Category: News
Timestep stability in a 1D heat diffusion model
Hi,
I have a 1D heat diffusion code which I was using on a timescale of 10s of years and I am now trying to use the same code to work on a scale of millions of years. Obviously if I keep my timestep the same this will take ages to calculate but if I increase my timestep I encounter numerical stability issues.
My questions are:
How should I approach this problem?
What affects the maximum stable timestep? And how do I calculate this?
Many thanks,
Alex
close all
clear all
dx = 4; % discretization step in m
dt = 0.0000001; % timestep in Myrs
h=1000; % height of box in m
nx=h/dx+1;
model_lenth=1; %length of model in Myrs
nt=ceil(model_lenth/dt)+1; % number of tsteps to reach end of model
kappa = 1e-6; % thermal diffusivity
x=0:dx:0+h; % finite difference mesh
T=38+0.05.*x; % initial T=Tm everywhere …
time=zeros(1,nt);
t=0;
Tnew = zeros(1,nx);
%Lower sill
sill_1_thickness=18;
Sill_1_top_position=590;
Sill_1_top=ceil(Sill_1_top_position/dx);
Sill_1_bottom=ceil((Sill_1_top_position+sill_1_thickness)/dx);
%Upper sill
sill_2_thickness=10;
Sill_2_top_position=260;
Sill_2_top=ceil(Sill_2_top_position/dx);
Sill_2_bottom=ceil((Sill_2_top_position+sill_2_thickness)/dx);
%Temperature of dolerite intrusions
Tm=1300;
T(Sill_1_top:Sill_1_bottom)=Tm; %Apply temperature to intrusion 1
% unit conversion to SI:
secinmyr=24*3600*365*1000000; % dt in sec
dt=dt*secinmyr;
%Plot initial conditions
figure(1), clf
f1 = figure(1); %Make full screen
set(f1,’Units’, ‘Normalized’, ‘OuterPosition’, [0 0 1 1]);
plot (T,x,’LineWidth’,2)
xlabel(‘T [^oC]’)
ylabel(‘x[m]’)
axis([0 1310 0 1000])
title(‘ Initial Conditions’)
set(gca,’YDir’,’reverse’);
%Main calculation
for it=1:nt
%Apply temperature to upper intrusion
if it==10;
T(Sill_2_top:Sill_2_bottom)=Tm;
end
for i = 2:nx-1
Tnew(i) = T(i) + kappa*dt*(T(i+1) – 2*T(i) + T(i-1))/dx/dx;
end
Tnew(1) = T(1);
Tnew(nx) = T(nx);
time(it) = t;
T = Tnew; %Set old Temp to = new temp for next loop
tmyears=(t/secinmyr);
%Plot a figure which updates in the loop of temperature against depth
figure(2), clf
plot (T,x,’LineWidth’,2)
xlabel(‘T [^oC]’)
ylabel(‘x[m]’)
title([‘ Temperature against Depth after ‘,num2str(tmyears),’ Myrs’])
axis([0 1300 0 1000])
set(gca,’YDir’,’reverse’);%Reverse y axis
%Make full screen
f2 = figure(2);
set(f2,’Units’, ‘Normalized’, ‘OuterPosition’, [0 0 1 1]);
drawnow
t=t+dt;
endHi,
I have a 1D heat diffusion code which I was using on a timescale of 10s of years and I am now trying to use the same code to work on a scale of millions of years. Obviously if I keep my timestep the same this will take ages to calculate but if I increase my timestep I encounter numerical stability issues.
My questions are:
How should I approach this problem?
What affects the maximum stable timestep? And how do I calculate this?
