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annotate +sbp/+implementations/d4_4.m @ 266:bfa130b7abf6 operator_remake

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Added error message for too few grid points to all implementation files.
author Martin Almquist <martin.almquist@it.uu.se>
date Fri, 09 Sep 2016 11:03:13 +0200
parents 6009f2712d13
children f7ac3cd6eeaa
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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261
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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1 function [H, HI, D1, D2, D3, D4, e_1, e_m, M, ...
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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2 M4,Q, Q3, S2_1, S2_m, S3_1, S3_m, S_1, S_m] = d4_4(m,h)
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3
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4
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5 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Martin Almquist <martin.almquist@it.uu.se>
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6 %%% 4:de ordn. SBP Finita differens %%%
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Martin Almquist <martin.almquist@it.uu.se>
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7 %%% operatorer framtagna av Ken Mattsson %%%
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Martin Almquist <martin.almquist@it.uu.se>
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8 %%% %%%
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Martin Almquist <martin.almquist@it.uu.se>
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9 %%% 6 randpunkter, diagonal norm %%%
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Martin Almquist <martin.almquist@it.uu.se>
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10 %%% %%%
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Martin Almquist <martin.almquist@it.uu.se>
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11 %%% Datum: 2013-11-11 %%%
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12 %%% %%%
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13 %%% %%%
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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14 %%% H (Normen) %%%
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Martin Almquist <martin.almquist@it.uu.se>
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15 %%% D1 (approx f?rsta derivatan) %%%
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Martin Almquist <martin.almquist@it.uu.se>
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16 %%% D2 (approx andra derivatan) %%%
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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17 %%% D3 (approx tredje derivatan) %%%
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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18 %%% D2 (approx fj?rde derivatan) %%%
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Martin Almquist <martin.almquist@it.uu.se>
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19 %%% %%%
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Martin Almquist <martin.almquist@it.uu.se>
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20 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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21
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Martin Almquist <martin.almquist@it.uu.se>
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22 % M?ste ange antal punkter (m) och stegl?ngd (h)
6009f2712d13 Moved and renamned all implementations.
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23 % Notera att dessa opetratorer ?r framtagna f?r att anv?ndas n?r
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Martin Almquist <martin.almquist@it.uu.se>
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24 % vi har 3de och 4de derivator i v?r PDE
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Martin Almquist <martin.almquist@it.uu.se>
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25 % I annat fall anv?nd de "traditionella" som har noggrannare
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Martin Almquist <martin.almquist@it.uu.se>
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26 % randsplutningar f?r D1 och D2
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27
6009f2712d13 Moved and renamned all implementations.
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28 % Vi b?rjar med normen. Notera att alla SBP operatorer delar samma norm,
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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29 % vilket ?r n?dv?ndigt f?r stabilitet
266
bfa130b7abf6 Added error message for too few grid points to all implementation files.
Martin Almquist <martin.almquist@it.uu.se>
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30
bfa130b7abf6 Added error message for too few grid points to all implementation files.
Martin Almquist <martin.almquist@it.uu.se>
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31 BP = 6;
bfa130b7abf6 Added error message for too few grid points to all implementation files.
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32 if(m<2*BP)
bfa130b7abf6 Added error message for too few grid points to all implementation files.
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33 error(['Operator requires at least ' num2str(2*BP) ' grid points']);
bfa130b7abf6 Added error message for too few grid points to all implementation files.
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34 end
261
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35
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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36 H=diag(ones(m,1),0);
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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37 H_U=[0.35809e5 / 0.100800e6 0 0 0 0 0; 0 0.13297e5 / 0.11200e5 0 0 0 0; 0 0 0.5701e4 / 0.5600e4 0 0 0; 0 0 0 0.45109e5 / 0.50400e5 0 0; 0 0 0 0 0.35191e5 / 0.33600e5 0; 0 0 0 0 0 0.33503e5 / 0.33600e5;];
6009f2712d13 Moved and renamned all implementations.
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38
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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39 H(1:6,1:6)=H_U;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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40 H(m-5:m,m-5:m)=fliplr(flipud(H_U));
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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41 H=H*h;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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42 HI=inv(H);
6009f2712d13 Moved and renamned all implementations.
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43
6009f2712d13 Moved and renamned all implementations.
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44
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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45 % First derivative SBP operator, 1st order accurate at first 6 boundary points
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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46
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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47 q2=-1/12;q1=8/12;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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48 Q=q2*(diag(ones(m-2,1),2) - diag(ones(m-2,1),-2))+q1*(diag(ones(m-1,1),1)-diag(ones(m-1,1),-1));
6009f2712d13 Moved and renamned all implementations.
