From 96dcd75380387e6d90bda2fee6a56896930ae4e4 Mon Sep 17 00:00:00 2001 From: Louis Wonnell Date: Wed, 4 Dec 2019 16:08:03 -0500 Subject: [PATCH 01/12] fokkerplanck2_6p1_withLHS has inhomogeneous Dirichlet BC at p_min. Run with asgard(fokkerplanck2_6p1_withLHS, 'implicit', true,'CFL', 'num_steps', 50, 1.0, 'lev', 4, 'deg', 4). BC implemented at termC1. --- PDE/fokkerplanck2_6p1_withLHS.m | 31 +++++++++++++++++++++++-------- two_scale/two_scale_rel_2.mat | Bin 415 -> 0 bytes 2 files changed, 23 insertions(+), 8 deletions(-) delete mode 100644 two_scale/two_scale_rel_2.mat diff --git a/PDE/fokkerplanck2_6p1_withLHS.m b/PDE/fokkerplanck2_6p1_withLHS.m index a024f96b..4cea7a46 100644 --- a/PDE/fokkerplanck2_6p1_withLHS.m +++ b/PDE/fokkerplanck2_6p1_withLHS.m @@ -15,7 +15,7 @@ % asgard(fokkerplanck2_6p1_withLHS) % % implicit -% asgard(fokkerplanck2_6p1_withLHS,'implicit',true,'num_steps',20,'CFL',1.0,'deg',3,'lev',4) +% asgard(fokkerplanck2_6p1_withLHS, 'implicit', true,'CFL', 'num_steps', 50, 1.0, 'lev', 4, 'deg', 4) pde.CFL = 0.01; @@ -32,7 +32,7 @@ tau = 10^5; gamma = @(p)sqrt(1+(delta*p).^2); vx = @(p)1/vT*(p./gamma(p)); -p_min = 0.005; +p_min = 0.001; Ca = @(p)nuEE*vT^2*(psi(vx(p))./vx(p)); @@ -123,7 +123,7 @@ case 0.5 Q = 0.361837; % for p_min = 0.5 case 1.0 - Q = 0.23975; % for p_min = 1.0 + Q = 0.23975; % for p_min = 1.0 end ret = Q * 4/sqrt(pi) * exp(-x.^2); end @@ -146,6 +146,19 @@ pde.dimensions = {dim_p,dim_z}; num_dims = numel(pde.dimensions); +%Inhomogeneous BC's set to analytical solution +BCL_fList = { ... + @(x,p,t) soln_p(x,t), ... %replace x with p_min + @(x,p,t) soln_z(x,t), ... + @(t,p) 1 + }; + +BCR_fList = { ... + @(x,p,t) soln_p(x,t), ... %replace x with 10 + @(x,p,t) soln_z(x,t), ... + @(t,p) 1 + }; + %% Setup the terms of the PDE %% @@ -164,14 +177,16 @@ % % becomes % -% termC1 == 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] +% termC1 == d/dp g2(p) r(p) [grad, g2(p) = p^2*Ca, BCL=N,BCR=N] +% r(p) == d/dp g3(p) f(p) [grad, g3(p) = 1, BCL=D,BCR=D] + +% Inhomogenous Dirichlet BC's for f(p_min) g2 = @(x,p,t,dat) x.^2.*Ca(x); g3 = @(x,p,t,dat) x.*0+1; -pterm2 = GRAD(num_dims,g2,+1,'D','N'); -pterm3 = GRAD(num_dims,g3,-1,'N','D'); +pterm2 = GRAD(num_dims,g2,+1,'N','N'); +pterm3 = GRAD(num_dims,g3,-1,'D','D', BCL_fList, BCR_fList); term1_p = TERM_1D({pterm2,pterm3}); termC1 = TERM_ND(num_dims,{term1_p,[]}); @@ -184,7 +199,7 @@ g2 = @(x,p,t,dat) x.^2.*Cf(x); -pterm2 = GRAD(num_dims,g2,+1,'N','D'); +pterm2 = GRAD(num_dims,g2,-1,'N','D'); term2_p = TERM_1D({pterm2}); termC2 = TERM_ND(num_dims,{term2_p,[]}); diff --git a/two_scale/two_scale_rel_2.mat b/two_scale/two_scale_rel_2.mat deleted file mode 100644 index a214909f48065f8053d8febcf6aae2996ab68b0a..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 415 zcmeZu4DoSvQZUssQ1EpO(M`+DN!3vZ$Vn_o%P-2cQgHY2i*PhE(NSS|dsxrE`6^=R`YX-m9{<&21$;VnXXP096M5c) zjIqUSOo=(f7zu#~TfydBf79RaGX3{dh+*5<86MQ}d;u9^2{)tz%`H>n=ggTgS!({A z^PDN#1_}qX=68sP-mbgtTp|A^@ezYz9_KNT0bXzeRv;O$nZZz4z}V?2myyxq$)6=9 uEE;pz74AJ0{ Date: Mon, 16 Dec 2019 12:44:28 -0500 Subject: [PATCH 02/12] Advection-Diffusion Equation added with Inhomogeneous Dirichlet BC's in advec_diffusion1.m file. Run with asgard(advec_diffusion1,'implicit',true). fokkerplanck2_6p1_withLHS modified to include inhomogeneous Dirichlet BC's, but oscillates at p_max. --- PDE/diffusion1.m | 4 ++-- PDE/fokkerplanck2_6p1.m | 2 +- PDE/fokkerplanck2_6p1_withLHS.m | 34 +++++++++++++++++++++------------ apply_A.m | 2 ++ asgard.m | 13 +++++++++---- time_advance.m | 2 +- 6 files changed, 37 insertions(+), 20 deletions(-) diff --git a/PDE/diffusion1.m b/PDE/diffusion1.m index 4fea9904..8e6608e9 100644 --- a/PDE/diffusion1.m +++ b/PDE/diffusion1.m @@ -46,7 +46,7 @@ % The function is defined for the plane % x = a and x = b BCL_fList = { ... - @(x,p,t) BCFunc(x), ... % replace x by a + @(x,p,t) x.*0, ... % replace x by a @(t,p) BCFunc_t(t) }; @@ -87,7 +87,7 @@ g2 = @(x,p,t,dat) x.*0+1; pterm1 = GRAD(num_dims,g1,+1,'N','N'); -pterm2 = GRAD(num_dims,g2,-1,'D','D',BCL_fList,BCR_fList); +pterm2 = GRAD(num_dims,g2,-1,'D','D', BCL_fList, BCR_fList); term1_x = TERM_1D({pterm1,pterm2}); term1 = TERM_ND(num_dims,{term1_x}); diff --git a/PDE/fokkerplanck2_6p1.m b/PDE/fokkerplanck2_6p1.m index 0492f6e2..a3a3611e 100644 --- a/PDE/fokkerplanck2_6p1.m +++ b/PDE/fokkerplanck2_6p1.m @@ -110,7 +110,7 @@ %% Setup the dimensions -dim_p.domainMin = 0; +dim_p.domainMin = 0.01; dim_p.domainMax = +10; dim_p.init_cond_fn = @(x,p,t) f0_p(x); diff --git a/PDE/fokkerplanck2_6p1_withLHS.m b/PDE/fokkerplanck2_6p1_withLHS.m index 4cea7a46..6be414cc 100644 --- a/PDE/fokkerplanck2_6p1_withLHS.m +++ b/PDE/fokkerplanck2_6p1_withLHS.m @@ -15,7 +15,7 @@ % asgard(fokkerplanck2_6p1_withLHS) % % implicit -% asgard(fokkerplanck2_6p1_withLHS, 'implicit', true,'CFL', 'num_steps', 50, 1.0, 'lev', 4, 'deg', 4) +% asgard(fokkerplanck2_6p1_withLHS, 'implicit', true,'CFL', 1.0, 'num_steps', 50, 'lev', 4, 'deg', 4) pde.CFL = 0.01; @@ -32,7 +32,7 @@ tau = 10^5; gamma = @(p)sqrt(1+(delta*p).