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annotate +sbp/D1Gauss.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 e1d11b6a68d8
children
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4d9d8064e58b Implementation of D1 based on Gauss quadrature formula with 4 nodes.
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1 classdef D1Gauss < sbp.OpSet
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2 % Diagonal-norm SBP operators based on the Gauss quadrature formula
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3 % with m nodes, which is of degree 2m-1. Hence, The operator D1 is
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4 % accurate of order m.
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5 properties
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6 D1 % SBP operator approximating first derivative
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7 H % Norm matrix
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8 HI % H^-1
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9 Q % Skew-symmetric matrix
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10 e_l % Left boundary operator
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11 e_r % Right boundary operator
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12 m % Number of grid points.
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13 h % Step size
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14 x % grid
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15 borrowing % Struct with borrowing limits for different norm matrices
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16 end
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18 methods
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19 function obj = D1Gauss(m,lim)
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21 x_l = lim{1};
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22 x_r = lim{2};
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23 L = x_r-x_l;
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24
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25 switch m
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26 case 4
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27 [obj.D1,obj.H,obj.x,obj.h,obj.e_l,obj.e_r] = ...
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28 sbp.implementations.d1_gauss_4(L);
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29 otherwise
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30 error('Invalid number of points: %d.', m);
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31 end
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34 obj.x = obj.x + x_l;
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35 obj.HI = inv(obj.H);
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36 obj.Q = obj.H*obj.D1 - obj.e_r*obj.e_r' + obj.e_l*obj.e_l';
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37
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38 obj.borrowing = [];
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39 end
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e1d11b6a68d8 Add string methods to OpSets that are missing them
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41 function str = string(obj)
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42 str = [class(obj) '_' num2str(obj.order)];
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43 end
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44 end
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45 end