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annotate +sbp/dissipationOperator.m @ 1037:2d7ba44340d0 feature/burgers1d

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Pass scheme specific parameters as cell array. This will enabale constructDiffOps to be more general. In addition, allow for schemes returning function handles as diffOps, which is currently how non-linear schemes such as Burgers1d are implemented.
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Fri, 18 Jan 2019 09:02:02 +0100
parents cda996e64925
children
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834
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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1 %% Function that constructs artificial dissipation operators using undivided differences
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2 function D = dissipationOperator(m, order, Hinv, scaling)
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3 % TBD: Add or remove D_2 and Dp/Dm?
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4 % d2=[1 2 1];
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5 % D_2=(diag(ones(m-1,1),-1)-2*diag(ones(m,1),0)+ ...
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6 % diag(ones(m-1,1),1));
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7 % D_2(1,1:3)=[d2];D_2(m,m-2:m)=[d2];
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8 % %Dm
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9 % DD_m=(diag(ones(m-1,1),+1)-diag(ones(m,1),0));
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10 % DD_m(m,m-1:m)=[-1 1];
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11 % %Dp
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12 % DD_p=(-diag(ones(m-1,1),-1)+diag(ones(m,1),0));
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13 % DD_p(1,1:2)=[-1 1];
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14
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15 switch order
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16 case 1
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17 DD_1=(diag(ones(m-1,1),+1)-diag(ones(m,1),0));
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18 DD_1(m,m-1:m)=[-1 1];
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19 D = DD_2'*DD_2;
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20 case 2
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21 dd2=0*[1 -2 1];
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22 DD_2=(diag(ones(m-1,1),-1)-2*diag(ones(m,1),0)+ ...
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23 diag(ones(m-1,1),1));
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24 DD_2(1,1:3)=[dd2];DD_2(m,m-2:m)=[dd2];
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25 D = DD_2'*DD_2;
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26 case 3
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27 d3=0*[-1 3 -3 1];
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28 DD_3=(-diag(ones(m-2,1),-2)+3*diag(ones(m-1,1),-1)-3*diag(ones(m,1),0)+ ...
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29 diag(ones(m-1,1),1));
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30 DD_3(1:2,1:4)=[d3;d3];
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31 DD_3(m,m-3:m)=[d3];
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32 D = DD_3'*DD_3;
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33 case 4
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34 default_arg('scaling', 1/12);
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35 d4=0*[1 -4 6 -4 1];
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36 DD_4=(diag(ones(m-2,1),2)-4*diag(ones(m-1,1),1)+6*diag(ones(m,1),0)-4*diag(ones(m-1,1),-1)+diag(ones(m-2,1),-2));
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37 DD_4(1:2,1:5)=[d4;d4];DD_4(m-1:m,m-4:m)=[d4;d4];
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38 D = DD_4'*DD_4;
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39 case 5
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40 d5=0*[-1 5 -10 10 -5 1];
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41 DD_5=(-diag(ones(m-3,1),-3)+5*diag(ones(m-2,1),-2)-10*diag(ones(m-1,1),-1)+10*diag(ones(m,1),0)-5*diag(ones(m-1,1),1)+diag(ones(m-2,1),2));
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42 DD_5(1:3,1:6)=[d5;d5;d5];
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43 DD_5(m-1:m,m-5:m)=[d5;d5];
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44 D = DD_5'*DD_5;
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45 case 6
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46 default_arg('scaling', 1/60);
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47 d6=0*[1 -6 15 -20 15 -6 1];
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48 DD_6=(diag(ones(m-3,1),3)-6*diag(ones(m-2,1),2)+15*diag(ones(m-1,1),1)-20*diag(ones(m,1),0)+15*diag(ones(m-1,1),-1)-6*diag(ones(m-2,1),-2)+diag(ones(m-3,1),-3));
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49 DD_6(1:3,1:7)=[d6;d6;d6];DD_6(m-2:m,m-6:m)=[d6;d6;d6];
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50 D = DD_6'*DD_6;
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51 case 7
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52 d7=0*[-1 7 -21 35 -35 21 -7 1];
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53 DD_7=(-diag(ones(m-4,1),-4)+7*diag(ones(m-3,1),-3)-21*diag(ones(m-2,1),-2)+35*diag(ones(m-1,1),-1)-35*diag(ones(m,1),0)+21*diag(ones(m-1,1),1)-7*diag(ones(m-2,1),2)+diag(ones(m-3,1),3));
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54 DD_7(1:4,1:8)=[d7;d7;d7;d7];
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55 DD_7(m-2:m,m-7:m)=[d7;d7;d7];
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56 D = DD_7'*DD_7;
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57 case 9
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58 d9=0*[-1 9 -36 84 -126 126 -84 36 -9 1];
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59 DD_9=(-diag(ones(m-5,1),-5)+9*diag(ones(m-4,1),-4)-36*diag(ones(m-3,1),-3)+84*diag(ones(m-2,1),-2)-126*diag(ones(m-1,1),-1)+126*diag(ones(m,1),0)-84*diag(ones(m-1,1),1)+36*diag(ones(m-2,1),2)-9*diag(ones(m-3,1),3)+diag(ones(m-4,1),4));
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60 DD_9(1:5,1:10)=[d9;d9;d9;d9;d9];
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61 DD_9(m-3:m,m-9:m)=[d9;d9;d9;d9];
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62 D = DD_9'*DD_9;
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63 otherwise
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64 error('Order not yet supported', order);
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65 end
853
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66 D = scaling*sparse(Hinv*D);
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67 end