^2); vx = @(p)1/vT*(p./gamma(p)); -p_min = 0.001; +p_min = 0.1; Ca = @(p)nuEE*vT^2*(psi(vx(p))./vx(p)); @@ -43,7 +43,6 @@ 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); @@ -131,7 +130,7 @@ %% Setup the dimensions dim_p.domainMin = p_min; -dim_p.domainMax = +10; +dim_p.domainMax = 10; dim_p.init_cond_fn = @(x,p,t) f0_p(x); dim_z.domainMin = -1; @@ -159,9 +158,20 @@ @(t,p) 1 }; +%BCL_rList = { ... +% @(x,p,t) -2*x.*soln_p(x,t), ... %replace x with p_min +% @(x,p,t) soln_z(x,t), ... +% @(t,p) 1 +% }; +%BCR_rList = { ... +% @(x,p,t) -2*x.*soln_p(x,t), ... %replace x with 10 +% @(x,p,t) soln_z(x,t), ... +% @(t,p) 1 +% }; + %% Setup the terms of the PDE -%% +%%r % termLHS == p^2 d/dt f(p,z,t) g1 = @(x,p,t,dat) x.^2; @@ -177,16 +187,16 @@ % % becomes % -% termC1 == d/dp g2(p) r(p) [grad, g2(p) = p^2*Ca, BCL=N,BCR=N] -% r(p) == d/dp g3(p) f(p) [grad, g3(p) = 1, BCL=D,BCR=D] +% termC1 == 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] % Inhomogenous Dirichlet BC's for f(p_min) g2 = @(x,p,t,dat) x.^2.*Ca(x); g3 = @(x,p,t,dat) x.*0+1; -pterm2 = GRAD(num_dims,g2,+1,'N','N'); -pterm3 = GRAD(num_dims,g3,-1,'D','D', BCL_fList, BCR_fList); +pterm2 = GRAD(num_dims,g2,+1,'D','N'); +pterm3 = GRAD(num_dims,g3,-1,'N','D', BCL_fList, BCR_fList); term1_p = TERM_1D({pterm2,pterm3}); termC1 = TERM_ND(num_dims,{term1_p,[]}); @@ -199,7 +209,7 @@ g2 = @(x,p,t,dat) x.^2.*Cf(x); -pterm2 = GRAD(num_dims,g2,-1,'N','D'); +pterm2 = GRAD(num_dims,g2,-1,'N','D', BCL_fList, BCR_fList); term2_p = TERM_1D({pterm2}); termC2 = TERM_ND(num_dims,{term2_p,[]}); @@ -219,8 +229,8 @@ 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'); +pterm1 = GRAD(num_dims,g2,+1,'D','N'); +pterm2 = GRAD(num_dims,g3,-1,'N','D', BCL_fList, BCR_fList); term3_z = TERM_1D({pterm1,pterm2}); termC3 = TERM_ND(num_dims,{term3_p,term3_z}); diff --git a/apply_A.m b/apply_A.m index a3113277..d71a9631 100644 --- a/apply_A.m +++ b/apply_A.m @@ -31,9 +31,11 @@ implicit = opts.implicit; totalDOF = nWork * elementDOF; +A = 0; if opts.implicit A = zeros(totalDOF,totalDOF); % Only filled if implicit end +ALHS = 0; if num_terms_LHS > 0 ALHS = zeros(totalDOF,totalDOF); % Only filled if non-identity LHS mass matrix end diff --git a/asgard.m b/asgard.m index 66136a6e..b628e372 100644 --- a/asgard.m +++ b/asgard.m @@ -166,7 +166,7 @@ err = 1e9; if ~opts.quiet; disp('Advancing time ...'); end for L = 1:num_steps - + fval_prev = fval; tic; timeStr = sprintf('Step %i of %i at %f seconds',L,num_steps,t); @@ -323,7 +323,6 @@ % Check the wavelet space solution with the analytic solution fval_analytic = exact_solution_vector(pde,opts,hash_table,t+dt); - assert(numel(fval)==numel(fval_analytic)); err_wavelet = sqrt(mean((fval(:) - fval_analytic(:)).^2)); @@ -331,6 +330,10 @@ disp([' num_dof : ', num2str(numel(fval))]); disp([' wavelet space absolute err : ', num2str(err_wavelet)]); disp([' wavelet space relative err : ', num2str(err_wavelet/max(abs(fval_analytic(:)))*100), ' %']); + if norm(fval_prev(:) - fval(:)) < 1e-6 + disp(['Converged']); + + end end %% @@ -371,9 +374,11 @@ %% % Save output - + deg = pde.deg; +% LevX = pde.lev_vec(1); +% LevV = pde.lev_vec(2); saveOutput = 0; - if saveOutput + if saveOutput && t > num_steps-2 stat = mkdir('output'); fName = ['output/f2d-' sprintf('%04.4d',L) '.mat']; f2d = reshape(fval_realspace,deg*2^LevX,deg*2^LevV)'; diff --git a/time_advance.m b/time_advance.m index c5864f0f..5411a2fc 100644 --- a/time_advance.m +++ b/time_advance.m @@ -48,7 +48,7 @@ b1 = 1/6; b2 = 2/3; b3 = 1/6; if applyLHS - [k1,A1,ALHS] = apply_A(pde,opts,A_data,f,deg,Vmax,Emax); + [k1,~,ALHS] = apply_A(pde,opts,A_data,f,deg,Vmax,Emax); rhs1 = source1 + bc1; % invMatLHS = inv(ALHS); % NOTE : assume time independent for now for speed. % k1 = invMatLHS * (k1 + rhs1); From 7652a9ac400a1c5911022c98c4cd83795aa776f6 Mon Sep 17 00:00:00 2001 From: Louis Wonnell Date: Thu, 19 Dec 2019 15:13:46 -0500 Subject: [PATCH 03/12] Advection-Diffusion equation file added in advec_diffusion1.m which works for inhomogeneous BC's. Run with asgard(advec_diffusion1) --- PDE/advec_diffusion1.m | 154 +++++++++++++++++++++++++++++++++++++++++ 1 file changed, 154 insertions(+) create mode 100644 PDE/advec_diffusion1.m diff --git a/PDE/advec_diffusion1.m