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annotate +time/SBPInTime.m @ 400:14f2be4fe9c1 feature/beams

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Add function to center colorlimits.
author Jonatan Werpers <jonatan@werpers.com>
date Tue, 31 Jan 2017 13:23:52 +0100
parents f908ce064f35
children 9ff24a14f9ef
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
365
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
1 classdef SBPInTime < time.Timestepper
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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2 % The SBP in time method.
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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3 % Implemented for v_t = A*v + f(t)
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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4 % k_local -- time-step
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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5 % Nblock -- number of points in each block
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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6 % nodes -- points such that t_n + nodes are the points in block n.
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7 % Each "step" takes one block step and thus advances
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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8 % k = k_local*(Nblock-1) in time.
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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9 % M -- matrix used in every solve.
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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10 % [L,U,P,Q] = lu(M);
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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11 properties
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12 M % System matrix
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13 L,U,P % LU factorization of M
365
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Martin Almquist <martin.almquist@it.uu.se>
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14 Q
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Martin Almquist <martin.almquist@it.uu.se>
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15 A
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Martin Almquist <martin.almquist@it.uu.se>
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16 Et_r
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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17 penalty
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Martin Almquist <martin.almquist@it.uu.se>
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18 f
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Martin Almquist <martin.almquist@it.uu.se>
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19 k_local
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Martin Almquist <martin.almquist@it.uu.se>
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20 k
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Martin Almquist <martin.almquist@it.uu.se>
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21 t
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Martin Almquist <martin.almquist@it.uu.se>
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22 v
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Martin Almquist <martin.almquist@it.uu.se>
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23 m
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Martin Almquist <martin.almquist@it.uu.se>
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24 n
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Martin Almquist <martin.almquist@it.uu.se>
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25 Nblock
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Martin Almquist <martin.almquist@it.uu.se>
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26 order
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27 nodes
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28 end
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29
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Martin Almquist <martin.almquist@it.uu.se>
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30 methods
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Martin Almquist <martin.almquist@it.uu.se>
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31 function obj = SBPInTime(A, f, k, order, Nblock, t0, v0, TYPE)
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Martin Almquist <martin.almquist@it.uu.se>
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32 default_arg('TYPE','equidistant');
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Martin Almquist <martin.almquist@it.uu.se>
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33 default_arg('Nblock',time.SBPInTime.smallestBlockSize(order,TYPE));
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34
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Martin Almquist <martin.almquist@it.uu.se>
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35 obj.A = A;
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Martin Almquist <martin.almquist@it.uu.se>
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36 obj.f = f;
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Martin Almquist <martin.almquist@it.uu.se>
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37 obj.k_local = k;
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Martin Almquist <martin.almquist@it.uu.se>
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38 obj.k = k*(Nblock-1);
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Martin Almquist <martin.almquist@it.uu.se>
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39 obj.Nblock = Nblock;
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Martin Almquist <martin.almquist@it.uu.se>
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40 obj.t = t0;
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Martin Almquist <martin.almquist@it.uu.se>
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41 obj.m = length(v0);
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Martin Almquist <martin.almquist@it.uu.se>
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42 obj.n = 0;
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43
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Martin Almquist <martin.almquist@it.uu.se>
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44 %==== Build the time discretization matrix =====%
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Martin Almquist <martin.almquist@it.uu.se>
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45 switch TYPE
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Martin Almquist <martin.almquist@it.uu.se>
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46 case 'equidistant'
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Martin Almquist <martin.almquist@it.uu.se>
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47 ops = sbp.D2Standard(Nblock,{0,obj.k},order);
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48 case 'optimal'
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49 ops = sbp.D1Nonequidistant(Nblock,{0,obj.k},order);
