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annotate +sbp/+implementations/d2_variable_2.m @ 774:66eb4a2bbb72 feature/grids

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Remove default scaling of the system. The scaling doens't seem to help actual solutions. One example that fails in the flexural code. With large timesteps the solutions seems to blow up. One particular example is profilePresentation on the tdb_presentation_figures branch with k = 0.0005
author Jonatan Werpers <jonatan@werpers.com>
date Wed, 18 Jul 2018 15:42:52 -0700
parents ded4156e53e2
children b758d1cf4c8e
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
362
ded4156e53e2 Added 2nd order accurate 2nd derivative with variable coefficents in a separate implementation file, used by the class D2Variable.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
1 function [H, HI, D1, D2, e_l, e_r, d1_l, d1_r] = d2_variable_2(m,h)
ded4156e53e2 Added 2nd order accurate 2nd derivative with variable coefficents in a separate implementation file, used by the class D2Variable.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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2
ded4156e53e2 Added 2nd order accurate 2nd derivative with variable coefficents in a separate implementation file, used by the class D2Variable.
Martin Almquist <martin.almquist@it.uu.se>
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3 BP = 1;
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Martin Almquist <martin.almquist@it.uu.se>
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4 if(m<2*BP)
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Martin Almquist <martin.almquist@it.uu.se>
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5 error(['Operator requires at least ' num2str(2*BP) ' grid points']);
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6 end
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7
ded4156e53e2 Added 2nd order accurate 2nd derivative with variable coefficents in a separate implementation file, used by the class D2Variable.
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8 % Norm
ded4156e53e2 Added 2nd order accurate 2nd derivative with variable coefficents in a separate implementation file, used by the class D2Variable.
Martin Almquist <martin.almquist@it.uu.se>
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9 Hv = ones(m,1);
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Martin Almquist <martin.almquist@it.uu.se>
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10 Hv(1) = 1/2;
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Martin Almquist <martin.almquist@it.uu.se>
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11 Hv(m:m) = 1/2;
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Martin Almquist <martin.almquist@it.uu.se>
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12 Hv = h*Hv;
ded4156e53e2 Added 2nd order accurate 2nd derivative with variable coefficents in a separate implementation file, used by the class D2Variable.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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13 H = spdiag(Hv, 0);
ded4156e53e2 Added 2nd order accurate 2nd derivative with variable coefficents in a separate implementation file, used by the class D2Variable.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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14 HI = spdiag(1./Hv, 0);
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15
ded4156e53e2 Added 2nd order accurate 2nd derivative with variable coefficents in a separate implementation file, used by the class D2Variable.
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16
ded4156e53e2 Added 2nd order accurate 2nd derivative with variable coefficents in a separate implementation file, used by the class D2Variable.
Martin Almquist <martin.almquist@it.uu.se>
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17 % Boundary operators
ded4156e53e2 Added 2nd order accurate 2nd derivative with variable coefficents in a separate implementation file, used by the class D2Variable.
Martin Almquist <martin.almquist@it.uu.se>
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18 e_l = sparse(m,1);
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19 e_l(1) = 1;
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Martin Almquist <martin.almquist@it.uu.se>
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20 e_r = rot90(e_l, 2);
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21
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22 d1_l = sparse(m,1);
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Martin Almquist <martin.almquist@it.uu.se>
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23 d1_l(1:3) = 1/h*[-3/2 2 -1/2];
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Martin Almquist <martin.almquist@it.uu.se>
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24 d1_r = -rot90(d1_l, 2);
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25
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26 % D1 operator
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Martin Almquist <martin.almquist@it.uu.se>
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27 diags = -1:1;
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28 stencil = [-1/2 0 1/2];
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29 D1 = stripeMatrix(stencil, diags, m);
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30
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Martin Almquist <martin.almquist@it.uu.se>
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31 D1(1,1)=-1;D1(1,2)=1;D1(m,m-1)=-1;D1(m,m)=1;
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32 D1(m,m-1)=-1;D1(m,m)=1;
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33 D1=D1/h;
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Martin Almquist <martin.almquist@it.uu.se>
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34 %Q=H*D1 + 1/2*(e_1*e_1') - 1/2*(e_m*e_m');
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35
ded4156e53e2 Added 2nd order accurate 2nd derivative with variable coefficents in a separate implementation file, used by the class D2Variable.
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36
ded4156e53e2 Added 2nd order accurate 2nd derivative with variable coefficents in a separate implementation file, used by the class D2Variable.
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37 M=sparse(m,m);
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38
ded4156e53e2 Added 2nd order accurate 2nd derivative with variable coefficents in a separate implementation file, used by the class D2Variable.
Martin Almquist <martin.almquist@it.uu.se>
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39 scheme_width = 3;
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Martin Almquist <martin.almquist@it.uu.se>
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40 scheme_radius = (scheme_width-1)/2;
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41 r = (1+scheme_radius):(m-scheme_radius);
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42
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43 function D2 = D2_fun(c)
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44
ded4156e53e2 Added 2nd order accurate 2nd derivative with variable coefficents in a separate implementation file, used by the class D2Variable.
Martin Almquist <martin.almquist@it.uu.se>
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45 Mm1 = -c(r-1)/2 - c(r)/2;
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Martin Almquist <martin.almquist@it.uu.se>
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46 M0 = c(r-1)/2 + c(r) + c(r+1)/2;
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47 Mp1 = -c(r)/2 - c(r+1)/2;
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48
ded4156e53e2 Added 2nd order accurate 2nd derivative with variable coefficents in a separate implementation file, used by the class D2Variable.
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49 M(r,:) = spdiags([Mm1 M0 Mp1],0:2*scheme_radius,length(r),m);
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50
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51
ded4156e53e2 Added 2nd order accurate 2nd derivative with variable coefficents in a separate implementation file, used by the class D2Variable.
Martin Almquist <martin.almquist@it.uu.se>
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52 M(1:2,1:2)=[c(1)/2 + c(2)/2 -c(1)/2 - c(2)/2; -c(1)/2 - c(2)/2 c(1)/2 + c(2) + c(3)/2;];
ded4156e53e2 Added 2nd order accurate 2nd derivative with variable coefficents in a separate implementation file, used by the class D2Variable.
Martin Almquist <martin.almquist@it.uu.se>
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53 M(m-1:m,m-1:m)=[c(m-2)/2 + c(m-1) + c(m)/2 -c(m-1)/2 - c(m)/2; -c(m-1)/2 - c(m)/2 c(m-1)/2 + c(m)/2;];
ded4156e53e2 Added 2nd order accurate 2nd derivative with variable coefficents in a separate implementation file, used by the class D2Variable.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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54 M=M/h;
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55
ded4156e53e2 Added 2nd order accurate 2nd derivative with variable coefficents in a separate implementation file, used by the class D2Variable.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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56 D2=HI*(-M-c(1)*e_l*d1_l'+c(m)*e_r*d1_r');
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57 end
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Martin Almquist <martin.almquist@it.uu.se>
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58 D2 = @D2_fun;
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59 end