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annotate +sbp/+implementations/d1_gauss_4.m @ 774:66eb4a2bbb72 feature/grids

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Remove default scaling of the system. The scaling doens't seem to help actual solutions. One example that fails in the flexural code. With large timesteps the solutions seems to blow up. One particular example is profilePresentation on the tdb_presentation_figures branch with k = 0.0005
author Jonatan Werpers <jonatan@werpers.com>
date Wed, 18 Jul 2018 15:42:52 -0700
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
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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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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
4d9d8064e58b Implementation of D1 based on Gauss quadrature formula with 4 nodes.
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>
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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);
4d9d8064e58b Implementation of D1 based on Gauss quadrature formula with 4 nodes.
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
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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>
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22 %%%%%%%%%%%%%%%%%%%%%%%%%
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23
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Martin Almquist <martin.almquist@it.uu.se>
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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>
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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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29 P(4,4) = 0.3478548451374539;
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Martin Almquist <martin.almquist@it.uu.se>
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30 %%%%%%%%%%%%%%%%%%%%%%%%%
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31
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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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34 %%%%%%%%%%%%%%%%%%%%%%%%%
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35
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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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38 D1(1,1) = -3.3320002363522817;
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parents:
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39 D1(1,2) = 4.8601544156851962;
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40 D1(1,3) = -2.1087823484951789;
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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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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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51 D1(3,4) = 0.7575576147992339;
405
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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52
4d9d8064e58b Implementation of D1 based on Gauss quadrature formula with 4 nodes.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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53 D1(4,1) = -0.5806281691622644;
4d9d8064e58b Implementation of D1 based on Gauss quadrature formula with 4 nodes.
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 %%%%%%%%%%%%%%%%%%%%%%%%%
4d9d8064e58b Implementation of D1 based on Gauss quadrature formula with 4 nodes.
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;