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annotate +sbp/+implementations/d1_gauss_4.m @ 577:e45c9b56d50d feature/grids

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Add an Empty grid class The need turned up for the flexural code when we may or may not have a grid for the open water and want to plot that solution. In case there is no open water we need an empty grid to plot the empty gridfunction against to avoid errors.
author Jonatan Werpers <jonatan@werpers.com>
date Thu, 07 Sep 2017 09:16:12 +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>
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1 function [D1,H,x,h,e_l,e_r] = d1_gauss_4(L)
405
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Martin Almquist <martin.almquist@it.uu.se>
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2
4d9d8064e58b Implementation of D1 based on Gauss quadrature formula with 4 nodes.
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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>
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4 default_arg('L',1);
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5
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42c4f0b545d6 Remove m as input to implementation function. Fix error message for invalid m to D1Gauss
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6 N = 4;
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7
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8 % Quadrature nodes on interval [-1, 1]
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9 x = [ -0.8611363115940526; -0.3399810435848563; 0.3399810435848563; 0.8611363115940526];
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10
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11 % Shift nodes to [0,L]
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12 x = (x+1)/2*L;
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13
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14 % Boundary extrapolation operators
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15 e_l = [1.5267881254572668; -0.8136324494869273; 0.4007615203116504; -0.1139171962819899];
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16 e_r = flipud(e_l);
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17 e_l = sparse(e_l);
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18 e_r = sparse(e_r);
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19
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20 %%%% Compute approximate h %%%%%%%%%%
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21 h = L/(N-1);
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22 %%%%%%%%%%%%%%%%%%%%%%%%%
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23
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24 %%%% Norm matrix on [-1,1] %%%%%%%%
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25 P = sparse(N,N);
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26 P(1,1) = 0.3478548451374539;
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27 P(2,2) = 0.6521451548625461;
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28 P(3,3) = 0.6521451548625461;
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29 P(4,4) = 0.3478548451374539;
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30 %%%%%%%%%%%%%%%%%%%%%%%%%
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31
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32 %%%% Norm matrix on [0,L] %%%%%%%%
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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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37 D1 = sparse(N,N);
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38 D1(1,1) = -3.3320002363522817;
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39 D1(1,2) = 4.8601544156851962;
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40 D1(1,3) = -2.1087823484951789;
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41 D1(1,4) = 0.5806281691622644;
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42
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43 D1(2,1) = -0.7575576147992339;
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44 D1(2,2) = -0.3844143922232086;
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45 D1(2,3) = 1.4706702312807167;
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46 D1(2,4) = -0.3286982242582743;
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47
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48 D1(3,1) = 0.3286982242582743;
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49 D1(3,2) = -1.4706702312807167;
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50 D1(3,3) = 0.3844143922232086;
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51 D1(3,4) = 0.7575576147992339;
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52
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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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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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57 %%%%%%%%%%%%%%%%%%%%%%%%%
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58
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59 % D1 on [0,L]
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60 D1 = D1*2/L;