diff --git a/PDE/f1d_FG_upper_1,5_ref.mat b/PDE/f1d_FG_upper_1,5_ref.mat new file mode 100644 index 00000000..6c7d8b8c Binary files /dev/null and b/PDE/f1d_FG_upper_1,5_ref.mat differ diff --git a/PDE/f1d_SG_upper_1,5s_ref2.mat b/PDE/f1d_SG_upper_1,5s_ref2.mat new file mode 100644 index 00000000..0ba88824 Binary files /dev/null and b/PDE/f1d_SG_upper_1,5s_ref2.mat differ diff --git a/PDE/f1d_SG_upper_1,5s_unadapted.mat b/PDE/f1d_SG_upper_1,5s_unadapted.mat new file mode 100644 index 00000000..0d0ffa13 Binary files /dev/null and b/PDE/f1d_SG_upper_1,5s_unadapted.mat differ diff --git a/PDE/fokkerplanck2_complete.m b/PDE/fokkerplanck2_complete.m index 47006a6a..2107cf95 100644 --- a/PDE/fokkerplanck2_complete.m +++ b/PDE/fokkerplanck2_complete.m @@ -42,7 +42,7 @@ %% % Select 6.1, 6.2, 6.3, etc where it goes as 6.test -test = '6p1b'; +test = 'full'; %% % Define a few relevant functions @@ -56,7 +56,7 @@ E = 0.0025; tau = 10^5; case '6p1b' - delta = 0.042; + delta = 3; Z = 1; E = 0.25; tau = 10^5; @@ -65,6 +65,11 @@ Z = 1; E = 0.0025; tau = 10^5; + case 'full' + delta = 0.3; + Z = 5; + E = 0.4; + tau = 10^5; end gamma = @(p)sqrt(1+(delta*p).^2); vx = @(p)1/vT*(p./gamma(p)); @@ -107,6 +112,8 @@ ret = ret + h(l) * P; end + case 'full' + ret = x.*0 + 1; end end @@ -129,12 +136,23 @@ ret = 2/(sqrt(pi)*a^3) * exp(-x.^2/a^2); case '6p1c' ret = 2/(3*sqrt(pi)) * exp(-x.^2); - + case 'full' + N = 1000; + h = 20/N; + Q = 0; + Fun = @(p)exp(-2/delta^2*sqrt(1+delta^2*p.^2)); + for i = 1:N + x0 = (i-1)*h; + x1 = i*h; + [xi,w] = lgwt(20,x0,x1); + Q = Q+sum(w.*Fun(xi).*xi.^2); + end + ret = exp(-2/delta^2*sqrt(1+delta^2*x.^2))/(2*Q); end end - function ret = soln_z(x,t) + function ret = soln_z(x,~) ret = x.*0+1; end function ret = soln_p(x,t) @@ -143,8 +161,8 @@ %% Setup the dimensions -dim_p.domainMin = 0.1; -dim_p.domainMax = +10; +dim_p.domainMin = 0; +dim_p.domainMax = +20; dim_p.init_cond_fn = @(x,p,t) f0_p(x); dim_z.domainMin = -1; @@ -236,7 +254,7 @@ termE1_z = TERM_1D({pterm1}); pterm1 = MASS(g2); -pterm2 = GRAD(num_dims,g3,1,'N','D');% Lin's Setting +pterm2 = GRAD(num_dims,g3,1,'N','N');% Lin's Setting termE1_p = TERM_1D({pterm1,pterm2}); termE1 = TERM_ND(num_dims,{termE1_p,termE1_z}); @@ -270,7 +288,7 @@ g3 = @(x,p,t,dat) 1-x.^2; pterm1 = MASS(g1);% This is not needed - by Lin -pterm2 = GRAD(num_dims,g2,1,'N','D');% Lin's Setting +pterm2 = GRAD(num_dims,g2,1,'N','N');% Lin's Setting termR1_p = TERM_1D({pterm1,pterm2}); @@ -300,7 +318,7 @@ %% % Add terms to the pde object -pde.terms = {termC1,termC2,termC3,termE1,termE2,termR1,termR2}; +pde.terms = {termC1, termC2, termC3, termE1, termE2, termR1, termR2}; %% Construct some