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Smol_RK3CN2_xpBC_zpBC_GPU.m
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Smol_RK3CN2_xpBC_zpBC_GPU.m
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%% Full Smoluchowski Time Stepping solver for the Fokker-Planck Equation (RK3-CN2)
% Loosely based on Spherefun, this solve uses Double Fourier Sphere (DFS)
% method to tranform the orientational space and time-marched in the DFS
% space. Time stepping is semi-implicit, with Advection terms in RK3 and
% Laplacian term in CN2. Implicit matrix inversion is done using the
% Spherefun Helmholtz Solver (only slightly modified to remove
% chebfun-based activiities).
%% Setting up
% RK3 coeff and constants
alpha=[4/15 1/15 1/6];
gamma=[8/15 5/12 3/4];
rho=[0 -17/60 -5/12];
% Preparing Constants
K2 = (1/(dt*diff_const)); % Helmholtz frequency for BDF1
%% Initialising Matrices
Msin=gpuArray(kron(spdiags(0.5i*ones(n,1)*[-1,1], [-1 1], n, n),speye(m)));
% mats=struct('Mint',settings.Mint,'S_profile',S_profile,'Mvor',Mvor,'Mgyro',Mgyro,'Mlap',Mlap,...
% 'Mp1',Mp1,'Mp3',Mp3,'Rdx',Rdx,'Rd2x',Rd2x); settings_CPU=settings; % If CPU PS is used.
Mint=gpuArray(settings.Mint);
settings.Mint=Mint;
MintSq=gpuArray(settings.MintSq);
Kp=settings.Kp;
% GPU stuff
U_profile=gpuArray(U_profile);
W_profile=gpuArray(W_profile);
curl_profile=gpuArray(curl_profile);
E_profile=gpuArray(E_profile);
Kp=gpuArray(Kp);int_const=gpuArray(int_const);
mKp_alpha1=gpuArray(-(Kp/alpha(1)));
mKp_alpha2=gpuArray(-(Kp/alpha(2)));
mKp_alpha3=gpuArray(-(Kp/alpha(3)));
mK2_alpha1=gpuArray(-K2/alpha(1));malpha1_K2=1/mK2_alpha1;
mK2_alpha2=gpuArray(-K2/alpha(2));malpha2_K2=1/mK2_alpha2;
mK2_alpha3=gpuArray(-K2/alpha(3));malpha3_K2=1/mK2_alpha3;
gamma_alpha1=gpuArray(gamma(1)/alpha(1)/diff_const);
gamma_alpha2=gpuArray(gamma(2)/alpha(2)/diff_const);
gamma_alpha3=gpuArray(gamma(3)/alpha(3)/diff_const);
rho_alpha2=gpuArray(rho(2)/alpha(2)/diff_const);
rho_alpha3=gpuArray(rho(3)/alpha(3)/diff_const);
% Advection
% Mvor=gpuArray(complex(adv_vor_mat(settings)));
% Mgyro=gpuArray(complex(settings.beta*adv_gyro_mat(settings)));
%For strange behaviour in MATLAB ver < R2020
Mvor=gpuArray(sparse(complex(full(Mvor))));
Mgyro=gpuArray(sparse(complex(full(Mgyro))));
%Laplacian
Mlap=gpuArray(sparse(complex(Mlap)));
helm=helmholtz_genGPU( n, m);
helm_inv_k1=helmholtz_precalGPU( -K2/alpha(1),helm);
helm_inv_k2=helmholtz_precalGPU( -K2/alpha(2),helm);
helm_inv_k3=helmholtz_precalGPU( -K2/alpha(3),helm);
%p1
Mp1 = gpuArray(complex(Mp1));