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49
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50 %Q=(-1/12*diag(ones(m-2,1),2)+8/12*diag(ones(m-1,1),1)-8/12*diag(ones(m-1,1),-1)+1/12*diag(ones(m-2,1),-2));
6009f2712d13 Moved and renamned all implementations.
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51
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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52 Q_U = [0 0.526249e6 / 0.907200e6 -0.10819e5 / 0.777600e6 -0.50767e5 / 0.907200e6 -0.631e3 / 0.28800e5 0.91e2 / 0.7776e4; -0.526249e6 / 0.907200e6 0 0.1421209e7 / 0.2721600e7 0.16657e5 / 0.201600e6 -0.8467e4 / 0.453600e6 -0.33059e5 / 0.5443200e7; 0.10819e5 / 0.777600e6 -0.1421209e7 / 0.2721600e7 0 0.631187e6 / 0.1360800e7 0.400139e6 / 0.5443200e7 -0.8789e4 / 0.302400e6; 0.50767e5 / 0.907200e6 -0.16657e5 / 0.201600e6 -0.631187e6 / 0.1360800e7 0 0.496403e6 / 0.907200e6 -0.308533e6 / 0.5443200e7; 0.631e3 / 0.28800e5 0.8467e4 / 0.453600e6 -0.400139e6 / 0.5443200e7 -0.496403e6 / 0.907200e6 0 0.1805647e7 / 0.2721600e7; -0.91e2 / 0.7776e4 0.33059e5 / 0.5443200e7 0.8789e4 / 0.302400e6 0.308533e6 / 0.5443200e7 -0.1805647e7 / 0.2721600e7 0;];
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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53 Q(1:6,1:6)=Q_U;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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54 Q(m-5:m,m-5:m)=flipud( fliplr( -Q_U ) );
6009f2712d13 Moved and renamned all implementations.
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55
6009f2712d13 Moved and renamned all implementations.
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56 e_1=zeros(m,1);e_1(1)=1;
6009f2712d13 Moved and renamned all implementations.
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57 e_m=zeros(m,1);e_m(m)=1;
6009f2712d13 Moved and renamned all implementations.
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58
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59
6009f2712d13 Moved and renamned all implementations.
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60 D1=HI*(Q-1/2*e_1*e_1'+1/2*e_m*e_m') ;
6009f2712d13 Moved and renamned all implementations.
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61
6009f2712d13 Moved and renamned all implementations.
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62 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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63
6009f2712d13 Moved and renamned all implementations.
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64
6009f2712d13 Moved and renamned all implementations.
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65
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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66 % Second derivative, 1st order accurate at first 6 boundary points
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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67 m2=1/12;m1=-16/12;m0=30/12;
6009f2712d13 Moved and renamned all implementations.
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68 M=m2*(diag(ones(m-2,1),2)+diag(ones(m-2,1),-2))+m1*(diag(ones(m-1,1),1)+diag(ones(m-1,1),-1))+m0*diag(ones(m,1),0);
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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69 %M=(1/12*diag(ones(m-2,1),2)-16/12*diag(ones(m-1,1),1)-16/12*diag(ones(m-1,1),-1)+1/12*diag(ones(m-2,1),-2)+30/12*diag(ones(m,1),0));
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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70 M_U=[0.2386127e7 / 0.2177280e7 -0.515449e6 / 0.453600e6 -0.10781e5 / 0.777600e6 0.61567e5 / 0.1360800e7 0.6817e4 / 0.403200e6 -0.1069e4 / 0.136080e6; -0.515449e6 / 0.453600e6 0.4756039e7 / 0.2177280e7 -0.1270009e7 / 0.1360800e7 -0.3751e4 / 0.28800e5 0.3067e4 / 0.680400e6 0.119459e6 / 0.10886400e8; -0.10781e5 / 0.777600e6 -0.1270009e7 / 0.1360800e7 0.111623e6 / 0.60480e5 -0.555587e6 / 0.680400e6 -0.551339e6 / 0.5443200e7 0.8789e4 / 0.453600e6; 0.61567e5 / 0.1360800e7 -0.3751e4 / 0.28800e5 -0.555587e6 / 0.680400e6 0.1025327e7 / 0.544320e6 -0.464003e6 / 0.453600e6 0.222133e6 / 0.5443200e7; 0.6817e4 / 0.403200e6 0.3067e4 / 0.680400e6 -0.551339e6 / 0.5443200e7 -0.464003e6 / 0.453600e6 0.5074159e7 / 0.2177280e7 -0.1784047e7 / 0.1360800e7; -0.1069e4 / 0.136080e6 0.119459e6 / 0.10886400e8 0.8789e4 / 0.453600e6 0.222133e6 / 0.5443200e7 -0.1784047e7 / 0.1360800e7 0.1812749e7 / 0.725760e6;];
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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71
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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72 M(1:6,1:6)=M_U;
6009f2712d13 Moved and renamned all implementations.