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Martin Almquist <martin.almquist@it.uu.se>
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50 case 'minimal'
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51 ops = sbp.D1Nonequidistant(Nblock,{0,obj.k},order,'minimal');
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52 end
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53
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54 D1 = ops.D1;
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Martin Almquist <martin.almquist@it.uu.se>
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55 HI = ops.HI;
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Martin Almquist <martin.almquist@it.uu.se>
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56 e_l = ops.e_l;
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Martin Almquist <martin.almquist@it.uu.se>
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57 e_r = ops.e_r;
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Martin Almquist <martin.almquist@it.uu.se>
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58 obj.nodes = ops.x;
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59
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Martin Almquist <martin.almquist@it.uu.se>
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60 Ix = speye(size(A));
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Martin Almquist <martin.almquist@it.uu.se>
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61 It = speye(Nblock,Nblock);
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62
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63 obj.Et_r = kron(e_r,Ix);
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64
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Martin Almquist <martin.almquist@it.uu.se>
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65 % Time derivative + penalty
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Martin Almquist <martin.almquist@it.uu.se>
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66 tau = 1;
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67 Mt = D1 + tau*HI*(e_l*e_l');
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68
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Martin Almquist <martin.almquist@it.uu.se>
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69 % penalty to impose "data"
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Martin Almquist <martin.almquist@it.uu.se>
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70 penalty = tau*HI*e_l;
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Martin Almquist <martin.almquist@it.uu.se>
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71 obj.penalty = kron(penalty,Ix);
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72
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73 Mx = kron(It,A);
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74 Mt = kron(Mt,Ix);
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75 obj.M = Mt - Mx;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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76 %==============================================%
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77
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Martin Almquist <martin.almquist@it.uu.se>
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78 % LU factorization
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Martin Almquist <martin.almquist@it.uu.se>
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79 [obj.L,obj.U,obj.P,obj.Q] = lu(obj.M);
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80
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Martin Almquist <martin.almquist@it.uu.se>
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81 % Pretend that the initial condition is the last level
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Martin Almquist <martin.almquist@it.uu.se>
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82 % of a previous step.
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Martin Almquist <martin.almquist@it.uu.se>
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83 obj.v = obj.Et_r * v0;
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84
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85 end
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86
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Martin Almquist <martin.almquist@it.uu.se>
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87 function [v,t] = getV(obj)
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Martin Almquist <martin.almquist@it.uu.se>
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88 v = obj.Et_r' * obj.v;
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Martin Almquist <martin.almquist@it.uu.se>
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89 t = obj.t;
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90 end
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91
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Martin Almquist <martin.almquist@it.uu.se>
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92 function obj = step(obj)
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Martin Almquist <martin.almquist@it.uu.se>
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93 obj.v = time.sbp.sbpintime(obj.v, obj.t, obj.nodes,...
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Martin Almquist <martin.almquist@it.uu.se>
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94 obj.penalty, obj.f, obj.Nblock,...
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Martin Almquist <martin.almquist@it.uu.se>
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95 obj.Et_r,...
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Martin Almquist <martin.almquist@it.uu.se>
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96 obj.L, obj.U, obj.P, obj.Q);
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Martin Almquist <martin.almquist@it.uu.se>
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97 obj.t = obj.t + obj.k;
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Martin Almquist <martin.almquist@it.uu.se>
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98 obj.n = obj.n + obj.Nblock-1;
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99 end
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100 end
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101
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102
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Martin Almquist <martin.almquist@it.uu.se>
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103 methods(Static)
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104
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105 %
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Martin Almquist <martin.almquist@it.uu.se>
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106 function [k,numberOfBlocks] = alignedTimeStep(k,Tend,Nblock)
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107
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108 % input k is the desired time-step
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Martin Almquist <martin.almquist@it.uu.se>
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109 % Nblock is the number of points per block.