%p3
Mp3 = gpuArray(complex(Mp3));
%Swimming and sedimentation
MSwim_dx=Vc*Mp1-(Vsmax-Vsmin)*Mp1p3;
MSwim_dz=Vc*Mp3-Vsmin*gpuArray(speye(n*m))-(Vsmax-Vsmin)*Mp3sq;
%% Initial Condition
if ti==0
f_init=zeros(n*m,1);
f_init(m*n/2+m/2+1,:)=int_const/4/pi;
ucoeff0=gather(f_init)*reshape(ones(Nx_mesh,Nz_mesh)/4,1,[]);
else
load(['./2D_run/t' num2str(ti) '.mat'],'ucoeff_t');
ucoeff0=ucoeff_t;
end
%% Initialise Recorded values
cell_den=NaN(floor(nsteps/saving_rate3),Nx_mesh*Nz_mesh);
%% Time-Stepping (RK3-CN2)
ucoeff=gpuArray(complex(ucoeff0));
adv_p_coeff =gpuArray(complex(zeros(n*m,Nx_mesh*Nz_mesh)));
adv_comb_coeff=gpuArray(complex(zeros(n*m,Nx_mesh*Nz_mesh)));
ucoeff_previous=gpuArray(complex(NaN(n*m,Nx_mesh*Nz_mesh,3)));
% ucoeff_previous2=gpuArray(complex(NaN(n*m,N_mesh,3)));
cell_den_loc=real(Mint*ucoeff*2*pi);
Nint_loc=sum(cell_den_loc)*dx*dz;
for i = 1:nsteps
%% RK step 1
%k=1;
dxu_coeff=ucoeff*Rdx;
dzu_coeff=ucoeff*Rdz;
adv_coeff=curl_profile.*(Mvor*ucoeff)+E_profile.*(Mstrain*ucoeff)...
+Mgyro*ucoeff...
+Minert*ucoeff;
adv_coeff=adv_coeff-Mint'*(Mint*adv_coeff)/MintSq;
lap_coeff=Mlap*ucoeff;
lap_coeff=lap_coeff-Mint'*(Mint*lap_coeff)/MintSq;
uadv_coeff=U_profile.*dxu_coeff+W_profile.*dzu_coeff;
swim_coeff=MSwim_dx*dxu_coeff+MSwim_dz*dzu_coeff;
DT_coeff=DT*(ucoeff*Rd2x+ucoeff*Rd2z);
adv_p_coeff=adv_coeff+swim_coeff+uadv_coeff-DT_coeff;
rhs_coeff = mK2_alpha1*ucoeff-lap_coeff+gamma_alpha1*adv_p_coeff...
+mKp_alpha1*(int_const-Nint_loc)*Mint'.*ucoeff;
F=permute(reshape(rhs_coeff,helm.n,helm.m,Nx_mesh*Nz_mesh),[2 1 3]);
int_constj = pagefun(@mtimes,malpha1_K2*helm.enG,F(:,helm.k,:));
F = pagefun(@mtimes,malpha1_K2*helm.L2G, F);
F(helm.floorm+1,helm.k,:)=int_constj;
CFS = helm_inv_k1*reshape(F,helm.n*helm.m,Nx_mesh*Nz_mesh);
ucoeff=reshape(permute(reshape(CFS,helm.m,helm.n,Nx_mesh*Nz_mesh),[2 1 3]),helm.n*helm.m,Nx_mesh*Nz_mesh);
cell_den_loc=real(Mint*ucoeff*2*pi);
Nint_loc=sum(cell_den_loc)*dx*dz;
%% RK step 2
%k=2;
dxu_coeff=ucoeff*Rdx;
dzu_coeff=ucoeff*Rdz;
adv_coeff=curl_profile.*(Mvor*ucoeff)+E_profile.*(Mstrain*ucoeff)...
+Mgyro*ucoeff...
+Minert*ucoeff;
adv_coeff=adv_coeff-Mint'*(Mint*adv_coeff)/MintSq;
lap_coeff=Mlap*ucoeff;
lap_coeff=lap_coeff-Mint'*(Mint*lap_coeff)/MintSq;
uadv_coeff=U_profile.*dxu_coeff+W_profile.*dzu_coeff;
swim_coeff=MSwim_dx*dxu_coeff+MSwim_dz*dzu_coeff;
DT_coeff=DT*(ucoeff*Rd2x+ucoeff*Rd2z);
adv_comb_coeff=adv_coeff+swim_coeff+uadv_coeff-DT_coeff;
rhs_coeff = mK2_alpha2*ucoeff-lap_coeff+gamma_alpha2*adv_comb_coeff+rho_alpha2*adv_p_coeff...
