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annotate +sbp/+implementations/d1_gauss_4.m @ 1337:bf2554f1825d feature/D2_boundary_opt

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Add periodic D1 and D2 operators for orders 8,10,12
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Fri, 13 May 2022 13:28:10 +0200
parents 0bc37a25ed88
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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409
42c4f0b545d6 Remove m as input to implementation function. Fix error message for invalid m to D1Gauss
Jonatan Werpers <jonatan@werpers.com>
parents: 408
diff changeset
1 function [D1,H,x,h,e_l,e_r] = d1_gauss_4(L)
405
4d9d8064e58b Implementation of D1 based on Gauss quadrature formula with 4 nodes.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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2
4d9d8064e58b Implementation of D1 based on Gauss quadrature formula with 4 nodes.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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3 % L: Domain length
434
0bc37a25ed88 Bug fix sbp in time gauss default arg
Martin Almquist <martin.almquist@it.uu.se>
parents: 409
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4 default_arg('L',1);
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4d9d8064e58b Implementation of D1 based on Gauss quadrature formula with 4 nodes.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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5
409
42c4f0b545d6 Remove m as input to implementation function. Fix error message for invalid m to D1Gauss
Jonatan Werpers <jonatan@werpers.com>
parents: 408
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6 N = 4;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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7
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Martin Almquist <martin.almquist@it.uu.se>
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8 % Quadrature nodes on interval [-1, 1]
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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9 x = [ -0.8611363115940526; -0.3399810435848563; 0.3399810435848563; 0.8611363115940526];
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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10
4d9d8064e58b Implementation of D1 based on Gauss quadrature formula with 4 nodes.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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11 % Shift nodes to [0,L]
4d9d8064e58b Implementation of D1 based on Gauss quadrature formula with 4 nodes.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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12 x = (x+1)/2*L;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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13
4d9d8064e58b Implementation of D1 based on Gauss quadrature formula with 4 nodes.
Martin Almquist <martin.almquist@it.uu.se>
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14 % Boundary extrapolation operators
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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15 e_l = [1.5267881254572668; -0.8136324494869273; 0.4007615203116504; -0.1139171962819899];
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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16 e_r = flipud(e_l);
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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17 e_l = sparse(e_l);
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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18 e_r = sparse(e_r);
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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19
4d9d8064e58b Implementation of D1 based on Gauss quadrature formula with 4 nodes.
Martin Almquist <martin.almquist@it.uu.se>
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20 %%%% Compute approximate h %%%%%%%%%%
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Martin Almquist <martin.almquist@it.uu.se>
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21 h = L/(N-1);
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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22 %%%%%%%%%%%%%%%%%%%%%%%%%
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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23
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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24 %%%% Norm matrix on [-1,1] %%%%%%%%
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Martin Almquist <martin.almquist@it.uu.se>
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25 P = sparse(N,N);
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Martin Almquist <martin.almquist@it.uu.se>
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26 P(1,1) = 0.3478548451374539;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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27 P(2,2) = 0.6521451548625461;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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28 P(3,3) = 0.6521451548625461;
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Martin Almquist <martin.almquist@it.uu.se>
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29 P(4,4) = 0.3478548451374539;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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30 %%%%%%%%%%%%%%%%%%%%%%%%%
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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31
4d9d8064e58b Implementation of D1 based on Gauss quadrature formula with 4 nodes.
Martin Almquist <martin.almquist@it.uu.se>
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32 %%%% Norm matrix on [0,L] %%%%%%%%
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Martin Almquist <martin.almquist@it.uu.se>
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33 H = P*L/2;
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Martin Almquist <martin.almquist@it.uu.se>
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34 %%%%%%%%%%%%%%%%%%%%%%%%%
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parents:
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35
4d9d8064e58b Implementation of D1 based on Gauss quadrature formula with 4 nodes.
Martin Almquist <martin.almquist@it.uu.se>
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36 %%%% D1 on [-1,1] %%%%%%%%
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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37 D1 = sparse(N,N);
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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38 D1(1,1) = -3.3320002363522817;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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39 D1(1,2) = 4.8601544156851962;
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Jonatan Werpers <jonatan@werpers.com>
parents: 405
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40 D1(1,3) = -2.1087823484951789;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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41 D1(1,4) = 0.5806281691622644;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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42
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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43 D1(2,1) = -0.7575576147992339;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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44 D1(2,2) = -0.3844143922232086;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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45 D1(2,3) = 1.4706702312807167;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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46 D1(2,4) = -0.3286982242582743;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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47
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Martin Almquist <martin.almquist@it.uu.se>
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48 D1(3,1) = 0.3286982242582743;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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49 D1(3,2) = -1.4706702312807167;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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50 D1(3,3) = 0.3844143922232086;
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Jonatan Werpers <jonatan@werpers.com>
parents: 405
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51 D1(3,4) = 0.7575576147992339;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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52
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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53 D1(4,1) = -0.5806281691622644;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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54 D1(4,2) = 2.1087823484951789;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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55 D1(4,3) = -4.8601544156851962;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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56 D1(4,4) = 3.3320002363522817;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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57 %%%%%%%%%%%%%%%%%%%%%%%%%
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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58
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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59 % D1 on [0,L]
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Martin Almquist <martin.almquist@it.uu.se>
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60 D1 = D1*2/L;