% Start with all matrix returns. When that works see how we should generalize to non-matrix stuff/nonlinear
classdef Scheme < handle
    properties (Abstract)
        m % Number of points in each direction, possibly a vector
        order % Order accuracy for the approximation

        % vectors u,v,w depending on dim that gives were gridpoints are in each dimension
        % vectors x,y,z containing the x,y,z values corresponding to each grid point
        % matrices X,Y,Z with point coordinates as multi dimensional vectors

        D % non-stabalized scheme operator
        H % Discrete norm

        % Should also containg:
        % the grid points used
        % the grid spacing
    end

    methods (Abstract)
        % Closure functions return the opertors applied to the own doamin to close the boundary
        % Penalty functions return the opertors to force the solution. In the case of an interface it returns the operator applied to the other doamin.
        %       boundary            is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
        %       type                is a string specifying the type of boundary condition if there are several.
        %       data                is a function returning the data that should be applied at the boundary.
        %       neighbour_scheme    is an instance of Scheme that should be interfaced to.
        %       neighbour_boundary  is a string specifying which boundary to interface to.
        m = boundary_condition(obj,boundary,type,data)
        m = interface(obj,boundary,neighbour_scheme,neighbour_boundary)
        N = size(obj) % Returns the number of degrees of freedom.

    end

    methods(Static)
        % Calculates the matrcis need for the inteface coupling between boundary bound_u of scheme schm_u
        % and bound_v of scheme schm_v.
        %   [uu, uv, vv, vu] = inteface_couplong(A,'r',B,'l')
        function [uu, uv, vv, vu] = interface_coupling(schm_u,bound_u,schm_v,bound_v)
            [uu,uv] = schm_u.interface(bound_u,schm_v,bound_v);
            [vv,vu] = schm_v.interface(bound_v,schm_u,bound_u);
        end
    end
end