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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 x % 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 M % Derivative norm
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10 D
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11
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12 D1
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13 Hi
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14 e_l
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15 e_r
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16 v0
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17 end
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18
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19
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20 methods
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21 function obj = Utux(m,xlim,order)
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22 default_arg('a',1);
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23 [x, h] = util.get_grid(xlim{:},m);
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24 ops = sbp.Ordinary(m,h,order);
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25
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26 obj.D1 = sparse(ops.derivatives.D1);
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27 obj.H = sparse(ops.norms.H);
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28 obj.Hi = sparse(ops.norms.HI);
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29 obj.M = sparse(ops.norms.M);
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30 obj.e_l = sparse(ops.boundary.e_1);
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31 obj.e_r = sparse(ops.boundary.e_m);
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32 obj.D=obj.D1;
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33
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34 obj.m = m;
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35 obj.h = h;
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36 obj.order = order;
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37 obj.x = x;
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38
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39 end
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40 % Closure functions return the opertors applied to the own doamin to close the boundary
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41 % 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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42 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
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43 % type is a string specifying the type of boundary condition if there are several.
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44 % data is a function returning the data that should be applied at the boundary.
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45 % neighbour_scheme is an instance of Scheme that should be interfaced to.
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46 % neighbour_boundary is a string specifying which boundary to interface to.
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47 function [closure, penalty] = boundary_condition(obj,boundary,type,data)
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48 default_arg('type','neumann');
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49 default_arg('data',0);
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50 tau = -1*obj.e_l;
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51 closure = obj.Hi*tau*obj.e_l';
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52 penalty = 0*obj.e_l;
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53
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54 end
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55
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56 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary)
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57 error('An interface function does not exist yet');
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58 end
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59
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60 function N = size(obj)
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61 N = obj.m;
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62 end
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63
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64 end
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65
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66 methods(Static)
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67 % Calculates the matrcis need for the inteface coupling between boundary bound_u of scheme schm_u
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68 % and bound_v of scheme schm_v.
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69 % [uu, uv, vv, vu] = inteface_couplong(A,'r',B,'l')
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70 function [uu, uv, vv, vu] = interface_coupling(schm_u,bound_u,schm_v,bound_v)
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71 [uu,uv] = schm_u.interface(bound_u,schm_v,bound_v);
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72 [vv,vu] = schm_v.interface(bound_v,schm_u,bound_u);
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73 end
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74 end
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75 end |
