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>
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);