parameters and add to pde object. % These might be used within the various functions below. diff --git a/PDE/fokkerplanck2_complete.m~ b/PDE/fokkerplanck2_complete.m~ new file mode 100644 index 00000000..58755a92 --- /dev/null +++ b/PDE/fokkerplanck2_complete.m~ @@ -0,0 +1,345 @@ +function pde = fokkerplanck2_complete +% Combining momentum and pitch angle dynamics +% +% Full PDE from the 2D runaway electron paper +% +% d/dt f(p,z) == -div(flux_C + flux_E + flux_R) +% +% where +% +% flux_C is flux due to electron-ion collisions +% flux_E is the flux due to E accleration +% flux_R is the flux due to radiation damping +% +% -div(flux_C) == termC1 + termC2 + termC3 +% +% termC1 == 1/p^2*d/dp*p^2*Ca*df/dp +% termC2 == 1/p^2*d/dp*p^2*Cf*f +% termC3 == termC3 == Cb(p)/p^4 * d/dz( (1-z^2) * df/dz ) +% +% -div(flux_E) == termE1 + termE2 +% +% termE1 == -E*z*f(z) * 1/p^2 (d/dp p^2 f(p)) +% termE2 == -E*p*f(p) * d/dz (1-z^2) f(z) +% +% -div(flux_R) == termR1 + termR2 +% +% termR1 == 1/p^2 d/dp p^2 gamma(p) p / tau f(p) * (1-z^2) * f(z) +% termR2 == -1/(tau*gam(p)) f(p) * d/dz z(1-z^2) f(z) +% +% Run with +% +% explicit +% asgard(fokkerplanck2_complete) +% +% implicit +% asgard(fokkerplanck2_complete,'implicit',true,'num_steps',20,'CFL',1.0,'deg',3,'lev',4) +% +% with adaptivity +% asgard(fokkerplanck2_complete,'implicit',true,'num_steps',20,'CFL',1.0,'deg',3,'lev',4, 'adapt', true) + +pde.CFL = 0.01; + +%% +% Select 6.1, 6.2, 6.3, etc where it goes as 6.test +test = '6p1b'; + +%% +% Define a few relevant functions + +nuEE = 1; +vT = 1; +switch test + case '6p1a' + delta = 0.042; + Z = 1; + E = 0.0025; + tau = 10^5; + case '6p1b' + delta = 3; + Z = 1; + E = 0.25; + tau = 10^5; + case '6p1c' + delta = 0.042; + Z = 1; + E = 0.0025; + tau = 10^5; +end +gamma = @(p)sqrt(1+(delta*p).^2); +vx = @(p)1/vT*(p./gamma(p)); + +Ca = @(p)nuEE*vT^2*(psi(vx(p))./vx(p)); + +Cb = @(p)1/2*nuEE*vT^2*1./vx(p).*(Z+phi(vx(p))-psi(vx(p))+delta^4*vx(p).^2/2); + +Cf = @(p)2*nuEE*vT*psi(vx(p)); + + function ret = phi(x) + ret = erf(x); + end + + function ret = psi(x,t) + dphi_dx = 2./sqrt(pi) * exp(-x.^2); + ret = 1./(2*x.^2) .* (phi(x) - x.*dphi_dx); + ix = find(abs(x)<1e-5); % catch singularity at boundary + ret(ix) = 0; + end + + + function ret = f0_z(x) + + ret = zeros(size(x)); + switch test + case '6p1a' + ret = x.*0+1; + case '6p1b' + ret = x.*0+1; + case '6p1c' + h = [3,0.5,1,0.7,3,0,3]; + + for l=1:numel(h) + + L = l-1; + P_m = legendre(L,x); % Use matlab rather than Lin's legendre. + P = P_m(1,:)'; + + ret = ret + h(l) * P; + + end + end + end + + function ret = f0_p(x) + + ret = zeros(size(x)); + switch test + + case '6p1a' + for i=1:numel(x) + if x(i) <= 5 + ret(i) = 3/(2*5^3); + else + ret(i) = 0; + end + end + + case '6p1b' + a = 2; + ret = 2/(sqrt(pi)*a^3) * exp(-x.