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Add getBoundaryOperator to all 1d schemes. Did not add getBoundaryQuadrature because it doesnt make sense in 1d (?)
author Martin Almquist <malmquist@stanford.edu>
date Sat, 12 Jan 2019 13:35:19 -0800
parents 6d2167719557
children 8d73fcdb07a5
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1 classdef Utux < scheme.Scheme
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2 properties
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3 m % Number of points in each direction, possibly a vector
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4 h % Grid spacing
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5 grid % Grid
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6 order % Order accuracy for the approximation
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7
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8 H % Discrete norm
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9 D
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10
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11 D1
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12 Hi
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13 e_l
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14 e_r
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15 v0
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16 end
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17
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18
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19 methods
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20 function obj = Utux(g, order, opSet)
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21 default_arg('opSet',@sbp.D2Standard);
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22
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23 m = g.size();
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24 xl = g.getBoundary('l');
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25 xr = g.getBoundary('r');
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26 xlim = {xl, xr};
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27
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28 ops = opSet(m, xlim, order);
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29 obj.D1 = ops.D1;
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31 obj.grid = g;
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32
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33 obj.H = ops.H;
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34 obj.Hi = ops.HI;
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36 obj.e_l = ops.e_l;
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37 obj.e_r = ops.e_r;
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38 obj.D = -obj.D1;
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39
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40 obj.m = m;
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41 obj.h = ops.h;
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42 obj.order = order;
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43
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44 end
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45 % Closure functions return the opertors applied to the own doamin to close the boundary
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46 % Penalty functions return the opertors to force the solution. In the case of an interface it returns the operator applied to the other doamin.
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47 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
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48 % type is a string specifying the type of boundary condition if there are several.
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49 % data is a function returning the data that should be applied at the boundary.
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50 % neighbour_scheme is an instance of Scheme that should be interfaced to.
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51 % neighbour_boundary is a string specifying which boundary to interface to.
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52 function [closure, penalty] = boundary_condition(obj,boundary,type)
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53 default_arg('type','dirichlet');
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54 tau =-1*obj.e_l;
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55 closure = obj.Hi*tau*obj.e_l';
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56 penalty = -obj.Hi*tau;
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57
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58 end
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59
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60 function [closure, penalty] = interface(obj, boundary, neighbour_scheme, neighbour_boundary, type)
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61 switch boundary
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62 % Upwind coupling
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63 case {'l','left'}
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64 tau = -1*obj.e_l;
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65 closure = obj.Hi*tau*obj.e_l';
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66 penalty = -obj.Hi*tau*neighbour_scheme.e_r';
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67 case {'r','right'}
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68 tau = 0*obj.e_r;
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69 closure = obj.Hi*tau*obj.e_r';
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70 penalty = -obj.Hi*tau*neighbour_scheme.e_l';
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71 end
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73 end
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74
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75 % Returns the boundary operator op for the boundary specified by the string boundary.
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76 % op -- string or a cell array of strings
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77 % boundary -- string
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78 function varargout = getBoundaryOperator(obj, op, boundary)
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79
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80 if ~iscell(op)
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81 op = {op};
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82 end
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83
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84 for i = 1:numel(op)
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85 switch op{i}
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86 case 'e'
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87 switch boundary
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88 case 'l'
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89 e = obj.e_l;
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90 case 'r'
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91 e = obj.e_r;
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92 otherwise
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93 error('No such boundary: boundary = %s',boundary);
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94 end
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95 varargout{i} = e;
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96 end
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97 end
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98 end
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99
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100 function N = size(obj)
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101 N = obj.m;
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102 end
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103
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104 end
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106 methods(Static)
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107 % Calculates the matrices needed for the inteface coupling between boundary bound_u of scheme schm_u
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108 % and bound_v of scheme schm_v.
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109 % [uu, uv, vv, vu] = inteface_coupling(A,'r',B,'l')
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110 function [uu, uv, vv, vu] = interface_coupling(schm_u,bound_u,schm_v,bound_v)
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111 [uu,uv] = schm_u.interface(bound_u,schm_v,bound_v);
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112 [vv,vu] = schm_v.interface(bound_v,schm_u,bound_u);
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113 end
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114 end
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115 end