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1 % Start with all matrix returns. When that works see how we should generalize to non-matrix stuff/nonlinear
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2 classdef Scheme < handle
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3 properties (Abstract)
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4 m % Number of points in each direction, possibly a vector
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5 order % Order accuracy for the approximation
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6
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7 % vectors u,v,w depending on dim that gives were gridpoints are in each dimension
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8 % vectors x,y,z containing the x,y,z values corresponding to each grid point
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9 % matrices X,Y,Z with point coordinates as multi dimensional vectors
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10
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11 D % non-stabalized scheme operator
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12 H % Discrete norm
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13
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14 % Should also containg:
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15 % the grid points used
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16 % the grid spacing
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17 end
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18
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19 methods (Abstract)
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20 % Closure functions return the opertors applied to the own doamin to close the boundary
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21 % 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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22 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
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23 % type is a string specifying the type of boundary condition if there are several.
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24 % data is a function returning the data that should be applied at the boundary.
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25 % neighbour_scheme is an instance of Scheme that should be interfaced to.
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26 % neighbour_boundary is a string specifying which boundary to interface to.
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27 m = boundary_condition(obj,boundary,type,data)
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28 m = interface(obj,boundary,neighbour_scheme,neighbour_boundary)
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29 N = size(obj) % Returns the number of degrees of freedom.
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30
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31 end
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32
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33 methods(Static)
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34 % Calculates the matrcis need for the inteface coupling between boundary bound_u of scheme schm_u
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35 % and bound_v of scheme schm_v.
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36 % [uu, uv, vv, vu] = inteface_couplong(A,'r',B,'l')
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37 function [uu, uv, vv, vu] = interface_coupling(schm_u,bound_u,schm_v,bound_v)
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38 [uu,uv] = schm_u.interface(bound_u,schm_v,bound_v);
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39 [vv,vu] = schm_v.interface(bound_v,schm_u,bound_u);
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40 end
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41 end
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42 end |