b/PDE/advec_diffusion1.m new file mode 100644 index 00000000..45c884ff --- /dev/null +++ b/PDE/advec_diffusion1.m @@ -0,0 +1,154 @@ +function pde = advec_diffusion1 +% Example PDE using the 1D Advection-Diffusion Equation. This example PDE is +% time dependent (although not all the terms are time dependent). This +% implies the need for an initial condition. +% PDE: +% +% df/dt = -df/dx + d^2 f/dx^2 + (cos(x) - sin(x))exp(-t) +% +% Domain is [0, pi/4] +% Inhomogeneous Dirichlet boundary condition +% Code is expected to be added to the 1d Advection Equation +% +% Diffusion terms are dealt with via LDG, i.e., splitting into two first +% order equations: +% +% d^2 f / dx^2 becomes +% +% dq/dx with free (homogeneous Neumann BC) +% +% and +% +% q=df/dx with Dirichlet BCs specified by analytic solution +% +% Run with +% +% explicit +% asgard(advec_diffusion1); +% +% implicit +% asgard(advec_diffusion1,'implicit',true); + +pde.CFL = 0.01; + +%% Setup the dimensions +% +% Here we setup a 1D problem (x,y) + +soln_x = @(x) cos(x) + sin(x); +soln_t = @(t) exp(-t); + +BCFunc = @(x) soln_x(x); +BCFunc_t = @(t) soln_t(t); + +% Domain is (a,b) + +% The function is defined for the plane +% x = a and x = b +BCL_fList = { ... + @(x,p,t) BCFunc(x), ... % replace x by a + @(t,p) BCFunc_t(t) + }; + +BCR_fList = { ... + @(x,p,t) BCFunc(x), ... % replace x by b + @(t,p) BCFunc_t(t) + }; +%Incorrect BC to check whether each term requires BC +%Each term DOES require correct BC +%BCIncorrect_fList= { ... +% @(x,p,t) x.*0 + 2, ... % replace x by b +% @(t,p) BCFunc_t(t) +% }; + +dim_x.name = 'x'; +dim_x.domainMin = 0; +dim_x.domainMax = pi/4; +dim_x.init_cond_fn = @(x,p,t) soln_x(x)*soln_t(t); + + +%% +% 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_x}; +num_dims = numel(pde.dimensions); + +%% Setup the terms of the PDE +% +% Here we have 2 terms, with each term having nDims (x) operators. + +%% +% Setup the -d_dx term + +g1 = @(x,p,t,dat) x.*0-1; +pterm1 = GRAD(num_dims,g1,-1,'D','D', BCL_fList, BCR_fList); + +term1_x = TERM_1D({pterm1}); +term1 = TERM_ND(num_dims,{term1_x}); + +%% +% Setup the d^2_dx^2 term + +% term1 +% +% eq1 : df/dt == d/dx g1(x) q(x,y) [grad,g1(x)=1, BCL=N, BCR=N] +% eq2 : q(x,y) == d/dx g2(x) f(x,y) [grad,g2(x)=1, BCL=D, BCR=D] +% +% coeff_mat = mat1 * mat2 + +g1 = @(x,p,t,dat) x.*0+1; +g2 = @(x,p,t,dat) x.*0+1; + +pterm1 = GRAD(num_dims,g1,+1,'N','N'); +pterm2 = GRAD(num_dims,g2,-1,'D','D', BCL_fList, BCR_fList); + +term2_x = TERM_1D({pterm1,pterm2}); +term2 = TERM_ND(num_dims,{term2_x}); + +%% +% Add terms to the pde object + + pde.terms = {term1, term2}; + +%% 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; + +%% +% Sources + +s1x = @(x,p,t) cos(x) - sin(x); +s1t = @(t,p) exp(-t); +source1 = {s1x, s1t}; + +pde.sources = {source1}; + +%% Define the analytic solution (optional). +% This requires nDims+time function handles. + +pde.analytic_solutions_1D = { ... + @(x,p,t) soln_x(x), ... + @(t,p) soln_t(t) + }; + + function dt=set_dt(pde,CFL) + + dims = pde.dimensions; + + % for Diffusion equation: dt = C * dx^2 + + lev = dims{1}.lev; + dx = 1/2^lev; + dt = CFL*dx^2; + + end + +pde.set_dt = @set_dt; + +end From dde583520582fa59f5a775fa0508ab619beba78a Mon Sep 17 00:00:00 2001 From: Louis Wonnell Date: Fri, 3 Jan 2020 13:11:01 -0500 Subject: [PATCH 04/12] WIP Tested fokkerplanck2_6p1_withLHs.m to attempt to fix Dirichlet BC at RHS for z-direction. --- PDE/fokkerplanck2_6p1_withLHS.m | 6 +++--- two_scale/two_scale_rel_2.mat | Bin 0 -> 415 bytes two_scale/two_scale_rel_3.mat | Bin 0 -> 517 bytes two_scale/two_scale_rel_4.mat | Bin 0 -> 692 bytes 4 files changed, 3 insertions(+), 3 deletions(-) create mode 100644 two_scale/two_scale_rel_2.mat create mode 100644 two_scale/two_scale_rel_3.mat create mode 100644 two_scale/two_scale_rel_4.mat diff --git a/PDE/fokkerplanck2_6p1_withLHS.m b/PDE/fokkerplanck2_6p1_withLHS.m index 6be414cc..7c67b6a6 100644 --- a/PDE/fokkerplanck2_6p1_withLHS.m +++ b/PDE/fokkerplanck2_6p1_withLHS.m @@ -227,10 +227,10 @@ pterm1 = MASS(g1); term3_p = TERM_1D({pterm1}); -g2 = @(x,p,t,dat) (1-x.^2); -g3 = @(x,p,t,dat) x.*0+1; +g2 = @(x,p,t,dat) 1-x.^2; +g3 = @(x,p,t,dat) x.*0 + 1; pterm1 = GRAD(num_dims,g2,+1,'D','N'); -pterm2 = GRAD(num_dims,g3,-1,'N','D', BCL_fList, BCR_fList); +pterm2 = GRAD(num_dims,g3,-1,'N','D'); term3_z = TERM_1D({pterm1,pterm2}); termC3 = TERM_ND(num_dims,{term3_p,term3_z}); diff --git a/two_scale/two_scale_rel_2.mat b/two_scale/two_scale_rel_2.mat new file mode 100644 index 0000000000000000000000000000000000000000..02bf8787348277c298d58777dacf8702f75c30f7 GIT binary patch literal 415 zcmeZu4DoSvQZUssQ1EpO(M`+DN!3vZ$Vn_o%P-2cQgHY2i*PhE(NSQZO{PGBvX@G*vJ%Ffvde5-`93qo*%FkZljd6>}aZCnRt%B$+8Z zYq+Fvfa|HTqoMMIF9rz-4_G#dHvHIAT6=2`>-jfdMJ!!