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annotate +sbp/+implementations/d4_lonely_4_min_boundary_points.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 b19e142fcae1
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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c0cbffcf6513 Created new operator class for lonely D4 operators. Removed some output parameters of implementations.
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1 function [H, HI, D4, e_l, e_r, M4, d2_l, d2_r, d3_l, d3_r, d1_l, d1_r] = d4_variable_4_min_boundary_points(m,h)
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2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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3 %%% 4:de ordn. SBP Finita differens %%%
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4 %%% operatorer framtagna av Mark Carpenter %%%
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5 %%% %%%
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6 %%% H (Normen) %%%
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7 %%% D1=H^(-1)Q (approx f?rsta derivatan) %%%
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8 %%% D2 (approx andra derivatan) %%%
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9 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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10 %H?r med endast 4 randpunkter
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parents: 312
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13 BP = 4;
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14 if(m<2*BP)
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15 error(['Operator requires at least ' num2str(2*BP) ' grid points']);
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parents: 312
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16 end
99005a80b4c2 Cleaned up d4_variable_4_min_boundary. Removed incorrect D2s from a bunch of files.
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parents: 312
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17
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18
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19 % Norm
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20 Hv = ones(m,1);
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21 Hv(1:4) = [17/48 59/48 43/48 49/48];
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22 Hv(m-3:m) = rot90(Hv(1:4),2);
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23 Hv = h*Hv;
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24 H = spdiag(Hv, 0);
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25 HI = spdiag(1./Hv, 0);
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27
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28 % Boundary operators
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parents: 312
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29 e_l = sparse(m,1);
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30 e_l(1) = 1;
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31 e_r = rot90(e_l, 2);
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33 d1_l = sparse(m,1);
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34 d1_l(1:4) = 1/h*[-11/6 3 -3/2 1/3];
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35 d1_r = -rot90(d1_l, 2);
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37 d2_l = sparse(m,1);
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38 d2_l(1:4) = 1/h^2*[2 -5 4 -1];
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39 d2_r = rot90(d2_l, 2);
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41 d3_l = sparse(m,1);
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42 d3_l(1:4) = 1/h^3*[-1 3 -3 1];
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43 d3_r = -rot90(d3_l, 2);
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46 % First derivative
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47 stencil = [1/12 -2/3 0 2/3 -1/12];
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48 diags = [-1 0 1];
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49
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50 Q_U = [
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51 0 0.59e2/0.96e2 -0.1e1/0.12e2 -0.1e1/0.32e2;
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52 -0.59e2/0.96e2 0 0.59e2/0.96e2 0;
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53 0.1e1/0.12e2 -0.59e2/0.96e2 0 0.59e2/0.96e2;
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54 0.1e1/0.32e2 0 -0.59e2/0.96e2 0;
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55 ];
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56
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57 Q = stripeMatrix(stencil, diags, m);
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58 Q(1:4,1:4)=Q_U;
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59 Q(m-3:m,m-3:m) = -rot90(Q_U, 2);
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61 D1 = HI*(Q - 1/2*e_l*e_l' + 1/2*e_r*e_r');
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63 % Fourth derivative
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64 stencil = [-1/6, 2, -13/2, 28/3, -13/2, 2, -1/6];
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65 diags = -3:3;
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66 M4 = stripeMatrix(stencil, diags, m);
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68 M4_U=[
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69 0.8e1/0.3e1 -0.37e2/0.6e1 0.13e2/0.3e1 -0.5e1/0.6e1;
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70 -0.37e2/0.6e1 0.47e2/0.3e1 -13 0.11e2/0.3e1;
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71 0.13e2/0.3e1 -13 0.44e2/0.3e1 -0.47e2/0.6e1;
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72 -0.5e1/0.6e1 0.11e2/0.3e1 -0.47e2/0.6e1 0.29e2/0.3e1;
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73 ];
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76 M4(1:4,1:4) = M4_U;
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77 M4(m-3:m,m-3:m) = rot90(M4_U, 2);
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78 M4 = 1/h^3*M4;
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80 D4=HI*(M4 - e_l*d3_l'+e_r*d3_r' + d1_l*d2_l'-d1_r*d2_r');
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81 end