Slightly more efficient mesh by making spacing dependent on steepness of tanh profile.

ternary_frap.m

@@ -8,17 +8,29 @@ b = 0.025;
 c = 1/100000;
 u0 = 0.05;
 e = 0.4;
+
+%% Make useful mesh (by inverting the tanh profile and using this as spacing)
+x = linspace(49.0, 51, 3000);
+g = gamma0(x, a, 1*b, e);
+g_unique = unique(g);
+x = linspace(g_unique(1), g_unique(end-1), 300);
+g_inv = spacing(x, a, 2*b, e);
+g_inv = g_inv(2:end-1);
+x = [linspace(49.0, g_inv(2), 30), g_inv(3:end-2), ...
+    linspace(g_inv(end-1), 51, 30), linspace(51.1, 200, 300)];
 %% Solve pde
-x = [linspace(49.0, 51, 3000), linspace(51.01, 200, 300)];
+tic
+% x = [linspace(49.0, 49.8, 30), linspace(49.81, 50.2, 1000), ...
+%      linspace(50.21, 51, 30) linspace(51.01, 200, 600)];
 t = linspace(0.001, 1, 1000);
 fh_ic = @(x) flory_ic(x, a, u0);
 fh_bc = @(xl, ul, xr, ur, t) flory_bc(xl, ul, xr, ur, t, u0);
 fh_pde = @(x, t, u, dudx) flory_hugg_pde(x, t, u, dudx, a, b, e, c, u0);
 sol = pdepe(0, fh_pde, fh_ic, fh_bc, x, t);
+toc
 %% Plotting
 figure(1); hold on;
 for i = 1:length(t)
-%     i = 800;
     cla; xlim([49, 53]); ylim([0, 0.7]); 
     ax = gca;
     ax.FontSize = 16;
@@ -30,13 +42,13 @@ end
 
 %% Plot and check derivatives of pt
 figure; hold on;
-x = linspace(40, 60, 10000);
+x = linspace(40, 60, 100000);
 plot(x, phi_tot(x, a, b, e, u0));
 plot(x, gradient_analytical(x, a, b, e));
 plot(x(1:end-1)+mean(diff(x))/2, ...
      diff(phi_tot(x, a, b, e, u0)/mean(diff(x))));
 plot(x, gamma0(x, a, b, e));
-max(gamma0(x, a, b, e))/min(gamma0(x, a, b, e))
+figure; plot(gamma0(x, a, b, e), spacing(gamma0(x, a, b, e), a, b, e));
 %% Function definitions for pde solver
 function [c, f ,s] = flory_hugg_pde(x, t, u, dudx, a, b, e, c_p, u0)  
 % Solve with full ternary model. Analytical derivatives.
@@ -76,6 +88,10 @@ function g0 = gamma0(x, a, b, e)
     g0 = 10*e*(tanh((x+a)/b)+1)/2+0.001;
 end
 
+function sp = spacing(x, a, b, e)
+    sp = b*atanh(2/(10*e)*(x-0.001)-1)-a;
+end
+
 function p = phi_tot(x, a, b, e, u0)
     p = e*(tanh(-(x+a)/b)+1)/2+u0;
 end