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110
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111 % Make sure that we reach the final time by advancing
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Martin Almquist <martin.almquist@it.uu.se>
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112 % an integer number of blocks
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Martin Almquist <martin.almquist@it.uu.se>
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113 kblock = (Nblock-1)*k;
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Martin Almquist <martin.almquist@it.uu.se>
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114 numberOfBlocks = ceil(Tend/kblock);
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Martin Almquist <martin.almquist@it.uu.se>
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115 kblock = Tend/(numberOfBlocks);
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116
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Martin Almquist <martin.almquist@it.uu.se>
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117 % Corrected time step
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118 k = kblock/(Nblock-1);
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119
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120 end
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121
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Martin Almquist <martin.almquist@it.uu.se>
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122 function N = smallestBlockSize(order,TYPE)
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Martin Almquist <martin.almquist@it.uu.se>
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123 default_arg('TYPE','equidistant')
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124
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125 switch TYPE
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126
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127 case 'equidistant'
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128 switch order
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Martin Almquist <martin.almquist@it.uu.se>
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129 case 2
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Martin Almquist <martin.almquist@it.uu.se>
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130 N = 2;
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Martin Almquist <martin.almquist@it.uu.se>
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131 case 4
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Martin Almquist <martin.almquist@it.uu.se>
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132 N = 8;
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Martin Almquist <martin.almquist@it.uu.se>
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133 case 6
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Martin Almquist <martin.almquist@it.uu.se>
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134 N = 12;
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Martin Almquist <martin.almquist@it.uu.se>
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135 case 8
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Martin Almquist <martin.almquist@it.uu.se>
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136 N = 16;
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Martin Almquist <martin.almquist@it.uu.se>
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137 case 10
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Martin Almquist <martin.almquist@it.uu.se>
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138 N = 20;
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Martin Almquist <martin.almquist@it.uu.se>
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139 case 12
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Martin Almquist <martin.almquist@it.uu.se>
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140 N = 24;
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Martin Almquist <martin.almquist@it.uu.se>
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141 otherwise
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Martin Almquist <martin.almquist@it.uu.se>
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142 error('Operator does not exist');
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143 end
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144
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145 case 'optimal'
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146
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Martin Almquist <martin.almquist@it.uu.se>
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147 switch order
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Martin Almquist <martin.almquist@it.uu.se>
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148 case 4
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Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
149 N = 8;
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
150 case 6
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
151 N = 12;
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
152 case 8
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
153 N = 16;
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
154 case 10
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
155 N = 20;
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
156 case 12
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
157 N = 24;
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
158 otherwise
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
159 error('Operator does not exist');
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
160 end
400
14f2be4fe9c1 Add function to center colorlimits.
Jonatan Werpers <jonatan@werpers.com>
parents: 365
diff changeset
161
365
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
162 case 'minimal'
400
14f2be4fe9c1 Add function to center colorlimits.
Jonatan Werpers <jonatan@werpers.com>
parents: 365
diff changeset
163
365
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
164 switch order
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
165 case 4
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
166 N = 6;
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
167 case 6
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
168 N = 10;
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
169 case 8
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
170 N = 12;
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
171 case 10
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
172 N = 16;
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
173 case 12
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
174 N = 20;
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
175 otherwise
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
176 error('Operator does not exist');
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
177 end
400
14f2be4fe9c1 Add function to center colorlimits.
Jonatan Werpers <jonatan@werpers.com>
parents: 365
diff changeset
178
365
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
179 end
400
14f2be4fe9c1 Add function to center colorlimits.
Jonatan Werpers <jonatan@werpers.com>
parents: 365
diff changeset
180
365
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
181 end
400
14f2be4fe9c1 Add function to center colorlimits.
Jonatan Werpers <jonatan@werpers.com>
parents: 365
diff changeset
182
365
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
183 end
400
14f2be4fe9c1 Add function to center colorlimits.
Jonatan Werpers <jonatan@werpers.com>
parents: 365
diff changeset
184
14f2be4fe9c1 Add function to center colorlimits.
Jonatan Werpers <jonatan@werpers.com>
parents: 365
diff changeset
185
365
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
186
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
187 end