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73
6009f2712d13 Moved and renamned all implementations.
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74 M(m-5:m,m-5:m)=flipud( fliplr( M_U ) );
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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75 M=M/h;
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76
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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77 S_U=[-0.11e2 / 0.6e1 3 -0.3e1 / 0.2e1 0.1e1 / 0.3e1;]/h;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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78 S_1=zeros(1,m);
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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79 S_1(1:4)=S_U;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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80 S_m=zeros(1,m);
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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81
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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82 S_m(m-3:m)=fliplr(-S_U);
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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83
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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84 D2=HI*(-M-e_1*S_1+e_m*S_m);
6009f2712d13 Moved and renamned all implementations.
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85
6009f2712d13 Moved and renamned all implementations.
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86
6009f2712d13 Moved and renamned all implementations.
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87 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
6009f2712d13 Moved and renamned all implementations.
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88
6009f2712d13 Moved and renamned all implementations.
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89
6009f2712d13 Moved and renamned all implementations.
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90
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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91 % Third derivative, 1st order accurate at first 6 boundary points
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Martin Almquist <martin.almquist@it.uu.se>
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92
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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93 q3=-1/8;q2=1;q1=-13/8;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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94 Q3=q3*(diag(ones(m-3,1),3)-diag(ones(m-3,1),-3))+q2*(diag(ones(m-2,1),2)-diag(ones(m-2,1),-2))+q1*(diag(ones(m-1,1),1)-diag(ones(m-1,1),-1));
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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95
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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96 %QQ3=(-1/8*diag(ones(m-3,1),3) + 1*diag(ones(m-2,1),2) - 13/8*diag(ones(m-1,1),1) +13/8*diag(ones(m-1,1),-1) -1*diag(ones(m-2,1),-2) + 1/8*diag(ones(m-3,1),-3));
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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97
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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98
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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99 Q3_U = [0 -0.88471e5 / 0.67200e5 0.58139e5 / 0.33600e5 -0.1167e4 / 0.2800e4 -0.89e2 / 0.11200e5 0.7e1 / 0.640e3; 0.88471e5 / 0.67200e5 0 -0.43723e5 / 0.16800e5 0.46783e5 / 0.33600e5 -0.191e3 / 0.3200e4 -0.1567e4 / 0.33600e5; -0.58139e5 / 0.33600e5 0.43723e5 / 0.16800e5 0 -0.4049e4 / 0.2400e4 0.29083e5 / 0.33600e5 -0.71e2 / 0.1400e4; 0.1167e4 / 0.2800e4 -0.46783e5 / 0.33600e5 0.4049e4 / 0.2400e4 0 -0.8591e4 / 0.5600e4 0.10613e5 / 0.11200e5; 0.89e2 / 0.11200e5 0.191e3 / 0.3200e4 -0.29083e5 / 0.33600e5 0.8591e4 / 0.5600e4 0 -0.108271e6 / 0.67200e5; -0.7e1 / 0.640e3 0.1567e4 / 0.33600e5 0.71e2 / 0.1400e4 -0.10613e5 / 0.11200e5 0.108271e6 / 0.67200e5 0;];
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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100
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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101 Q3(1:6,1:6)=Q3_U;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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102 Q3(m-5:m,m-5:m)=flipud( fliplr( -Q3_U ) );
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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103 Q3=Q3/h^2;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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104
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105
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106
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Martin Almquist <martin.almquist@it.uu.se>
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107 S2_U=[2 -5 4 -1;]/h^2;
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108 S2_1=zeros(1,m);
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Martin Almquist <martin.almquist@it.uu.se>
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109 S2_1(1:4)=S2_U;
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Martin Almquist <martin.almquist@it.uu.se>
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110 S2_m=zeros(1,m);
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111 S2_m(m-3:m)=fliplr(S2_U);
6009f2712d13 Moved and renamned all implementations.
