classdef RungekuttaRvMultiGrid < time.Timestepper
    properties
        F         % RHS of the ODE
        F_coarse  % RHS of the untabilized coarse grid ODE
        k       % Time step
        t       % Time point
        v       % Solution vector
        n       % Time level
        rkScheme  % The particular RK scheme used for time integration
        RV              % Residual Viscosity operator
        DvDt            % Function for computing the time deriative used for the RV evaluation
        v_coarse
        viscosity
    end
    methods

        function obj = RungekuttaRvMultiGrid(F, F_coarse, k, t0, v0, RV, DvDt, order)
            obj.F = F;
            obj.F_coarse = F_coarse;
            obj.k = k;
            obj.t = t0;
            obj.v = v0;
            obj.n = 0;
            
            if (order == 4) % Use specialized RK4 scheme
                obj.rkScheme = @time.rk.rungekutta_4;
            else
                % Extract the coefficients for the specified order
                % used for the RK updates from the Butcher tableua.
                [s,a,b,c] = time.rk.butcherTableau(order);
                coeffs = struct('s',s,'a',a,'b',b,'c',c);
                obj.rkScheme = @(v,t,dt,F) time.rk.rungekutta(v, t , dt, F, coeffs);
            end
        
            obj.RV = RV;
            obj.DvDt = DvDt;
            obj.v_coarse = 0*v0;
            obj.viscosity = 0*v0;
        end

        function [v, t] = getV(obj)
            v = obj.v;
            t = obj.t;
        end

        function state = getState(obj)
            dvdt = obj.DvDt(obj.v_coarse);
            [viscosity, Df, firstOrderViscosity, residualViscosity] = obj.RV.evaluate(obj.v, dvdt);
            state = struct('v', obj.v, 'dvdt', dvdt, 'Df', Df, 'viscosity', obj.viscosity, 'residualViscosity', residualViscosity, 'firstOrderViscosity', firstOrderViscosity, 't', obj.t);
        end

        % Advances the solution vector one time step using the Runge-Kutta method given by
        % obj.coeffs, using a fixed residual viscosity for the Runge-Kutta substeps
        function obj = step(obj)
            % Fix the viscosity of the stabilized RHS            
            m = length(obj.viscosity);
            F_stable = @(v,t) obj.F(v,t,spdiags(obj.viscosity,0,m,m));
            % Advance solution on unstabilized coarse mesh based on current solution
            obj.v_coarse = obj.rkScheme(obj.v, obj.t, obj.k, obj.F_coarse);
            % Advance solution on on stabilized mesh based on current viscosity
            obj.v = obj.rkScheme(obj.v, obj.t, obj.k, F_stable);
            % Compute viscosity for the next time time level using the advanced solution
            obj.viscosity = obj.RV.evaluateViscosity(obj.v, obj.DvDt(obj.v_coarse));
            obj.t = obj.t + obj.k;
            obj.n = obj.n + 1;
        end
    end
end