^rPi$ literal 0 HcmV?d00001 diff --git a/two_scale/two_scale_rel_3.mat b/two_scale/two_scale_rel_3.mat new file mode 100644 index 0000000000000000000000000000000000000000..f8c87555b49395f9cef696e043e2e752afa0c618 GIT binary patch literal 517 zcmeZu4DoSvQZUssQ1EpO(M`+DN!3vZ$Vn_o%P-2cQgHY2i*PhE(NSQZO{PGBvR>GE*=zFfvde5-`93qo*%FknIn|6>}aZCnT(3NHSA+ z)^JJT0M}DvXG3LX;pTQmW@hyXZyAp~U;Fy~4s$2OBu!qOUJM8(olV-xHt1{78Otc+eA( zm$N@s{AbC*TgJ!0cST$rWUvq1;0!ePPKlp0XU1fy`E$;5rc@gw zG}*tOWZb*H$nwCC)ip|SA-TVE`&YeUp0oea=`S~*_S?T>XE4ha{sA(x5^kmi(L^Bn03D06g6t0}Sr1%oYP$NxRv=S=pkDt++qqxZB!`%Psf5+2w_++mFU z!x-|HZ+?e(=(!sBSa9i*=lgSce= O)e1N&%OI2IoCN?*fxx=} literal 0 HcmV?d00001 diff --git a/two_scale/two_scale_rel_4.mat b/two_scale/two_scale_rel_4.mat new file mode 100644 index 0000000000000000000000000000000000000000..8804ab8286895d6aa226740842116f9553cb0f0f GIT binary patch literal 692 zcmeZu4DoSvQZUssQ1EpO(M`+DN!3vZ$Vn_o%P-2cQgHY2i*PhE(NSQZTfzGBC0-G*mD$Ffvde5-`93qo*%FkX;JI6>}aZCnVfpIFjRV zhHV({rdXE`+I&LtShOMs9+1* zepZfQv9|h6kmVKlEH8&x-pFWPF}3)=&&_`BZ!aDlHT#B*0a3)Lrc8v zht~WK@zC3Kw-5jLxU~A!xA)KO86MU)bg%zmR9p7*asThc8it>Tq%%Pl9fMo6At5Cp zf%%dQkAM_Q#KIbZG{z*i6)}!(X*ET5%*^V{E*CO){}%Zfw4RwgCQimn>~m2=Ryqd< zE8|DzM*@}XF`qKkeXqywm#aDO)j0gW@lS#F_T&1IT>r1xFa(RUOf_#lA@49fU-xeC z_WJ#Q8UJ6Z?&5Qol_~q-vS-DuWwj4}*9%N2?Pxn;&EoJh-0_KQ!lxj6{k3bZC)s|u swe`!N>9gPPO`YafRqnSzhJ$f;|5Zn6E%~Qx)9f46>KPb{`3q+N0BbQIO8@`> literal 0 HcmV?d00001 From 48abbe9c94c6cd752a303c7c44c84000662c1dd7 Mon Sep 17 00:00:00 2001 From: Louis Wonnell Date: Mon, 6 Jan 2020 18:14:38 -0500 Subject: [PATCH 05/12] Removed inhomogeneous Dirichlet BC's to attempt to solve problem of oscillations at p_max. --- compute_boundary_condition.m | 23 +++++++++++++++++++++-- 1 file changed, 21 insertions(+), 2 deletions(-) diff --git a/compute_boundary_condition.m b/compute_boundary_condition.m index 3fe13b2a..e5ab59a2 100644 --- a/compute_boundary_condition.m +++ b/compute_boundary_condition.m @@ -10,6 +10,7 @@ L = xMax-xMin; Tol_Cel_Num = 2^(Lev); h = L / Tol_Cel_Num; +small_dx = h*1e-7; %Parameter to fix problem with Inhomogeneous BC DoF = Deg * Tol_Cel_Num; bc = sparse(DoF,1); @@ -22,14 +23,32 @@ WorkCel = 0; c = [1:Deg]; IntVal = p_L'*Fun(xMin,p,t) ; - bc(c) = - g_func(xMin,p,t).*IntVal; + if isfinite(g_func(xMin,p,t)) %make sure g_func is finite + + bc(c) = -g_func(xMin,p,t).*IntVal; + else + + xLclose = xMin + small_dx; %Move away from xMin by small_dx + bc(c) = -g_func(xLclose,p,t).*IntVal; + + end else WorkCel = Tol_Cel_Num - 1; c = Deg*WorkCel+[1:Deg]; IntVal = p_R'*Fun(xMax,p,t); - bc(c) = g_func(xMax,p,t).*IntVal; + + if isfinite(g_func(xMax,p,t)) %make sure g_func is finite + + bc(c) = g_func(xMax,p,t).*IntVal; + + else + + xRclose = xMax - small_dx; %Move away from xMax by small_dx + bc(c) = g_func(xRclose,p,t).*Intval; + + end end From 1ca85e1954b3674dfa7f0cadac22445bd74f780c Mon Sep 17 00:00:00 2001 From: Louis Wonnell Date: Mon, 6 Jan 2020 18:15:01 -0500 Subject: [PATCH 06/12] Removed inhomogeneous Dirichlet BC's to attempt to solve problem of oscillations at p_max. --- PDE/fokkerplanck2_6p1_withLHS.m | 4 ++-- compute_boundary_condition.m | 2 +- 2 files changed, 3 insertions(+), 3 deletions(-) diff --git a/PDE/fokkerplanck2_6p1_withLHS.m b/PDE/fokkerplanck2_6p1_withLHS.m index 7c67b6a6..079fdd78 100644 --- a/PDE/fokkerplanck2_6p1_withLHS.m +++ b/PDE/fokkerplanck2_6p1_withLHS.m @@ -196,7 +196,7 @@ g3 = @(x,p,t,dat) x.*0+1; pterm2 = GRAD(num_dims,g2,+1,'D','N'); -pterm3 = GRAD(num_dims,g3,-1,'N','D', BCL_fList, BCR_fList); +pterm3 = GRAD(num_dims,g3,-1,'N','D'); term1_p = TERM_1D({pterm2,pterm3}); termC1 = TERM_ND(num_dims,{term1_p,[]}); @@ -209,7 +209,7 @@ g2 = @(x,p,t,dat) x.^2.*Cf(x); -pterm2 = GRAD(num_dims,g2,-1,'N','D', BCL_fList, BCR_fList); +pterm2 = GRAD(num_dims,g2,-1,'N','D'); term2_p = TERM_1D({pterm2}); termC2 = TERM_ND(num_dims,{term2_p,[]}); diff --git a/compute_boundary_condition.m b/compute_boundary_condition.m index e5ab59a2..4bec475c 100644 --- a/compute_boundary_condition.m +++ b/compute_boundary_condition.m @@ -10,7 +10,7 @@ L = xMax-xMin; Tol_Cel_Num = 2^(Lev); h = L / Tol_Cel_Num; -small_dx = h*1e-7; %Parameter to fix problem with Inhomogeneous BC +small_dx = h*1e-6; %Parameter to fix problem with Inhomogeneous BC DoF = Deg * Tol_Cel_Num; bc = sparse(DoF,1); From 179560b5b88c445cbb18ac81148609dd834c7e73 Mon Sep 17 00:00:00 2001 From: Louis Wonnell Date: Thu, 9 Jan 2020 12:18:36 -0500 Subject: [PATCH 07/12] Added inhomogeneous Dirichlet BC's back into