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comparison +rv/+time/RungekuttaExteriorRv.m @ 1154:3108963cc42c feature/rv

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Improve efficiency of diffOps in Burgers2d, the artificial diffusion operator in rv.constructDiffOps and the RungekuttaExteriorRv time-steppers
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Wed, 06 Mar 2019 09:45:52 +0100
parents 010bb2677230
children
comparison
equal deleted inserted replaced
1153:635386c073b9 1154:3108963cc42c
3 F % RHS of the ODE 3 F % RHS of the ODE
4 k % Time step 4 k % Time step
5 t % Time point 5 t % Time point
6 v % Solution vector 6 v % Solution vector
7 n % Time level 7 n % Time level
8 coeffs % The coefficents used for the RK time integration 8 rkScheme % The particular RK scheme used for time integration
9 RV % Residual Viscosity operator 9 RV % Residual Viscosity operator
10 DvDt % Function for computing the time deriative used for the RV evaluation 10 DvDt % Function for computing the time deriative used for the RV evaluation
11 end 11 end
12 methods 12 methods
13 13
15 obj.F = F; 15 obj.F = F;
16 obj.k = k; 16 obj.k = k;
17 obj.t = t0; 17 obj.t = t0;
18 obj.v = v0; 18 obj.v = v0;
19 obj.n = 0; 19 obj.n = 0;
20 % Extract the coefficients for the specified order 20
21 % used for the RK updates from the Butcher tableua. 21 if (order == 4) % Use specialized RK4 scheme
22 [s,a,b,c] = time.rk.butcherTableau(order); 22 obj.rkScheme = @time.rk.rungekutta_4;
23 obj.coeffs = struct('s',s,'a',a,'b',b,'c',c); 23 else
24 % Extract the coefficients for the specified order
25 % used for the RK updates from the Butcher tableua.
26 [s,a,b,c] = time.rk.butcherTableau(order);
27 coeffs = struct('s',s,'a',a,'b',b,'c',c);
28 obj.rkScheme = @(v,t,dt,F) time.rk.rungekutta(v, t , dt, F, coeffs);
29 end
24 30
25 obj.RV = RV; 31 obj.RV = RV;
26 obj.DvDt = DvDt; 32 obj.DvDt = DvDt;
27 end 33 end
28 34
39 45
40 % Advances the solution vector one time step using the Runge-Kutta method given by 46 % Advances the solution vector one time step using the Runge-Kutta method given by
41 % obj.coeffs, using a fixed residual viscosity for the Runge-Kutta substeps 47 % obj.coeffs, using a fixed residual viscosity for the Runge-Kutta substeps
42 function obj = step(obj) 48 function obj = step(obj)
43 % Fix the viscosity of the RHS function F 49 % Fix the viscosity of the RHS function F
44 F_visc = @(v,t) obj.F(v,t,obj.RV.evaluateViscosity(obj.v, obj.DvDt(obj.v))); 50 viscosity = obj.RV.evaluateViscosity(obj.v, obj.DvDt(obj.v));
45 obj.v = time.rk.rungekutta(obj.v, obj.t, obj.k, F_visc, obj.coeffs); 51 m = length(viscosity);
52 F_visc = @(v,t) obj.F(v,t,spdiags(viscosity,0,m,m));
53 obj.v = obj.rkScheme(obj.v, obj.t, obj.k, F_visc);
46 obj.t = obj.t + obj.k; 54 obj.t = obj.t + obj.k;
47 obj.n = obj.n + 1; 55 obj.n = obj.n + 1;
48 end 56 end
49 end 57 end
50 end 58 end