Many thanks,
Alex
close all
clear all
dx = 4; % discretization step in m
dt = 0.0000001; % timestep in Myrs
h=1000; % height of box in m
nx=h/dx+1;
model_lenth=1; %length of model in Myrs
nt=ceil(model_lenth/dt)+1; % number of tsteps to reach end of model
kappa = 1e-6; % thermal diffusivity
x=0:dx:0+h; % finite difference mesh
T=38+0.05.*x; % initial T=Tm everywhere …
time=zeros(1,nt);
t=0;
Tnew = zeros(1,nx);
%Lower sill
sill_1_thickness=18;
Sill_1_top_position=590;
Sill_1_top=ceil(Sill_1_top_position/dx);
Sill_1_bottom=ceil((Sill_1_top_position+sill_1_thickness)/dx);
%Upper sill
sill_2_thickness=10;
Sill_2_top_position=260;
Sill_2_top=ceil(Sill_2_top_position/dx);
Sill_2_bottom=ceil((Sill_2_top_position+sill_2_thickness)/dx);
%Temperature of dolerite intrusions
Tm=1300;
T(Sill_1_top:Sill_1_bottom)=Tm; %Apply temperature to intrusion 1
% unit conversion to SI:
secinmyr=24*3600*365*1000000; % dt in sec
dt=dt*secinmyr;
%Plot initial conditions
figure(1), clf
f1 = figure(1); %Make full screen
set(f1,’Units’, ‘Normalized’, ‘OuterPosition’, [0 0 1 1]);
plot (T,x,’LineWidth’,2)
xlabel(‘T [^oC]’)
ylabel(‘x[m]’)
axis([0 1310 0 1000])
title(‘ Initial Conditions’)
set(gca,’YDir’,’reverse’);
%Main calculation
for it=1:nt
%Apply temperature to upper intrusion
if it==10;
T(Sill_2_top:Sill_2_bottom)=Tm;
end
for i = 2:nx-1
Tnew(i) = T(i) + kappa*dt*(T(i+1) – 2*T(i) + T(i-1))/dx/dx;
end
Tnew(1) = T(1);
Tnew(nx) = T(nx);
time(it) = t;
T = Tnew; %Set old Temp to = new temp for next loop
tmyears=(t/secinmyr);
%Plot a figure which updates in the loop of temperature against depth
figure(2), clf
plot (T,x,’LineWidth’,2)
xlabel(‘T [^oC]’)
ylabel(‘x[m]’)
title([‘ Temperature against Depth after ‘,num2str(tmyears),’ Myrs’])
axis([0 1300 0 1000])
set(gca,’YDir’,’reverse’);%Reverse y axis
%Make full screen
f2 = figure(2);
set(f2,’Units’, ‘Normalized’, ‘OuterPosition’, [0 0 1 1]);
drawnow
t=t+dt;
end Hi,
I have a 1D heat diffusion code which I was using on a timescale of 10s of years and I am now trying to use the same code to work on a scale of millions of years. Obviously if I keep my timestep the same this will take ages to calculate but if I increase my timestep I encounter numerical stability issues.
My questions are:
How should I approach this problem?
What affects the maximum stable timestep? And how do I calculate this?
Many thanks,
Alex
close all
clear all
dx = 4; % discretization step in m
dt = 0.0000001; % timestep in Myrs
h=1000; % height of box in m
nx=h/dx+1;
model_lenth=1; %length of model in Myrs
nt=ceil(model_lenth/dt)+1; % number of tsteps to reach end of model
kappa = 1e-6; % thermal diffusivity
x=0:dx:0+h; % finite difference mesh
T=38+0.05.*x; % initial T=Tm everywhere …
time=zeros(1,nt);
t=0;
Tnew = zeros(1,nx);
%Lower sill
sill_1_thickness=18;
Sill_1_top_position=590;
Sill_1_top=ceil(Sill_1_top_position/dx);
Sill_1_bottom=ceil((Sill_1_top_position+sill_1_thickness)/dx);
%Upper sill
sill_2_thickness=10;
Sill_2_top_position=260;
Sill_2_top=ceil(Sill_2_top_position/dx);
Sill_2_bottom=ceil((Sill_2_top_position+sill_2_thickness)/dx);
%Temperature of dolerite intrusions
Tm=1300;
T(Sill_1_top:Sill_1_bottom)=Tm; %Apply temperature to intrusion 1
% unit conversion to SI:
secinmyr=24*3600*365*1000000; % dt in sec
dt=dt*secinmyr;
%Plot initial conditions
figure(1), clf
f1 = figure(1); %Make full screen
set(f1,’Units’, ‘Normalized’, ‘OuterPosition’, [0 0 1 1]);
plot (T,x,’LineWidth’,2)
xlabel(‘T [^oC]’)
ylabel(‘x[m]’)
axis([0 1310 0 1000])
title(‘ Initial Conditions’)
set(gca,’YDir’,’reverse’);
%Main calculation
for it=1:nt
%Apply temperature to upper intrusion
if it==10;
T(Sill_2_top:Sill_2_bottom)=Tm;
end
for i = 2:nx-1
Tnew(i) = T(i) + kappa*dt*(T(i+1) – 2*T(i) + T(i-1))/dx/dx;
end
Tnew(1) = T(1);
Tnew(nx) = T(nx);
time(it) = t;
T = Tnew; %Set old Temp to = new temp for next loop
tmyears=(t/secinmyr);
%Plot a figure which updates in the loop of temperature against depth
figure(2), clf
plot (T,x,’LineWidth’,2)
xlabel(‘T [^oC]’)
ylabel(‘x[m]’)
title([‘ Temperature against Depth after ‘,num2str(tmyears),’ Myrs’])
axis([0 1300 0 1000])
set(gca,’YDir’,’reverse’);%Reverse y axis
%Make full screen
f2 = figure(2);
set(f2,’Units’, ‘Normalized’, ‘OuterPosition’, [0 0 1 1]);
drawnow
t=t+dt;
end time step; heat diffusion MATLAB Answers — New Questions
How to set the theorem of floquet for Linear variational equation with periodic equation?
