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For easier comparison, return both the first order and residual viscosity when evaluating the residual. Add the first order and residual viscosity to the state of the RungekuttaRV time steppers
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Thu, 17 Jan 2019 10:25:06 +0100
parents 8b8672134be8
children
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1 function [H, HI, D1, D2, e_1, e_m, M, Q, S_1, S_m] = d2_4(m,h)
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2
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3 BP = 4;
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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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8 e_1=sparse(m,1);e_1(1)=1;
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9 e_m=sparse(m,1);e_m(m)=1;
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10
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11 e=ones(m,1);
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12 H=spdiags(e,0,m,m);
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13 %H=speye(m,m);
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15 H(1:4,1:4)=diag([17/48 59/48 43/48 49/48]);
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16 H(m-3:m,m-3:m)=rot90(diag([17/48 59/48 43/48 49/48]),2);
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17 H=H*h;
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18 HI=inv(H);
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21 Q=spdiags([e -8*e 0*e 8*e -e], -2:2, m, m)/12;
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22 %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));
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23 Q_U = [
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24 0 0.59e2/0.96e2 -0.1e1/0.12e2 -0.1e1/0.32e2;
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25 -0.59e2/0.96e2 0 0.59e2/0.96e2 0;
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26 0.1e1/0.12e2 -0.59e2/0.96e2 0 0.59e2/0.96e2;
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27 0.1e1/0.32e2 0 -0.59e2/0.96e2 0;
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28 ];
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29 Q(1:4,1:4)=Q_U;
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30 Q(m-3:m,m-3:m)=rot90( -Q_U(1:4,1:4) ,2 );
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32 D1=H\(Q-1/2*(e_1*e_1')+1/2*(e_m*e_m')) ;
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34 M=-spdiags([-e 16*e -30*e 16*e -e], -2:2, m, m)/12;
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35
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36 %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));
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37
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38 M_U=[
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39 0.9e1/0.8e1 -0.59e2/0.48e2 0.1e1/0.12e2 0.1e1/0.48e2;
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40 -0.59e2/0.48e2 0.59e2/0.24e2 -0.59e2/0.48e2 0;
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41 0.1e1/0.12e2 -0.59e2/0.48e2 0.55e2/0.24e2 -0.59e2/0.48e2;
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42 0.1e1/0.48e2 0 -0.59e2/0.48e2 0.59e2/0.24e2;
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43 ];
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44 M(1:4,1:4)=M_U;
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46 M(m-3:m,m-3:m)=rot90( M_U ,2 );
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47 M=M/h;
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48
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49 S_U=[-0.11e2/0.6e1 3 -0.3e1/0.2e1 0.1e1/0.3e1;]/h;
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50 S_1=sparse(sparse(1,m));
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51 S_1(1:4)=S_U;
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52 S_m=sparse(sparse(1,m));
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53 S_m(m-3:m)=fliplr(-S_U);
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56 D2=H\(-M-e_1*S_1+e_m*S_m);
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57 S_1 = S_1';
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58 S_m = S_m';
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59 end