ceil(tot/2)*h;
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34 index=1:tot;
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35 pol=(x(1:tot)-x(1))/(x(tot)-x(1));
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36 x_0=(x_0in-x(1))/(x(tot)-x(1));
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37 norm=fnorm(1:tot)/h;
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38
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39 % Use last tot grid points
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40 elseif length(poss)<tot && x_0in > x(end) - ceil(tot/2)*h;
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41 index = length(x)-tot+1:length(x);
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42 pol = (x(end-tot+1:end)-x(end-tot+1))/(x(end)-x(end-tot+1));
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43 norm = fnorm(end-tot+1:end)/h;
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44 x_0 = (x_0in-x(end-tot+1))/(x(end)-x(end-tot+1));
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45
b29892853daf Refactor diracDiscr.m by moving the helper function diracDiscr1D to a separate file.
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46 % Interior, compensate for round-off errors.
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47 elseif length(poss) < tot
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48 if poss(end)<m
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49 poss = [poss; poss(end)+1];
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50 else
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51 poss = [poss(1)-1; poss];
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52 end
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53 pol = (x(poss)-x(poss(1)))/(x(poss(end))-x(poss(1)));
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54 x_0 = (x_0in-x(poss(1)))/(x(poss(end))-x(poss(1)));
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55 norm = fnorm(poss)/h;
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56 index = poss;
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57
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58 % Interior
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59 else
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60 pol = (x(poss)-x(poss(1)))/(x(poss(end))-x(poss(1)));
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61 x_0 = (x_0in-x(poss(1)))/(x(poss(end))-x(poss(1)));
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62 norm = fnorm(poss)/h;
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63 index = poss;
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64 end
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65
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66 h_pol = pol(2)-pol(1);
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67 b = zeros(m_order+s_order,1);
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68
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69 for i = 1:m_order
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70 b(i,1) = x_0^(i-1);
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71 end
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72
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73 for i = 1:(m_order+s_order)
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74 for j = 1:m_order
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75 M(j,i) = pol(i)^(j-1)*h_pol*norm(i);
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76 end
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77 end
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78
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79 for i = 1:(m_order+s_order)
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80 for j = 1:s_order
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81 S(j,i) = (-1)^(i-1)*pol(i)^(j-1);
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82 end
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83 end
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84
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85 A = [M;S];
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86
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87 d = A\b;
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88 ret = x*0;
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89 ret(index) = d/h*h_pol;
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90 end
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91
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92 end