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annotate +sbp/+implementations/intOpMC_orders_4to4_ratio2to1.m @ 1198:2924b3a9b921 feature/d2_compatible

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Add OpSet for fully compatible D2Variable, created from regular D2Variable by replacing d1 by first row of D1. Formal reduction by one order of accuracy at the boundary point.
author Martin Almquist <malmquist@stanford.edu>
date Fri, 16 Aug 2019 14:30:28 -0700
parents c923fe6197ff
children
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c923fe6197ff Add inerpolation operator classes and implementations for MC and AWW.
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1 % Marks New interpolation operators
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2 % 4th order to 2nd order accurate (diagonal norm)
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3 % M=9 is the minimum amount of points on the coarse mesh
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4
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5 function [IC2F,IF2C] = intOpMC_orders_4to4_ratio2to1(M_C)
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6
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7 M_F=M_C*2-1;
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8
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9 % Coarse to fine
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10 I1=zeros(M_F,M_C);
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11 t1=[ 2047/2176 , 129/1088 , -129/2176 , 0 , 0 , 0 , 0 ,...
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12 0 ;...
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13 429/944 , 279/472 , -43/944 , 0 , 0 , 0 , 0 , 0 ;...
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14 111/2752 , 4913/5504 , 3/32 , -147/5504 ,...
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15 0 , 0 , 0 , 0 ;...
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16 -103/784 , 549/784 , 387/784 , -1/16 , 0 ,...
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17 0 , 0 , 0 ;...
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18 -335/3072 , 205/768 , 2365/3072 , 49/512 ,...
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19 -3/128 , 0 , 0 , 0 ;...
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20 -9/256 , 5/256 , 129/256 , 147/256 ,...
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21 -1/16 , 0 , 0 , 0 ;...
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22 5/192 , -59/1024 , 43/512 , 2695/3072 ,...
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23 3/32 , -3/128 , 0 , 0 ;...
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24 23/768 , -37/768 , -43/768 , 147/256 ,...
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25 9/16 , -1/16 , 0 , 0 ;...
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26 13/2048 , -11/1024 , -43/2048 , 49/512 ,...
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27 55/64 , 3/32 , -3/128 , 0 ;...
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28 -1/384 , 1/256 , 0 , -49/768 , 9/16 ,...
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29 9/16 , -1/16 , 0 ;...
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30 -1/1024 , 3/2048 , 0 , -49/2048 , 3/32 ,...
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31 55/64 , 3/32 , -3/128];
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32
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33
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34 t2=[-3/128 3/32 55/64 3/32 -3/128];
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35 t3=[-1/16 9/16 9/16 -1/16];
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36 I1(1:11,1:8)=t1;
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37 I1(M_F-10:M_F,M_C-7:M_C)=fliplr(flipud(t1));
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38 I1(12,5:8)=t3;
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39 for i=13:2:M_F-12
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40 j=(i-1)/2;
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41 I1(i,j-1:j+3)=t2;
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42 I1(i+1,j:j+3)=t3;
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43 end
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44
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45 % Fine to coarse
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46 I2=zeros(M_C,M_F);
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47
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48 t1=[ 2047/4352 , 429/544 , 111/2176 , -103/544 ...
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49 , -335/2176 , -27/544 , 5/136 , 23/544 ,...
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50 39/4352 , -1/272 , -3/2176 ;...
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51 129/7552 , 279/944 , 4913/15104 , 549/1888 ...
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52 , 205/1888 , 15/1888 , -3/128 , -37/1888 ...
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53 , -33/7552 , 3/1888 , 9/15104 ];
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54 t2=[-3/256 -1/32 3/64 9/32 55/128 9/32 3/64 -1/32 -3/256];
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55
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56 I2(1:2,1:11)=t1;
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57
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58 I2(M_C-1:M_C,M_F-10:M_F)=fliplr(flipud(t1));
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59
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60 for i=3:M_C-2
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61 j=2*(i-3)+1;
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62 I2(i,j:j+8)=t2;
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63 end
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64
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65 IC2F = sparse(I1);
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66 IF2C = sparse(I2);