I’m trying to analyze the stability regions of the equation of motion of a system with periodic coefficients (whirlflutter). I have only written its polynomial equation and examined its roots, but my plot did not match the reference implementation correctly.
If I wanna write the Hill function and use the ode45 code, is it possible for someone to correct my code and my approach to finding the monodromy matrix and calculating the Floquet multipliers?
clc;
clear all;
% Define parameters
N = 2; % Number of blades
I_thetaoverI_b = 2; % Moment of inertia pitch axis over I_b
I_psioverI_b = 2; % Moment of inertia yaw axis over I_b
C_thetaoverI_b = 0.00; % Damping coefficient over I_b
C_psioverI_b = 0.00; % Damping coefficient over I_b
h = 0.3; % rotor mast height, wing tip spar to rotor hub [m]
hoverR = 0.34;
R = h / hoverR; % radius [m]
gamma = 4; % lock number
V_knots = 325; % the rotor forward velocity [knots]
% Convert velocity from [knots] to [meters per second]
% 1 knot = 0.51444 meters per second
V = V_knots * 0.51444;
% Calculate angular velocity in radians per second
omega_rad_s = V / R;
% Convert angular velocity from radians per second to RPM
% 1 radian per second = (60 / (2 * pi)) RPM
Omega = omega_rad_s * (60 / (2 * pi));
freq_1_over_Omega = 1 / Omega;
%the flap moment aerodynamic coefficients for large V
M_b = -(1/10)*V;
M_u = 1/6;
%the propeller aerodynamic coefficients
H_u = V/2;
% Frequency ranges
f_pitch= 5:3:140;
f_yaw= 5:3:140;
divergence_map = [];
Rdivergence_map = [];
unstable = [];
% Modify the loop to iterate over time points
for i = 1:length(f_pitch)
for j = 1:length(f_yaw)
phi_steps = linspace(0, pi, 100); % Time steps within one period
for phi = phi_steps
% Angular frequencies for the current time point
w_omega_pitch = 2 * pi* f_pitch(i);
w_omega_yaw = 2 * pi * f_yaw(j);
K_psi = (w_omega_pitch^2) * I_psioverI_b;
K_theta = (w_omega_yaw^2) * I_thetaoverI_b;
% Define inertia matrix [M]
M_matrix = [I_thetaoverI_b + 1 + cos(2*phi), -sin(2*phi);
-sin(2*phi), I_psioverI_b + 1 – cos(2*phi)];
% Define damping matrix [D]
D11 = C_thetaoverI_b + h^2*gamma*H_u*(1 – cos(2*phi)) – gamma*M_b*(1 + cos(2*phi)) – (2 + 2*h*gamma*M_u)*sin(2*phi);
D12 = h^2*gamma*H_u*sin(2*phi) + gamma*M_b*sin(2*phi) – 2*(1 + cos(2*phi)) – 2*h*gamma*M_u*cos(2*phi);
D21 = h^2*gamma*H_u*sin(2*phi) + gamma*M_b*sin(2*phi) + 2*(1 – cos(2*phi)) – 2*h*gamma*M_u*cos(2*phi);
D22 = C_psioverI_b + h^2*gamma*H_u*(1 + cos(2*phi)) – gamma*M_b*(1 – cos(2*phi)) + (2 + 2*h*gamma*M_u)*sin(2*phi);
D_matrix = [D11, D12;
D21, D22];
% Define stiffness matrix [K]
K11 = K_theta – h*gamma*V*H_u*(1 – cos(2*phi)) + gamma*V*M_u*sin(2*phi);
K12 = -h*V*gamma*H_u*sin(2*phi) + gamma*V*M_u*(1 + cos(2*phi));
K21 = -h*gamma*V*H_u*sin(2*phi) – gamma*V*M_u*(1 – cos(2*phi));
K22 = K_psi – h*gamma*V*H_u*(1 + cos(2*phi)) – gamma*V*M_u*sin(2*phi);
K_matrix = [K11, K12;
K21, K22];
% Compute the system matrices
M11 = M_matrix(1, 1); M12 = M_matrix(1, 2); M21 = M_matrix(2, 1); M22 = M_matrix(2, 2);
D11 = D_matrix(1, 1); D12 = D_matrix(1, 2); D21 = D_matrix(2, 1); D22 = D_matrix(2, 2);
K11 = K_matrix(1, 1); K12 = K_matrix(1, 2); K21 = K_matrix(2, 1); K22 = K_matrix(2, 2);
% Find the roots of the polynomial equation
P0 = M11*M22-M12*M21;
P1 = (- D11*M22*1j – D22*M11*1j + M12*D21*j + D12*M21*j);