^2/a^2); + case '6p1c' + ret = 2/(3*sqrt(pi)) * exp(-x.^2); + + end + end + + + function ret = soln_z(x,t) + ret = x.*0+1; + end + function ret = soln_p(x,t) + ret = 2/sqrt(pi) * exp(-x.^2); + end + +%% Setup the dimensions + +dim_p.domainMin = 0.1; +dim_p.domainMax = +7; +dim_p.init_cond_fn = @(x,p,t) f0_p(x); + +dim_z.domainMin = -1; +dim_z.domainMax = +1; +dim_z.init_cond_fn = @(x,p,t) f0_z(x); + +%% +% Add dimensions to the pde object +% Note that the order of the dimensions must be consistent with this across +% the remainder of this PDE. + +pde.dimensions = {dim_p,dim_z}; +num_dims = numel(pde.dimensions); + +%% Setup the terms of the PDE + +%% -div(flux_C) == termC1 + termC2 + termC3 + +%% +% termC1 == 1/p^2*d/dp*p^2*Ca*df/dp +% +% becomes +% +% termC1 == g1(p) q(p) [mass, g1(p) = 1/p^2, BC N/A] +% q(p) == d/dp g2(p) r(p) [grad, g2(p) = p^2*Ca, BCL=D,BCR=N] +% r(p) == d/dp g3(p) f(p) [grad, g3(p) = 1, BCL=N,BCR=D] + +g1 = @(x,p,t,dat) 1./x.^2; +g2 = @(x,p,t,dat) x.^2.*Ca(x); +g3 = @(x,p,t,dat) x.*0+1; + +pterm1 = MASS(g1); +pterm2 = GRAD(num_dims,g2,+1,'D','D'); +pterm3 = GRAD(num_dims,g3,-1,'N','N'); +term1_p = TERM_1D({pterm1,pterm2,pterm3}); +termC1 = TERM_ND(num_dims,{term1_p,[]}); + +%% +% termC2 == 1/p^2*d/dp*p^2*Cf*f +% +% becomes +% +% termC2 == g1(p) q(p) [mass, g1(p)=1/p^2, BC N/A] +% q(p) == d/dp g2(p) f(p) [grad, g2(p)=p^2*Cf, BCL=N,BCR=D] + +g1 = @(x,p,t,dat) 1./x.^2; +g2 = @(x,p,t,dat) x.^2.*Cf(x); + +pterm1 = MASS(g1); +pterm2 = GRAD(num_dims,g2,+1,'N','N'); +term2_p = TERM_1D({pterm1,pterm2}); +termC2 = TERM_ND(num_dims,{term2_p,[]}); + +%% +% termC3 == Cb(p)/p^4 * d/dz( (1-z^2) * df/dz ) +% +% becomes +% +% termC3 == q(p) r(z) +% q(p) == g1(p) [mass, g1(p) = Cb(p)/p^4, BC N/A] +% r(z) == d/dz g2(z) s(z) [grad, g2(z) = 1-z^2, BCL=D,BCR=D] +% s(z) == d/dz g3(z) f(z) [grad, g3(z) = 1, BCL=N,BCR=N] + +g1 = @(x,p,t,dat) Cb(x)./x.^4; +pterm1 = MASS(g1); +term3_p = TERM_1D({pterm1}); + +g2 = @(x,p,t,dat) (1-x.^2); +g3 = @(x,p,t,dat) x.*0+1; +pterm1 = GRAD(num_dims,g2,+1,'D','D'); +pterm2 = GRAD(num_dims,g3,-1,'N','N'); +term3_z = TERM_1D({pterm1,pterm2}); + +termC3 = TERM_ND(num_dims,{term3_p,term3_z}); + +%% -div(flux_E) == termE1 + termE2 + +% termE1 == -E*z*f(z) * 1/p^2 (d/dp p^2 f(p)) +% == r(z) * q(p) +% r(z) == g1(z) f(z) [mass, g1(z) = -E*z, BC N/A] +% q(p) == g2(p) u(p) [mass, g2(p) = 1/p^2, BC N/A] +% u(p) == d/dp g3(p) f(p) [grad, g3(p) = p^2, BCL=N,BCR=D] + +g1 = @(x,p,t,dat) -E.*x; +g2 = @(x,p,t,dat) 1./x.^2; +g3 = @(x,p,t,dat) x.