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annotate +sbp/+implementations/d1_gauss_4.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 0bc37a25ed88
children
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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)
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2
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3 % L: Domain length
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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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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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54 D1(4,2) = 2.1087823484951789;
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55 D1(4,3) = -4.8601544156851962;
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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;