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annotate +time/SBPInTime.m @ 365:f908ce064f35

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Added SBP in time timestepper.
author Martin Almquist <martin.almquist@it.uu.se>
date Tue, 24 Jan 2017 14:01:18 +0100
parents
children fccd746d8573 14f2be4fe9c1
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
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
2 % The SBP in time method.
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
3 % Implemented for v_t = A*v + f(t)
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
4 % k_local -- time-step
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Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
5 % Nblock -- number of points in each block
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
6 % nodes -- points such that t_n + nodes are the points in block n.
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
7 % Each "step" takes one block step and thus advances
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
8 % k = k_local*(Nblock-1) in time.
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
9 % M -- matrix used in every solve.
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
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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Martin Almquist <martin.almquist@it.uu.se>
parents:
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12 M
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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13 L
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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14 U
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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15 P
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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16 Q
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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17 A
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Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
18 Et_r
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Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
19 penalty
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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20 f
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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21 k_local
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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22 k
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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23 t
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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24 v
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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25 m
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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26 n
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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27 Nblock
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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28 order
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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29 nodes
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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30 end
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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31
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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32 methods
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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33 function obj = SBPInTime(A, f, k, order, Nblock, t0, v0, TYPE)
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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34 default_arg('TYPE','equidistant');
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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35 default_arg('Nblock',time.SBPInTime.smallestBlockSize(order,TYPE));
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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36
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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37 obj.A = A;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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38 obj.f = f;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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39 obj.k_local = k;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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40 obj.k = k*(Nblock-1);
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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41 obj.Nblock = Nblock;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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42 obj.t = t0;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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43 obj.m = length(v0);
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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44 obj.n = 0;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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45
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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46 %==== Build the time discretization matrix =====%
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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47 switch TYPE
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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48 case 'equidistant'
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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49 ops = sbp.D2Standard(Nblock,{0,obj.k},order);
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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50 case 'optimal'
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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51 ops = sbp.D1Nonequidistant(Nblock,{0,obj.k},order);
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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52 case 'minimal'
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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53 ops = sbp.D1Nonequidistant(Nblock,{0,obj.k},order,'minimal');
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Martin Almquist <martin.almquist@it.uu.se>
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54 end
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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55
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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56 D1 = ops.D1;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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57 HI = ops.HI;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
58 e_l = ops.e_l;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
59 e_r = ops.e_r;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
60 obj.nodes = ops.x;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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61
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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62 Ix = speye(size(A));
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Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
63 It = speye(Nblock,Nblock);
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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64
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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65 obj.Et_r = kron(e_r,Ix);
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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66
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Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
67 % Time derivative + penalty
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
68 tau = 1;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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69 Mt = D1 + tau*HI*(e_l*e_l');
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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70
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Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
71 % penalty to impose "data"
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Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
72 penalty = tau*HI*e_l;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
73 obj.penalty = kron(penalty,Ix);
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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74
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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75 Mx = kron(It,A);
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Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
76 Mt = kron(Mt,Ix);
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Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
77 obj.M = Mt - Mx;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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78 %==============================================%
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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79
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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80 % LU factorization
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Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
81 [obj.L,obj.U,obj.P,obj.Q] = lu(obj.M);
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Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
82
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Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
83 % Pretend that the initial condition is the last level
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Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
84 % of a previous step.
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Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
85 obj.v = obj.Et_r * v0;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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86
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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87 end
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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88
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Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
89 function [v,t] = getV(obj)
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Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
90 v = obj.Et_r' * obj.v;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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91 t = obj.t;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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92 end
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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93
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Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
94 function obj = step(obj)
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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95 obj.v = time.sbp.sbpintime(obj.v, obj.t, obj.nodes,...
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Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
96 obj.penalty, obj.f, obj.Nblock,...
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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97 obj.Et_r,...
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Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
98 obj.L, obj.U, obj.P, obj.Q);
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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99 obj.t = obj.t + obj.k;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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100 obj.n = obj.n + obj.Nblock-1;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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101 end
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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102 end
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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103
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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104
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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105 methods(Static)
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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106
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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107 %
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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108 function [k,numberOfBlocks] = alignedTimeStep(k,Tend,Nblock)
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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109
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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110 % input k is the desired time-step
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Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
111 % Nblock is the number of points per block.
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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112
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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113 % Make sure that we reach the final time by advancing
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Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
114 % an integer number of blocks
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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115 kblock = (Nblock-1)*k;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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116 numberOfBlocks = ceil(Tend/kblock);
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Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
117 kblock = Tend/(numberOfBlocks);
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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118
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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119 % Corrected time step
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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120 k = kblock/(Nblock-1);
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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121
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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122 end
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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123
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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124 function N = smallestBlockSize(order,TYPE)
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Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
125 default_arg('TYPE','equidistant')
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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126
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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127 switch TYPE
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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128
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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129 case 'equidistant'
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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130 switch order
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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131 case 2
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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132 N = 2;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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133 case 4
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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134 N = 8;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
135 case 6
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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136 N = 12;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
137 case 8
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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138 N = 16;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
139 case 10
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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140 N = 20;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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141 case 12
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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142 N = 24;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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143 otherwise
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Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
144 error('Operator does not exist');
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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145 end
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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146
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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147 case 'optimal'
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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148
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Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
149 switch order
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Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
150 case 4
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Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
151 N = 8;
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
152 case 6
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
153 N = 12;
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
154 case 8
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
155 N = 16;
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
156 case 10
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
157 N = 20;
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
158 case 12
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
159 N = 24;
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
160 otherwise
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
161 error('Operator does not exist');
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
162 end
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
163
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
164 case 'minimal'
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
165
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
166 switch order
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
167 case 4
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
168 N = 6;
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
169 case 6
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
170 N = 10;
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
171 case 8
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
172 N = 12;
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
173 case 10
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
174 N = 16;
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
175 case 12
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
176 N = 20;
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
177 otherwise
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
178 error('Operator does not exist');
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
179 end
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
180
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
181 end
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
182
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
183 end
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
184
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
185 end
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
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
188
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
189 end