^2; + +pterm1 = MASS(g1); +termE1_z = TERM_1D({pterm1}); + +pterm1 = MASS(g2); +pterm2 = GRAD(num_dims,g3,1,'N','N');% Lin's Setting +termE1_p = TERM_1D({pterm1,pterm2}); + +termE1 = TERM_ND(num_dims,{termE1_p,termE1_z}); + +% termE2 == -E*p*f(p) * d/dz (1-z^2) f(z) +% == q(p) * r(z) +% q(p) == g1(p) f(p) [mass, g1(p) = -E*p, BC N/A] +% r(z) == d/dz g2(z) f(z) [grad, g2(z) = 1-z^2, BCL=N,BCR=N] + +g1 = @(x,p,t,dat) -E.*x; +g2 = @(x,p,t,dat) 1-x.^2; + +pterm1 = MASS(g1); +termE2_p = TERM_1D({pterm1}); + +pterm1 = GRAD(num_dims,g2,0,'N','N');% Lin's Setting +termE2_z = TERM_1D({pterm1}); + +termE2 = TERM_ND(num_dims,{termE2_p,termE2_z}); + +%% -div(flux_R) == termR1 + termR2 + +% termR1 == 1/p^2 d/dp p^2 gamma(p) p / tau f(p) * (1-z^2) * f(z) +% == q(p) * r(z) +% q(p) == g1(p) u(p) [mass, g1(p) = 1/p^2, BC N/A] +% u(p) == d/dp g2(p) f(p) [grad, g2(p) = p^3 * gamma(p) / tau, BCL=N,BCR=D] +% r(z) == g3(z) f(z) [mass, g3(z) = 1-z^2, BC N/A] + +g1 = @(x,p,t,dat) 1./x.^2; +g2 = @(x,p,t,dat) x.^3 .* gamma(x) ./ tau; +g3 = @(x,p,t,dat) 1-x.^2; + +pterm1 = MASS(g1);% This is not needed - by Lin +pterm2 = GRAD(num_dims,g2,1,'N','N');% Lin's Setting + +termR1_p = TERM_1D({pterm1,pterm2}); + +pterm1 = MASS(g3); +termR1_z = TERM_1D({pterm1}); + +termR1 = TERM_ND(num_dims,{termR1_p,termR1_z}); + +% termR2 == -1/(tau*gam(p)) f(p) * d/dz z(1-z^2) f(z) +% == q(p) * r(z) +% q(p) == g1(p) f(p) [mass, g1(p) = -1/(tau*gamma(p)), BC N/A] +% r(z) == d/dz g2(z) f(z) [grad, g2(z) = z(1-z^2), BCL=N,BCR=N] + +g1 = @(x,p,t,dat) -1./(tau.*gamma(x)); +g2 = @(x,p,t,dat) x.*(1-x.^2); + +pterm1 = MASS(g1); +termR2_p = TERM_1D({pterm1}); + +pterm1 = GRAD(num_dims,g2,0,'N','N');% Lin's Setting +termR2_z = TERM_1D({pterm1}); + + +termR2 = TERM_ND(num_dims,{termR2_p, termR2_z}); + + +%% +% Add terms to the pde object + +pde.terms = {termC1, termC2, termC3, termE1, termE2, termR1, termR2}; + +%% Construct some parameters and add to pde object. +% These might be used within the various functions below. + +params.parameter1 = 0; +params.parameter2 = 1; + +pde.params = params; + +%% Add an arbitrary number of sources to the RHS of the PDE +% Each source term must have nDims + 1 + +%% +% Add sources to the pde data structure +pde.sources = {}; + +%% Define the analytic solution (optional). +% This requires nDims+time function handles. + +pde.analytic_solutions_1D = { ... + @(x,p,t) soln_p(x,t), ... + @(x,p,t) soln_z(x,t), ... + @(t,p) 1 + }; + +%% +% Function to set time step + function dt=set_dt(pde,CFL) + + dims = pde.dimensions; + xRange = dims{1}.domainMax-dims{1}.domainMin; + lev = dims{1}.lev; + dx = xRange/2^lev; + dt = CFL * dx; + + end + +pde.set_dt = @set_dt; + +end + + diff --git a/PDE/output_adapt/f1d_x-deg_3.mat b/PDE/output_adapt/f1d_x-deg_3.mat new file mode 100644 index 00000000..06835c8b Binary files /dev/null and b/PDE/output_adapt/f1d_x-deg_3.mat differ diff --git a/PDE/output_adapt/f1d_y_adapt-deg_3.mat b/PDE/output_adapt/f1d_y_adapt-deg_3.mat new file mode 100644 index 00000000..2219820b Binary files /dev/null and b/PDE/output_adapt/f1d_y_adapt-deg_3.mat differ diff --git a/PDE/output_adapt/f2d_adapt-deg_3.mat b/PDE/output_adapt/f2d_adapt-deg_3.mat new file mode 100644 index 00000000..5b39ec3a Binary files /dev/null and b/PDE/output_adapt/f2d_adapt-deg_3.mat differ diff --git a/SG_FG_2DComplete_AllFigs.fig b/SG_FG_2DComplete_AllFigs.fig new file mode 100644 index 00000000..d03b87d9 Binary files /dev/null and b/SG_FG_2DComplete_AllFigs.fig differ diff --git a/SG_FG_2DComplete_FGFigs.fig b/SG_FG_2DComplete_FGFigs.fig new file mode 100644 index 00000000..c84fd1fd Binary files /dev/null and b/SG_FG_2DComplete_FGFigs.fig differ diff --git a/asgard.m b/asgard.m index 69283e88..b845a2c1 100644 --- a/asgard.m +++ b/asgard.m @@ -136,7 +136,7 @@ [~,fval_check] ... = adapt(pde,opts,fval,hash_table,nodes,fval_realspace,0,1); if (length(fval_check)>pre_refinement_num_DOF) -% error('Initial grid was insifficient for requested accuracy'); + error('Initial grid was insifficient for requested accuracy'); end clear fval_check; end @@ -295,6 +295,12 @@ fval_realspace = wavelet_to_realspace(pde,opts,Meval,fval,hash_table); + for i = 1:length(fval_realspace) + if fval_realspace(i) < 1e-15 + fval_realspace(i) = 1e-15; + end + end + %% % Try with function convertToRealSpace @@ -376,9 +382,12 @@ % Save output saveOutput = 0; + deg = pde.deg; + LevX = pde.lev_vec(1); + LevV = pde.lev_vec(2); if saveOutput stat = mkdir('output'); - fName = ['output/f2d-' sprintf('%04.4d',L) '.mat']; + fName = ['output/f2d-' sprintf('deg_%d_lev_%d',deg, LevX) '.mat']; f2d = reshape(fval_realspace,deg*2^LevX,deg*2^LevV)'; save(fName,'f2d','fval'); end diff --git a/f1d_FG_deg4_Vert.mat b/f1d_FG_deg4_Vert.mat new file mode 100644 index 00000000..71a954c1 Binary files /dev/null and b/f1d_FG_deg4_Vert.mat differ diff --git a/f1d_FG_deg5_Vert.mat b/f1d_FG_deg5_Vert.mat new file mode 100644 index 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b/output_dt_0,05/f2d-deg_5_lev_3.mat differ diff --git a/output_dt_0,05/f2d-deg_6_lev_3.mat b/output_dt_0,05/f2d-deg_6_lev_3.mat new file mode 100644 index 00000000..c7941d0d Binary files /dev/null and b/output_dt_0,05/f2d-deg_6_lev_3.mat differ diff --git a/output_dt_0,05/f2d-deg_7_lev_3.mat b/output_dt_0,05/f2d-deg_7_lev_3.mat new file mode 100644 index 00000000..25dd2516 Binary