+mKp_alpha2*(int_const-Nint_loc)*Mint'.*ucoeff;
F=permute(reshape(rhs_coeff,helm.n,helm.m,Nx_mesh*Nz_mesh),[2 1 3]);
int_constj = pagefun(@mtimes,malpha2_K2*helm.enG,F(:,helm.k,:));
F = pagefun(@mtimes,malpha2_K2*helm.L2G, F);
F(helm.floorm+1,helm.k,:)=int_constj;
CFS = helm_inv_k2*reshape(F,helm.n*helm.m,Nx_mesh*Nz_mesh);
ucoeff=reshape(permute(reshape(CFS,helm.m,helm.n,Nx_mesh*Nz_mesh),[2 1 3]),helm.n*helm.m,Nx_mesh*Nz_mesh);
cell_den_loc=real(Mint*ucoeff*2*pi);
Nint_loc=sum(cell_den_loc)*dx*dz;
%% RK step 3
%k=3;
adv_p_coeff=adv_comb_coeff;
dxu_coeff=ucoeff*Rdx;
dzu_coeff=ucoeff*Rdz;
adv_coeff=curl_profile.*(Mvor*ucoeff)+E_profile.*(Mstrain*ucoeff)...
+Mgyro*ucoeff...
+Minert*ucoeff;
adv_coeff=adv_coeff-Mint'*(Mint*adv_coeff)/MintSq;
lap_coeff=Mlap*ucoeff;
lap_coeff=lap_coeff-Mint'*(Mint*lap_coeff)/MintSq;
uadv_coeff=U_profile.*dxu_coeff+W_profile.*dzu_coeff;
swim_coeff=MSwim_dx*dxu_coeff+MSwim_dz*dzu_coeff;
DT_coeff=DT*(ucoeff*Rd2x+ucoeff*Rd2z);
adv_comb_coeff=adv_coeff+swim_coeff+uadv_coeff-DT_coeff;
rhs_coeff = mK2_alpha3*ucoeff-lap_coeff+gamma_alpha3*adv_comb_coeff+rho_alpha3*adv_p_coeff...
+mKp_alpha3*(int_const-Nint_loc)*Mint'.*ucoeff;
F=permute(reshape(rhs_coeff,helm.n,helm.m,Nx_mesh*Nz_mesh),[2 1 3]);
int_constj = pagefun(@mtimes,malpha3_K2*helm.enG,F(:,helm.k,:));
F = pagefun(@mtimes,malpha3_K2*helm.L2G, F);
F(helm.floorm+1,helm.k,:)=int_constj;
CFS = helm_inv_k3*reshape(F,helm.n*helm.m,Nx_mesh*Nz_mesh);
ucoeff=reshape(permute(reshape(CFS,helm.m,helm.n,Nx_mesh*Nz_mesh),[2 1 3]),helm.n*helm.m,Nx_mesh*Nz_mesh);
cell_den_loc=real(Mint*ucoeff*2*pi);
Nint_loc=sum(cell_den_loc)*dx*dz;
%% Saving for Post-Processing
% Saving full Psi and it time derivative
% PS=PS.RunTimeCall(ucoeff,i);
if ( mod(i, saving_rate1) == 0 )
ucoeff_t=gather(ucoeff);
t=i*dt+ti;
save(['./2D_run/t' num2str(t) '.mat'],'ucoeff_t','t','Mint','x','z','-v7.3');
end
% Saving Cell Density
if ( mod(i, saving_rate3) == 0 )
cell_den(i/saving_rate3,:)=gather(cell_den_loc);
disp([num2str(i) '/' num2str(nsteps)]);
if any(isnan(cell_den(i/saving_rate3,:)))
disp('NaN detected in cell_den');
break;
end
end
end