fokkerplanck2_6p1_withLHS. Looking to resolve Dirichlet BC at small p_max. Looking at the influence of wavelet_to_realspace code in artificially moving fval_realspace to higher orders of magnitude. --- PDE/fokkerplanck2_6p1_withLHS.m | 14 +++++++------- compute_boundary_condition.m | 2 +- plot_fval.m | 3 ++- two_scale/two_scale_rel_2.mat | Bin 415 -> 0 bytes two_scale/two_scale_rel_3.mat | Bin 517 -> 0 bytes two_scale/two_scale_rel_4.mat | Bin 692 -> 0 bytes 6 files changed, 10 insertions(+), 9 deletions(-) delete mode 100644 two_scale/two_scale_rel_2.mat delete mode 100644 two_scale/two_scale_rel_3.mat delete mode 100644 two_scale/two_scale_rel_4.mat diff --git a/PDE/fokkerplanck2_6p1_withLHS.m b/PDE/fokkerplanck2_6p1_withLHS.m index 079fdd78..29288b58 100644 --- a/PDE/fokkerplanck2_6p1_withLHS.m +++ b/PDE/fokkerplanck2_6p1_withLHS.m @@ -32,7 +32,7 @@ tau = 10^5; gamma = @(p)sqrt(1+(delta*p).^2); vx = @(p)1/vT*(p./gamma(p)); -p_min = 0.1; +p_min = 0.01; Ca = @(p)nuEE*vT^2*(psi(vx(p))./vx(p)); @@ -130,7 +130,7 @@ %% Setup the dimensions dim_p.domainMin = p_min; -dim_p.domainMax = 10; +dim_p.domainMax = 2.4; dim_p.init_cond_fn = @(x,p,t) f0_p(x); dim_z.domainMin = -1; @@ -190,13 +190,13 @@ % termC1 == 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] -% Inhomogenous Dirichlet BC's for f(p_min) +% Inhomogenous Dirichlet BC's for f(p_max) g2 = @(x,p,t,dat) x.^2.*Ca(x); g3 = @(x,p,t,dat) x.*0+1; pterm2 = GRAD(num_dims,g2,+1,'D','N'); -pterm3 = GRAD(num_dims,g3,-1,'N','D'); +pterm3 = GRAD(num_dims,g3,-1,'N','D', BCL_fList, BCR_fList); term1_p = TERM_1D({pterm2,pterm3}); termC1 = TERM_ND(num_dims,{term1_p,[]}); @@ -209,7 +209,7 @@ g2 = @(x,p,t,dat) x.^2.*Cf(x); -pterm2 = GRAD(num_dims,g2,-1,'N','D'); +pterm2 = GRAD(num_dims,g2,-1,'N','D', BCL_fList, BCR_fList); term2_p = TERM_1D({pterm2}); termC2 = TERM_ND(num_dims,{term2_p,[]}); @@ -229,8 +229,8 @@ g2 = @(x,p,t,dat) 1-x.^2; g3 = @(x,p,t,dat) x.*0 + 1; -pterm1 = GRAD(num_dims,g2,+1,'D','N'); -pterm2 = GRAD(num_dims,g3,-1,'N','D'); +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}); diff --git a/compute_boundary_condition.m b/compute_boundary_condition.m index 4bec475c..e5ab59a2 100644 --- a/compute_boundary_condition.m +++ b/compute_boundary_condition.m @@ -10,7 +10,7 @@ L = xMax-xMin; Tol_Cel_Num = 2^(Lev); h = L / Tol_Cel_Num; -small_dx = h*1e-6; %Parameter to fix problem with Inhomogeneous BC +small_dx = h*1e-7; %Parameter to fix problem with Inhomogeneous BC DoF = Deg * Tol_Cel_Num; bc = sparse(DoF,1); diff --git a/plot_fval.m b/plot_fval.m index a4ec5483..4bea6761 100644 --- a/plot_fval.m +++ b/plot_fval.m @@ -75,7 +75,8 @@ function plot_fval(pde,nodes,fval_realspace,fval_realspace_analytic,Meval,coordi x = nodes{1}; y = nodes{2}; ax1 = subplot(2,2,1); - plot(x,f1d,'-o'); + %plot(x,f1d,'-o'); + semilogy(x,f1d, '-o'); title('1D slice (vertical)'); %% diff --git a/two_scale/two_scale_rel_2.mat 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a/two_scale/two_scale_rel_4.mat b/two_scale/two_scale_rel_4.mat deleted file mode 100644 index 8804ab8286895d6aa226740842116f9553cb0f0f..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 692 zcmeZu4DoSvQZUssQ1EpO(M`+DN!3vZ$Vn_o%P-2cQgHY2i*PhE(NSQZTfzGBC0-G*mD$Ffvde5-`93qo*%FkX;JI6>}aZCnVfpIFjRV zhHV({rdXE`+I&LtShOMs9+1* zepZfQv9|h6kmVKlEH8&x-pFWPF}3)=&&_`BZ!aDlHT#B*0a3)Lrc8v zht~WK@zC3Kw-5jLxU~A!xA)KO86MU)bg%zmR9p7*asThc8it>Tq%%Pl9fMo6At5Cp zf%%dQkAM_Q#KIbZG{z*i6)}!(X*ET5%*^V{E*CO){}%Zfw4RwgCQimn>~m2=Ryqd< zE8|DzM*@}XF`qKkeXqywm#aDO)j0gW@lS#F_T&1IT>r1xFa(RUOf_#lA@49fU-xeC z_WJ#Q8UJ6Z?&5Qol_~q-vS-DuWwj4}*9%N2?Pxn;&EoJh-0_KQ!lxj6{k3bZC)s|u swe`!N>9gPPO`YafRqnSzhJ$f;|5Zn6E%~Qx)9f46>KPb{`3q+N0BbQIO8@`> From 64b7bfdb76198d701973ba38320e331b1641ac7c Mon Sep 17 00:00:00 2001 From: Louis Wonnell Date: Thu, 30 Jan 2020 14:37:39 -0500 Subject: [PATCH 08/12] Created test function for taking a moment with respect to some distribution function. --- 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dimension.domainMin; -xMax = dimension.domainMax; -FMWT = dimension.FMWT; - -%% -% Jacobi of variable - -n = 2^(lev); -h = (xMax-xMin)/n; -dof_1D = deg*n; -nodes = zeros(dof_1D,1); - - -%% -% Quadrature points (quad_x) and weights (quad_w) -[quad_x,quad_w]=lgwt(deg,-1,1); - -%% -% Uncomment to add end points to plot -% -% quad_x = [-1 quad_x' +1]'; - -dof = numel(quad_x); - -p_val = lin_legendre(quad_x,deg)*sqrt(1/h); % TODO : this call and normalization happens in several places. We should consolidate. - -Meval = sparse(dof*n,dof_1D); - -for i=0:n-1 - - %% - % Mapping from [-1,1] to physical domain - xi = ((quad_x+1)/2+i)*h+xMin; - - %% - % Coefficients for DG bases - Iu = [dof*i+1:dof*(i+1)]; - Iv = [deg*i+1:deg*(i+1)]; - - Meval(Iu,Iv) = p_val; - nodes(Iu) = xi; - -end - -%% -% Transform back to real space from wavelet space - -Meval = Meval*FMWT'; - - - - - - +function [Meval,nodes] = matrix_plot_D(pde,dimension, quad_x_in) + +%% +% Generate the evaluation matrix and plotting points +% TODO : probably should be renamed to something more descriptive + +%% +% Setup a few shortcuts + +lev = dimension.lev; +deg = pde.deg; +xMin = dimension.domainMin; +xMax = dimension.domainMax; +FMWT = dimension.FMWT; + +%% +% Jacobi of variable + +n = 2^(lev); +h = (xMax-xMin)/n; +dof_1D = deg*n; +nodes = zeros(dof_1D,1); +Meval = sparse(dof_1D,dof_1D); + +%% +% Quadrature points (quad_x) and weights (quad_w) +if (nargin >= 3) + quad_x = quad_x_in; +else + [quad_x,quad_w]=lgwt(deg,-1,1); +end + +p_val = lin_legendre(quad_x,deg)*sqrt(1/h); % TODO : this call and normalization happens in several places. We should consolidate. + +for i=0:n-1 + + %% + % Mapping from [-1,1] to physical domain + xi = ((quad_x+1)/2+i)*h+xMin; + + %% + % Coefficients for DG bases + Iu = [deg*i+1:deg*(i+1)]; + + Meval(Iu,Iu) = p_val; + nodes(Iu) = xi; + +end + +%% +% Transform back to real space from wavelet space + +Meval = Meval*FMWT'; + + + + + + diff --git a/moment_integral.m b/moment_integral.m new file mode 100644 index 00000000..ee2c0321 --- /dev/null +++ b/moment_integral.m @@ -0,0 +1,43 @@ +function MomentValue = moment_integral(pde, fval_realspace, gfunc) + +xmin = pde.dimensions{1,1}.domainMin; +xmax = pde.dimensions{1,1}.domainMax; +Lev = pde.lev_vec; +h = (xmax - xmin)/2^(Lev(1)); +deg = pde.deg; +num_dimensions = length(pde.dimensions); + +[quad_xx, quad_ww] = lgwt(deg, -1, 1); + +quad_ww = 2^(-Lev(1))/2*quad_ww; + +ww = repmat(quad_ww, 2^Lev(1), 1); + +ww = ww.*(xmax - xmin); %for 2D use Kronmult + +if num_dimensions >= 2 + for i = 2:num_dimensions + domainMin = pde.dimensions{1,i}.domainMin; + domainMax = pde.dimensions{1,i}.domainMax; + ww = kron(ww,ww)*(domainMax - domainMin); + end +end + +[x, w] = lgwt(deg, 0, h); + +points = []; +%num = 2^Lev*deg; + + +for i = 0:2^Lev-1 + points = [points; xmin + x + i*h]; +end + +%points2 = repmat(points, [num 1]); + +%points2 = reshape(reshape(points2,num,num)',num*num,1); + +MomentValue = sum(ww.*fval_realspace.*gfunc); + +end + diff --git a/plot_fval.m b/plot_fval.m index 4bea6761..76dcf4cb 100644 --- a/plot_fval.m +++ b/plot_fval.m @@ -72,20 +72,28 @@ function plot_fval(pde,nodes,fval_realspace,fval_realspace_analytic,Meval,coordi end f1d = f2d(sy,:); + f1d_SG_lev5 = f1d; x = nodes{1}; + x_SG_lev5 = x; + save('f1d_SG_lev5', 'f1d_SG_lev5', 'x_SG_lev5'); y = nodes{2}; ax1 = subplot(2,2,1); %plot(x,f1d,'-o'); - semilogy(x,f1d, '-o'); - title('1D slice (vertical)'); - + load('f1d_SG_lev5', 'f1d_SG_lev5', 'x_SG_lev5'); + load('f1d_FG_lev4', 'f1d_FG_lev4', 'x_FG_lev4'); +% load('f1d_lev5_deg4', 'f1d_lev5', 'x_lev5'); + semilogy(x_SG_lev5,f1d_SG_lev5, '-b', 'LineWidth', 2); + hold on; + semilogy(x_FG_lev4,f1d_FG_lev4, '-m', 'LineWidth', 2); +% semilogy(x_lev5,f1d_lev5, '-k', 'LineWidth', 2); + hold off; %% % Overplot analytic solution if pde.checkAnalytic f1d_analytic = f2d_analytic(sy,:); hold on; - plot(x,f1d_analytic,'-'); + plot(x,f1d_analytic,'-r'); hold off; end diff --git a/test_matrix_plot_D.m b/test_matrix_plot_D.m new file mode 100644 index 00000000..d7d42226 --- /dev/null +++ b/test_matrix_plot_D.m @@ -0,0 +1,59 @@ +function [Meval,nodes] = matrix_plot_D(pde,dimension, quad_x_in) + +%% +% Generate the evaluation matrix and plotting points +% TODO : probably should be renamed to something more descriptive + +%% +% Setup a few shortcuts + +lev = dimension.lev; +deg = pde.deg; +xMin = dimension.domainMin; +xMax = dimension.domainMax; +FMWT = dimension.FMWT; + +%% +% Jacobi of variable + +n = 2^(lev); +h = (xMax-xMin)/n; +dof_1D = deg*n; +nodes = zeros(dof_1D,1); +Meval = sparse(dof_1D,dof_1D); + +%% +% Quadrature points (quad_x) and weights (quad_w) +if (nargin >= 3), + quad_x = quad_x_in; +else + [quad_x,quad_w]=lgwt(deg,-1,1); +end; + +p_val = lin_legendre(quad_x,deg)*sqrt(1/h); % TODO : this call and normalization happens in several places. We should consolidate. + +for i=0:n-1 + + %% + % Mapping from [-1,1] to physical domain + xi = ((quad_x+1)/2+i)*h+xMin; + + %% + % Coefficients for DG bases + Iu = [deg*i+1:deg*(i+1)]; + + Meval(Iu,Iu) = p_val; + nodes(Iu) = xi; + +end + +%% +% Transform back to real space from wavelet space + +Meval = Meval*FMWT'; + + + + + + From 1010c3eb7daa5605245b93f62a2231273de00512 Mon Sep 17 00:00:00 2001 From: Louis Wonnell Date: Tue, 4 Feb 2020 11:44:37 -0500 Subject: [PATCH 