files /dev/null and b/output_dt_0,05/f2d-deg_7_lev_3.mat differ diff --git a/plot_fval.m b/plot_fval.m index e503c46b..10cc2b97 100644 --- a/plot_fval.m +++ b/plot_fval.m @@ -63,19 +63,56 @@ function plot_fval(pde,nodes,fval_realspace,fval_realspace_analytic,Meval,coordi nx = numel(x); ny = numel(y); + stat = mkdir('output_adapt'); + fName = ['output_adapt/f2d_adapt-' sprintf('deg_%d',deg1) '.mat']; + save(fName, 'x', 'y', 'f2d'); %% % Plot a 1D line through the solution - sy = max(1,floor(ny/2)); - if ny > 2 - sy = sy+2; % just to get off the exact middle - end + sy = max(1,ceil(ny-1)); + % if ny > 2 + % sy = sy+2; % just to get off the exact middle + % end f1d = f2d(sy,:); x = nodes{1}; y = nodes{2}; ax1 = subplot(2,2,1); - plot(x,f1d,'-o'); + %plot(x,f1d,'-o'); + %load('f1d_FG_upper_1,5_deg4', 'x_FG_deg4', 'f1d_FG_deg4'); + %load('f1d_FG_upper_1,5_deg7', 'x_FG_deg7', 'f1d_FG_deg7'); + fNamex = ['output_adapt/f1d_x-' sprintf('deg_%d',deg1) '.mat']; + save(fNamex, 'x', 'f1d'); + %load('f1d_FG_upper_1,5_deg5', 'x_FG_deg5', 'f1d_FG_deg5'); + %load('f1d_FG_upper_1,5_ref', 'x_FG_ref', 'f1d_FG_ref'); + %load('f1d_SG_upper_1,5s_unadapted', 'x_SG_unadapt', 'f1d_SG_unadapt'); + %load('f1d_SG_upper_1,5s_ref2', 'x_SG_ref2', 'f1d_SG_ref2'); + %load('f1d_FG_upper_1,5_coarse', 'x_FG_coarse', 'f1d_FG_coarse'); + % load('f1d_SG_upper_1,8s_ref1', 'x_SG_ref1', 'f1d_SG_ref1'); + %load('f1d_SG_upper_1,8s_ref', 'x_SG_ref', 'f1d_SG_ref'); + %load('f1d_FG_upper_1,8s', 'x_FG', 'f1d_FG'); + %load('f1d_SG_upper_1,8s', 'x_SG', 'f1d_SG'); + + % load('f1d_SG', 'x_SG', 'f1d_SG'); + % load('f1d_SG_mid', 'x_SG_mid','f1d_SG_mid'); + % load('f1d_FG', 'x_FG', 'f1d_FG'); + % load('f1d_FG_mid_neu_minusE2', 'x_FG_mid_neu', 'f1d_FG_mid_neu'); + % semilogy(x_SG, f1d_SG, '--m', 'LineWidth', 2); + ylim([10^-10, 10^0]); + semilogy(x, f1d, '-m', 'LineWidth', 2); + % semilogy(x_FG_ref, f1d_FG_ref, '-k', 'LineWidth', 2); + % semilogy(x_FG_deg4, f1d_FG_deg4, '-r', 'LineWidth', 2); + % hold on; + % semilogy(x_FG_coarse, f1d_FG_coarse, '-g', 'LineWidth', 2); + % semilogy(x_FG_deg5, f1d_FG_deg5, '-m', 'LineWidth', 2); + % semilogy(x_FG_deg6, f1d_FG_deg6, '-k', 'LineWidth', 2); + % semilogy(x_FG_deg7, f1d_FG_deg7, '-ob'); + % semilogy(x_FG_deg7, f1d_FG_deg7, '-og'); + % semilogy(x_SG_ref, f1d_SG_ref, 'b--', 'LineWidth', 2); + % semilogy(x_SG_ref1, f1d_SG_ref1, 'r--', 'LineWidth', 2); + % semilogy(x_SG_ref2, f1d_SG_ref2, 'k--', 'LineWidth', 2); + % semilogy(x_SG_unadapt, f1d_SG_unadapt, 'c--', 'LineWidth',2); + % hold off; title('1D slice (vertical)'); %% @@ -96,8 +133,16 @@ function plot_fval(pde,nodes,fval_realspace,fval_realspace_analytic,Meval,coordi f1d = f2d(:,sx); x = nodes{1}; y = nodes{2}; + fNamey = ['output_adapt/f1d_y_adapt-' sprintf('deg_%d',deg1) '.mat']; + save(fNamey, 'y', 'f1d'); + %load('f1d_FG_deg5_Vert', 'y_FG_deg5_vert', 'f1d_FG_deg5_vert'); + %load('f1d_FG_deg4_Vert', 'y_FG_deg4_vert', 'f1d_FG_deg4_vert'); ax1 = subplot(2,2,2); - plot(y,f1d,'-o'); + % plot(y_FG_deg4_vert,f1d_FG_deg4_vert,'-r', 'LineWidth', 2); + % hold on; + semilogy(y,f1d,'-m', 'LineWidth', 2); + % plot(y_FG_deg6_vert,f1d_FG_deg6_vert, '-k', 'LineWidth', 2); + % hold off; title('1D slice (horizontal)'); if pde.checkAnalytic @@ -115,6 +160,7 @@ function plot_fval(pde,nodes,fval_realspace,fval_realspace_analytic,Meval,coordi f2d_with_noise(1,1) = f2d_with_noise(1,1)*1.0001; contourf(x,y,f2d_with_noise,'LineColor','none'); title('numeric 2D solution'); + yline(y(sy), 'LineWidth', 2); if nargin >= 6 hold on diff --git a/runtime_defaults.m b/runtime_defaults.m index 0e187ce8..c8b92871 100644 --- a/runtime_defaults.m +++ b/runtime_defaults.m @@ -22,7 +22,7 @@ default_time_independent_A = false; default_many_solution_capable = false; default_max_lev = 8; -default_adapt_threshold = 1e-3; +default_adapt_threshold = 1e-6; default_refinement_method = 1; default_adapt_initial_condition = false; diff --git a/scan.sh b/scan.sh new file mode 100755 index 00000000..795e3d9c --- /dev/null +++ b/scan.sh @@ -0,0 +1,9 @@ +#!/bin/bash +MATLAB=/usr/local/bin/matlab +for lev in {5..5} +do +for deg in {3..7} +do +$MATLAB -noFigureWindows -batch "addpath(genpath('./'));asgard(fokkerplanck2_complete,'lev',$lev,'deg',$deg,'implicit',true, 'dt', 0.1, 'num_steps', 8, 'grid_type', 'SG', 'adapt', true, 'adapt_initial_condition', true, 'adapt_threshold', 1e-6);" & +done +done diff --git a/time_advance.m b/time_advance.m index c5864f0f..afbb3367 100644 --- a/time_advance.m +++ b/time_advance.m @@ -151,10 +151,10 @@ if ~opts.quiet; disp([' rcond(AA) : ', num2str(rcond(AA))]); end - AA_inv = inv(AA); +% AA_inv = inv(AA); -% f1 = AA\b; % Solve at each timestep - f1 = AA_inv * b; + f1 = AA\b; % Solve at each timestep +% f1 = gmres(AA, b, 1000); else applyLHS = ~isempty(pde.termsLHS); @@ -167,8 +167,8 @@ AA = 2*I - dt*A; b = 2*f0 + dt*A*f0 + dt*(s0+s1) + dt*(bc0+bc1); end - - f1 = AA_inv * b; + f1 = AA_inv*b; + % f1 = gmres(AA, b, 1000); end end diff --git a/two_scale/two_scale_rel_2.mat b/two_scale/two_scale_rel_2.mat index be266753..d96e6497 100644 Binary files a/two_scale/two_scale_rel_2.mat and b/two_scale/two_scale_rel_2.mat differ diff --git a/two_scale/two_scale_rel_3.mat b/two_scale/two_scale_rel_3.mat new file mode 100644 index 00000000..e4c0d632 Binary files /dev/null and b/two_scale/two_scale_rel_3.mat differ