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annotate +sbp/+implementations/d2_variable_2.m @ 577:e45c9b56d50d feature/grids

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Add an Empty grid class The need turned up for the flexural code when we may or may not have a grid for the open water and want to plot that solution. In case there is no open water we need an empty grid to plot the empty gridfunction against to avoid errors.
author Jonatan Werpers <jonatan@werpers.com>
date Thu, 07 Sep 2017 09:16:12 +0200
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)
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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2
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Martin Almquist <martin.almquist@it.uu.se>
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3 BP = 1;
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4 if(m<2*BP)
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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
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8 % Norm
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Martin Almquist <martin.almquist@it.uu.se>
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9 Hv = ones(m,1);
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10 Hv(1) = 1/2;
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11 Hv(m:m) = 1/2;
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12 Hv = h*Hv;
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Martin Almquist <martin.almquist@it.uu.se>
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13 H = spdiag(Hv, 0);
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Martin Almquist <martin.almquist@it.uu.se>
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14 HI = spdiag(1./Hv, 0);
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15
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16
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17 % Boundary operators
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18 e_l = sparse(m,1);
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19 e_l(1) = 1;
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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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23 d1_l(1:3) = 1/h*[-3/2 2 -1/2];
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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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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
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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
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39 scheme_width = 3;
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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.
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45 Mm1 = -c(r-1)/2 - c(r)/2;
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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;];
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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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>
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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.
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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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58 D2 = @D2_fun;
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59 end