09/12] Tweaking plot_fval to produce SG vs FG plots for degrees 2 and 3 --- PDE/f1d_FG_lev3.mat | Bin 0 -> 508 bytes PDE/f1d_FG_lev5.mat | Bin 0 -> 1282 bytes PDE/f1d_SG_lev4.mat | Bin 0 -> 507 bytes PDE/fokkerplanck2_6p1_withLHS.m | 8 ++++---- asgard.m | 6 +++--- f1d_FG_lev5.mat | Bin 1282 -> 1282 bytes f1d_SG_lev3.mat | Bin 0 -> 508 bytes f1d_SG_lev4.mat | Bin 770 -> 770 bytes f1d_SG_lev5.mat | Bin 794 -> 1279 bytes fp_6p1b_deg2_SGvsFG_levlow.fig | Bin 0 -> 150604 bytes moment_integral.m | 2 +- plot_fval.m | 25 ++++++++++++++++--------- 12 files changed, 24 insertions(+), 17 deletions(-) create mode 100644 PDE/f1d_FG_lev3.mat create mode 100644 PDE/f1d_FG_lev5.mat create mode 100644 PDE/f1d_SG_lev4.mat create mode 100644 f1d_SG_lev3.mat create mode 100644 fp_6p1b_deg2_SGvsFG_levlow.fig diff --git a/PDE/f1d_FG_lev3.mat b/PDE/f1d_FG_lev3.mat new file mode 100644 index 0000000000000000000000000000000000000000..7e76a1f34658e16d4c27a75cc5795a02b2cdbe87 GIT binary patch literal 508 zcmeZu4DoSvQZUssQ1EpO(M`+DN!3vZ$Vn_o%P-2cQgHY2i*PhE(NSU7mX%*WZ-$ca_WKL=er&xuhvj$MO@6=Y z@m%-r2R#1&>EyzU>b4o8M(*~J@7Wm&r@QP1xqk~*_lq+mxoJFOdDK;5{{6?CD@MsH ztR_S-3(VdVqxdcK?S#Gge||r({=@%f?&O>6u3g{1A>3-ymJc?U)vG1Vofo%;-GB4^ z9>=|%58vlkzu)>km(R=4;!90-!iPVHpIq4Z_Xe{wXIT4W9zpN2e<|e_Wd(Vsl>+tH z%kpaZ*S@#mJCp8Z($e}Bw)$CCxY&J%&+#Xosw0y)-i;X0;&>v|<vr~}%@8qGLX?XxTVd{^y)o!a=V%_SrEc%IRj@(YCeo`;M5;%J-vu@aJ-i=l zGNpS=!QJfg_m`-Ru_9#ANm^elkw*XgMQ~W~Nri-EEGNvnB zXO-sWrXI|4YSh51#Na&bqMkeb=c;PKhY<;i^lC2!=aMimstUa4OEn0Zc@SK)wUpCd zY~}kH3k;)H!Rt?shhG(H{45JOnsY%rZd;7NjQw?=r)}j&V%qN!xdw&DHqt8f3NLbd z&l#R*v8ij&Z?tSXD8{ViPL5Y$)^hyGwPM{xI^h$8^swk^8XuuUt(w~T&oQU|>lg?S zl^2NvIE85xhR6@$nBSyVgwpv)SwBtR(h4SIU4816qc3tnriY&m?vAxmF54yRY5>bL zYj@QZ0q0vJ{@ujOtdJ`MJrp$;LjTf85r{frD~a6{Z;KyxA&R}~q&&(JE#~GQtsx9iveV$XjRBtk#?o+T( zbw_HW#6o!^B>x+8gjDK5wEKK7DhkrP?d&1Q2!p}*;qF#M5K_b@oiXfCd$yjutb=I6 zAwg^RJ1(2lL{O?qzo%@UHW2h(j}t27U9PYR=i)4L*z3f>Dha7xIlS1aNqG=y?^xNl zzA!Wh+Sx()Dcpub1kaSC?-Hith zFLOn&pPm!k%C^|B#E$E3XOZP;iPuU$ac%*xN)9yIcEiJZ8^%-N>q?C-l-)COmVq}- z?mTQ=KWbsWpj!Dg&+ug=2I5Cg*t@Fz3CeUo1R-77lXNO$@ZDx|ZHf0BwrAqDuNU+P h)VUwmu{YJ_%w(9&=mCW)V&%Qp0PPV}XD#r}^j|(QdNcq4 literal 0 HcmV?d00001 diff --git a/PDE/f1d_SG_lev4.mat b/PDE/f1d_SG_lev4.mat new file mode 100644 index 0000000000000000000000000000000000000000..5c3be07842e531bd91a9e3bc08769f421b21d2b4 GIT binary patch literal 507 zcmeZu4DoSvQZUssQ1EpO(M`+DN!3vZ$Vn_o%P-2cQgHY2i*PhE(NSM+H%#xw=XWi8 z?_U39qq|u7+o_Mz%}#5--@0EhXS2qcoZWk`vIgfq?R@?A>^7O3dvywz*3R1@^xf?( z>$iLA#XY>|&TO#Xx^;`v^rgq^E|$t(_Wq>%%{Z$smAyu5+x73if2VyrsZ-rtJ$3h6 z=EHBrRnGL?l6;zde?p#Fz3KFowhU6b_JttlZ^7z(afT!}jb|*6x_%^l|1sx^k?;zu z2@%W!v-iX(ehYm&VQ>DQ-w&++@V}Wm`R2N7*Y|G-x7xJjgUx02YDshF#jRoY-#ov^ zac}3t_xaWDx4zHi^D?yfQj?wV;m_eG7dHOA!R*W#);^g>(7WtkO1VW@LEdSlKt1-d zyjuRX?``R(`^Pf;bK*ic$XC^wIc$n~i_v1BF5AiYVJZ+r`08n)so<5Er(kTTU}#`vY+_|(u3%(fWH2#Md13>Btt$%jG>f^<@>{FdDdY)|m zHtUVge{*-+jnki9ONtV%J{h-j+1Ky#Q-!}V&F9+I89y_1zTm{CX}7i=*>^C!_T~5g zs=t}J7FX6k*>*#HO=acV#<+9;nkL!DPUNfnW~q1G&u3!iZTSb+e;ms4Yx>)`o8Rwx zJlDPZ2`~PCI=L{Tx-DHhrLS(&J${Bme_b;{?%#sd{o)KsZW_;69(Dal`2J(g6{F-8 zRudwa1!nJwQT!JAcEaBLKffPX|KWc#ck<13*RJp15N@?;%Lkjw>eZ6w&Wl^a?!S3{ zkK^9Xhwt;N-*0`N%jaci@uem^;lrQ9PcCfydxP1TGpv0wkDzzizm#%|vVy$RN`ZRp zWqGyyYv0@Ook{mHX=(i_D^_SY{pUZSf`E#(zs^i_KJhT&|L(_YrXJ#B*lBH@0RV=c B+|2+0 literal 0 HcmV?d00001 diff --git a/f1d_SG_lev4.mat b/f1d_SG_lev4.mat index 9b6858d4f4f136dedc214999e9e611ca4b35f1cb..67a435c45c6bd375651274a5a7d50c72f9951c29 100644 GIT binary patch delta 41 wcmZo-Yhs&VBH>n)so<5Er(kTTU}$7zWMO4wtYBndWH2#Md13(^b delta 41 wcmZo-Yhs&VBH^2#r{I;Cr(k5RU}$1xVr*q>qF`iTWH2#Md13Bg^%_t zXCIe*IrpQzY6kba7LAYgMzMEobZS4?E2Z6+>#likuN^Vx(4&;M_8VCp4wSdOw%-=+ z`C8@k3;VAMN(=PgKC@@4IKgmE>xq4troAJJ(Ifj_Yt$deDBt*=FYa zqr2=iSSEix?6l3kCPikAf%*pf3cWVpowcj%XT;7D37E9VeuKup;81~i_6Emx=`4+y zV(-xQV8&Y43HA%hX1!Zt*J|JJ@aLbta}D+kEId}zRZHy|f`7g0t0xxNJLrq9N)k%3 zXK1=LuiGHrp20PIpS(_xJ;O@f&xg2t>=~{YMg2*&w`X8`xKCTc!k%HB_WcV_H0>FJ z__a5jR<>t25;2uERm2_`h_8L*`Ry5ge0;68`JWww!>YWMIp6IV8jPPxN<6b;n9wH1 z|MY|qFos|KQ1Oq`(vq7NLA zUwuh~nyWn`RGamT)M`>_Xx5fAK7F+?ocY5Cax*ul9i zi$b5;vww5zduW-zuxB|_q9Gjo%HCC!?aeHcxAu*M*6c`}Kk2XiO@GeS7bh?HXK#Cb=grj|3=Y-qrv;bw zGdP@?xt@u`gVBMT>!20Wc}9omn5Eh&?Mx1{&TLDL<70MsB{w_dz%gbAt^PGVyL?$3 zDj!a$m0@Fb*cG^Ft5`3q1Lu;qWfiV$4xS=2?iHP3bC{71i2@bQ|24clTt2T6u*6Z8Lq z4wgG62W)W?a!7p0>iKk@kVE54zSN{gLJlhqHN;M~6LvUJ)mbUfB<%2E@$W*%d%_L? 