Mercurial > repos > public > sbplib
view +sbp/+implementations/intOpMC_orders_4to4_ratio2to1.m @ 1198:2924b3a9b921 feature/d2_compatible
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> |
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date | Fri, 16 Aug 2019 14:30:28 -0700 |
parents | c923fe6197ff |
children |
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% Marks New interpolation operators % 4th order to 2nd order accurate (diagonal norm) % M=9 is the minimum amount of points on the coarse mesh function [IC2F,IF2C] = intOpMC_orders_4to4_ratio2to1(M_C) M_F=M_C*2-1; % Coarse to fine I1=zeros(M_F,M_C); t1=[ 2047/2176 , 129/1088 , -129/2176 , 0 , 0 , 0 , 0 ,... 0 ;... 429/944 , 279/472 , -43/944 , 0 , 0 , 0 , 0 , 0 ;... 111/2752 , 4913/5504 , 3/32 , -147/5504 ,... 0 , 0 , 0 , 0 ;... -103/784 , 549/784 , 387/784 , -1/16 , 0 ,... 0 , 0 , 0 ;... -335/3072 , 205/768 , 2365/3072 , 49/512 ,... -3/128 , 0 , 0 , 0 ;... -9/256 , 5/256 , 129/256 , 147/256 ,... -1/16 , 0 , 0 , 0 ;... 5/192 , -59/1024 , 43/512 , 2695/3072 ,... 3/32 , -3/128 , 0 , 0 ;... 23/768 , -37/768 , -43/768 , 147/256 ,... 9/16 , -1/16 , 0 , 0 ;... 13/2048 , -11/1024 , -43/2048 , 49/512 ,... 55/64 , 3/32 , -3/128 , 0 ;... -1/384 , 1/256 , 0 , -49/768 , 9/16 ,... 9/16 , -1/16 , 0 ;... -1/1024 , 3/2048 , 0 , -49/2048 , 3/32 ,... 55/64 , 3/32 , -3/128]; t2=[-3/128 3/32 55/64 3/32 -3/128]; t3=[-1/16 9/16 9/16 -1/16]; I1(1:11,1:8)=t1; I1(M_F-10:M_F,M_C-7:M_C)=fliplr(flipud(t1)); I1(12,5:8)=t3; for i=13:2:M_F-12 j=(i-1)/2; I1(i,j-1:j+3)=t2; I1(i+1,j:j+3)=t3; end % Fine to coarse I2=zeros(M_C,M_F); t1=[ 2047/4352 , 429/544 , 111/2176 , -103/544 ... , -335/2176 , -27/544 , 5/136 , 23/544 ,... 39/4352 , -1/272 , -3/2176 ;... 129/7552 , 279/944 , 4913/15104 , 549/1888 ... , 205/1888 , 15/1888 , -3/128 , -37/1888 ... , -33/7552 , 3/1888 , 9/15104 ]; t2=[-3/256 -1/32 3/64 9/32 55/128 9/32 3/64 -1/32 -3/256]; I2(1:2,1:11)=t1; I2(M_C-1:M_C,M_F-10:M_F)=fliplr(flipud(t1)); for i=3:M_C-2 j=2*(i-3)+1; I2(i,j:j+8)=t2; end IC2F = sparse(I1); IF2C = sparse(I2);