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112
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113
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114
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Martin Almquist <martin.almquist@it.uu.se>
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115 D3=HI*(Q3 - e_1*S2_1 + e_m*S2_m +1/2*S_1'*S_1 -1/2*S_m'*S_m ) ;
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116
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Martin Almquist <martin.almquist@it.uu.se>
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117 % Fourth derivative, 0th order accurate at first 6 boundary points (still
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118 % yield 4th order convergence if stable: for example u_tt=-u_xxxx
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119
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Martin Almquist <martin.almquist@it.uu.se>
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120 m3=-1/6;m2=2;m1=-13/2;m0=28/3;
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121 M4=m3*(diag(ones(m-3,1),3)+diag(ones(m-3,1),-3))+m2*(diag(ones(m-2,1),2)+diag(ones(m-2,1),-2))+m1*(diag(ones(m-1,1),1)+diag(ones(m-1,1),-1))+m0*diag(ones(m,1),0);
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122
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Martin Almquist <martin.almquist@it.uu.se>
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123 %M4=(-1/6*(diag(ones(m-3,1),3)+diag(ones(m-3,1),-3) ) + 2*(diag(ones(m-2,1),2)+diag(ones(m-2,1),-2)) -13/2*(diag(ones(m-1,1),1)+diag(ones(m-1,1),-1)) + 28/3*diag(ones(m,1),0));
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124
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Martin Almquist <martin.almquist@it.uu.se>
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125 M4_U=[0.4596181e7 / 0.1814400e7 -0.10307743e8 / 0.1814400e7 0.160961e6 / 0.43200e5 -0.535019e6 / 0.907200e6 0.109057e6 / 0.1814400e7 -0.29273e5 / 0.604800e6; -0.10307743e8 / 0.1814400e7 0.8368543e7 / 0.604800e6 -0.9558943e7 / 0.907200e6 0.2177057e7 / 0.907200e6 -0.11351e5 / 0.86400e5 0.204257e6 / 0.1814400e7; 0.160961e6 / 0.43200e5 -0.9558943e7 / 0.907200e6 0.4938581e7 / 0.453600e6 -0.786473e6 / 0.151200e6 0.1141057e7 / 0.907200e6 -0.120619e6 / 0.907200e6; -0.535019e6 / 0.907200e6 0.2177057e7 / 0.907200e6 -0.786473e6 / 0.151200e6 0.3146581e7 / 0.453600e6 -0.4614143e7 / 0.907200e6 0.24587e5 / 0.14400e5; 0.109057e6 / 0.1814400e7 -0.11351e5 / 0.86400e5 0.1141057e7 / 0.907200e6 -0.4614143e7 / 0.907200e6 0.185709e6 / 0.22400e5 -0.11293343e8 / 0.1814400e7; -0.29273e5 / 0.604800e6 0.204257e6 / 0.1814400e7 -0.120619e6 / 0.907200e6 0.24587e5 / 0.14400e5 -0.11293343e8 / 0.1814400e7 0.16787381e8 / 0.1814400e7;];
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126
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Martin Almquist <martin.almquist@it.uu.se>
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127 M4(1:6,1:6)=M4_U;
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128
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Martin Almquist <martin.almquist@it.uu.se>
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129 M4(m-5:m,m-5:m)=flipud( fliplr( M4_U ) );
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130 M4=M4/h^3;
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Martin Almquist <martin.almquist@it.uu.se>
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131
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132 S3_U=[-1 3 -3 1;]/h^3;
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133 S3_1=zeros(1,m);
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134 S3_1(1:4)=S3_U;
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135 S3_m=zeros(1,m);
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136 S3_m(m-3:m)=fliplr(-S3_U);
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137
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Martin Almquist <martin.almquist@it.uu.se>
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138 D4=HI*(M4-e_1*S3_1+e_m*S3_m + S_1'*S2_1-S_m'*S2_m);
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139
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140
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Martin Almquist <martin.almquist@it.uu.se>
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141 % L=h*(m-1);
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Martin Almquist <martin.almquist@it.uu.se>
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142 %
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Martin Almquist <martin.almquist@it.uu.se>
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143 % x1=linspace(0,L,m)';
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Martin Almquist <martin.almquist@it.uu.se>
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144 % x2=x1.^2/fac(2);
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Martin Almquist <martin.almquist@it.uu.se>
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145 % x3=x1.^3/fac(3);
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Martin Almquist <martin.almquist@it.uu.se>
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146 % x4=x1.^4/fac(4);
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Martin Almquist <martin.almquist@it.uu.se>
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147 % x5=x1.^5/fac(5);
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Martin Almquist <martin.almquist@it.uu.se>
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148 %
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Martin Almquist <martin.almquist@it.uu.se>
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149 % x0=x1.^0/fac(1);
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150
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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151 S_1 = S_1';
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Martin Almquist <martin.almquist@it.uu.se>
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152 S2_1 = S2_1';
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Martin Almquist <martin.almquist@it.uu.se>
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153 S3_1 = S3_1';
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Martin Almquist <martin.almquist@it.uu.se>
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154 S_m = S_m';
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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155 S2_m = S2_m';
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Martin Almquist <martin.almquist@it.uu.se>
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156 S3_m = S3_m';
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Martin Almquist <martin.almquist@it.uu.se>
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157
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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158
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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159
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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160 end