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-dim_p.domainMin = 0.1; -dim_p.domainMax = +10; +dim_p.domainMin = 0.01; +dim_p.domainMax = +5; dim_p.init_cond_fn = @(x,p,t) f0_p(x); dim_z.domainMin = -1; diff --git a/asgard.m b/asgard.m index 5755da55..4697cda4 100644 --- a/asgard.m +++ b/asgard.m @@ -151,9 +151,9 @@ % test_moment_matrix = 1; %test matrix for moment_integral % for j = 1:length(nodes{1,2}) - for i = 1:length(nodes{1,1}) - test_func(i,1) = exp(-0.5*((nodes{1,1}(i))^2))/sqrt(2*pi); - end +% for i = 1:length(nodes{1,1}) +% test_func(i,1) = exp(-0.5*((nodes{1,1}(i))^2))/sqrt(2*pi); +% end % end %test_moment = moment_integral(pde,fval_realspace_analytic,test_moment_matrix); @@ -304,6 +304,11 @@ % Get the real space solution 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 @@ -397,10 +402,9 @@ f2d = reshape(fval_realspace,deg*2^LevX,deg*2^LevV)'; 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zO^5>rxNL~i#A(N}glQ8BjTjT$kQ-brnrBCe(=qOo_A@x5{Rwv5Pe4ff0q`qu>Ueds ztZTDw)kL23o^dcAA)=W1M|fU9dp9|VEAkmm)JqvCB8Qu zej4*Cseh5i^Gox0Kj-fyQ7Vw`yUq{jgW7ARm Z#ufeN*OU6Uo0N{#*;0NI`3ICK&q|4 Date: Mon, 10 Feb 2020 11:00:38 -0500 Subject: [PATCH 10/12] Further changes to plot_fval to test sparse grid for complete 2D Fokker-Planck runs --- A_matrix_250.mat | Bin 0 -> 4515424 bytes PDE/f1d_SG_lev2_deg3.mat | Bin 0 -> 998 bytes PDE/fokkerplanck2_complete.m | 6 ++--- asgard.m | 14 ++++++---- f1d_FG_lev3_deg3_complete.mat | Bin 0 -> 779 bytes f1d_FG_lev3_deg4_complete.mat | Bin 0 -> 779 bytes f1d_FG_lev4_deg2_complete.mat | Bin 0 -> 667 bytes f1d_FG_lev4_deg3_complete.mat | Bin 0 -> 1000 bytes f1d_FG_lev4_deg4_complete.mat | Bin 0 -> 1302 bytes f1d_FG_lev4_deg4_complete_mid.mat | Bin 0 -> 1308 bytes f1d_FG_lev4_deg4_complete_upper.mat | Bin 0 -> 1318 bytes f1d_FG_lev5_deg2_complete.mat | Bin 0 -> 1318 bytes f1d_FG_lev5_deg4_complete.mat | Bin 0 -> 2311 bytes f1d_SG_lev2_deg3.mat | Bin 0 -> 465 bytes f1d_SG_lev3_deg3_complete.mat | Bin 0 -> 548 bytes f1d_SG_lev3_deg4_complete.mat | Bin 0 -> 710 bytes f1d_SG_lev4_deg2_complete.mat | Bin 0 -> 674 bytes f1d_SG_lev4_deg3_complete.mat | Bin 0 -> 911 bytes f1d_SG_lev4_deg4_complete.mat | Bin 0 -> 1166 bytes f1d_SG_lev5_deg2_complete.mat | Bin 0 -> 1153 bytes f1d_SG_lev5_deg3_complete.mat | Bin 0 -> 571 bytes f1d_SG_lev5_deg4_complete.mat | Bin 0 -> 2009 bytes f1d_SG_lev5_deg4_complete_dt_0,0625.mat | Bin 0 -> 2111 bytes f1d_SG_lev5_deg4_complete_dt_0,125.mat | Bin 0 -> 2043 bytes f1d_SG_lev5_deg4_complete_dt_0,25.mat | Bin 0 -> 2052 bytes f1d_SG_lev5_deg4_complete_mid.mat | Bin 0 -> 2100 bytes f1d_SG_lev5_deg4_complete_upper.mat | Bin 0 -> 2037 bytes f1d_SG_lev5_deg5_complete.mat | Bin 0 -> 2243 bytes f1d_SG_lev6_deg2_complete.mat | Bin 0 -> 2043 bytes f1d_SG_lev6_deg2_complete_dt_0,125.mat | Bin 0 -> 2064 bytes f1d_SG_lev6_deg2_complete_dt_0,25.mat | Bin 0 -> 2063 bytes f1d_SG_lev6_deg3_complete.mat | Bin 0 -> 3155 bytes f1d_SG_lev6_deg4_complete.mat | Bin 0 -> 3605 bytes f1d_SG_lev7_deg2_complete.mat | Bin 0 -> 1025 bytes fval_realspace_0018.mat | Bin 0 -> 8881 bytes fval_realspace_0076.mat | Bin 0 -> 9078 bytes output_Sebastian.zip | Bin 0 -> 6685944 bytes output_Sebastian/A_matrix_250.mat | Bin 0 -> 4515424 bytes output_Sebastian/f2d-0250.mat | Bin 0 -> 2193414 bytes plot_fval.m | 33 ++++++++++++------------ 40 files changed, 29 insertions(+), 24 deletions(-) create mode 100644 A_matrix_250.mat create mode 100644 PDE/f1d_SG_lev2_deg3.mat create mode 100644 f1d_FG_lev3_deg3_complete.mat create mode 100644 f1d_FG_lev3_deg4_complete.mat create mode 100644 f1d_FG_lev4_deg2_complete.mat create mode 100644 f1d_FG_lev4_deg3_complete.mat create mode 100644 f1d_FG_lev4_deg4_complete.mat create mode 100644 f1d_FG_lev4_deg4_complete_mid.mat create mode 100644 f1d_FG_lev4_deg4_complete_upper.mat create mode 100644 f1d_FG_lev5_deg2_complete.mat create mode 100644 f1d_FG_lev5_deg4_complete.mat create mode 100644 f1d_SG_lev2_deg3.mat create mode 100644 f1d_SG_lev3_deg3_complete.mat create mode 100644 f1d_SG_lev3_deg4_complete.mat create mode 100644 f1d_SG_lev4_deg2_complete.mat create mode 100644 f1d_SG_lev4_deg3_complete.mat create mode 100644 f1d_SG_lev4_deg4_complete.mat create mode 100644 f1d_SG_lev5_deg2_complete.mat create mode 100644 f1d_SG_lev5_deg3_complete.mat create mode 100644 f1d_SG_lev5_deg4_complete.mat create mode 100644 f1d_SG_lev5_deg4_complete_dt_0,0625.mat create mode 100644 f1d_SG_lev5_deg4_complete_dt_0,125.mat create mode 100644 f1d_SG_lev5_deg4_complete_dt_0,25.mat create mode 100644 f1d_SG_lev5_deg4_complete_mid.mat create mode 100644 f1d_SG_lev5_deg4_complete_upper.mat create mode 100644 f1d_SG_lev5_deg5_complete.mat create mode 100644 f1d_SG_lev6_deg2_complete.mat create mode 100644 f1d_SG_lev6_deg2_complete_dt_0,125.mat create mode 100644 f1d_SG_lev6_deg2_complete_dt_0,25.mat create mode 100644 f1d_SG_lev6_deg3_complete.mat create mode 100644 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