P2 = (D11*D22*(1j)^2 – K22*M11 – K11*M22 – D12*D21*(1j)^2 + M12*K21 + M21*K12);
P3 = (D11*K22*1j – D12*K21*1j – D21*K12*1j + D22*K11*1j);
P4 = K11*K22 – K12*K21;
P = roots([P0, P1, P2, P3, P4]);
r = 1 * P;
%Flutter
for k = 1:length(r)
if (real(r(k)) > 0)
if (imag(r(k)) <= 0)
unstable = [unstable; phi, K_psi, K_theta];
% Proximity check for 1/Ω divergence
if abs(real(r(k)) – freq_1_over_Omega) < 0.1
Rdivergence_map = [Rdivergence_map; phi, K_psi, K_theta];
end
end
end
end
%Divergence
if (real(det(K_matrix)) < 0)
divergence_map = [divergence_map; phi, K_psi, K_theta];
end
end
end
end
% Plotting section
figure;
hold on;
scatter(unstable(:,2), unstable(:,3), ‘filled’);
scatter(divergence_map(:,2), divergence_map(:,3), ‘filled’, ‘r’);
scatter(Rdivergence_map(:,2), Rdivergence_map(:,3), ‘filled’, ‘g’);
xlabel(‘K_psi’);
ylabel(‘K_theta’);
title(‘Whirl Flutter Diagram’);
legend(‘Flutter area’, ‘Divergence area’, ‘1/Ω Divergence area’);
hold off;I’m trying to analyze the stability regions of the equation of motion of a system with periodic coefficients (whirlflutter). I have only written its polynomial equation and examined its roots, but my plot did not match the reference implementation correctly.
If I wanna write the Hill function and use the ode45 code, is it possible for someone to correct my code and my approach to finding the monodromy matrix and calculating the Floquet multipliers?
clc;
clear all;
% Define parameters
N = 2; % Number of blades
I_thetaoverI_b = 2; % Moment of inertia pitch axis over I_b
I_psioverI_b = 2; % Moment of inertia yaw axis over I_b
C_thetaoverI_b = 0.00; % Damping coefficient over I_b
C_psioverI_b = 0.00; % Damping coefficient over I_b
h = 0.3; % rotor mast height, wing tip spar to rotor hub [m]
hoverR = 0.34;
R = h / hoverR; % radius [m]
gamma = 4; % lock number
V_knots = 325; % the rotor forward velocity [knots]
% Convert velocity from [knots] to [meters per second]
% 1 knot = 0.51444 meters per second
V = V_knots * 0.51444;
% Calculate angular velocity in radians per second
omega_rad_s = V / R;
% Convert angular velocity from radians per second to RPM
% 1 radian per second = (60 / (2 * pi)) RPM
Omega = omega_rad_s * (60 / (2 * pi));
freq_1_over_Omega = 1 / Omega;
%the flap moment aerodynamic coefficients for large V
M_b = -(1/10)*V;
M_u = 1/6;
%the propeller aerodynamic coefficients
H_u = V/2;
% Frequency ranges
f_pitch= 5:3:140;
f_yaw= 5:3:140;
divergence_map = [];
Rdivergence_map = [];
unstable = [];
% Modify the loop to iterate over time points
for i = 1:length(f_pitch)
for j = 1:length(f_yaw)
phi_steps = linspace(0, pi, 100); % Time steps within one period
for phi = phi_steps
% Angular frequencies for the current time point
w_omega_pitch = 2 * pi* f_pitch(i);
w_omega_yaw = 2 * pi * f_yaw(j);
K_psi = (w_omega_pitch^2) * I_psioverI_b;
K_theta = (w_omega_yaw^2) * I_thetaoverI_b;
% Define inertia matrix [M]
M_matrix = [I_thetaoverI_b + 1 + cos(2*phi), -sin(2*phi);
-sin(2*phi), I_psioverI_b + 1 – cos(2*phi)];
% Define damping matrix [D]
D11 = C_thetaoverI_b + h^2*gamma*H_u*(1 – cos(2*phi)) – gamma*M_b*(1 + cos(2*phi)) – (2 + 2*h*gamma*M_u)*sin(2*phi);
D12 = h^2*gamma*H_u*sin(2*phi) + gamma*M_b*sin(2*phi) – 2*(1 + cos(2*phi)) – 2*h*gamma*M_u*cos(2*phi);
D21 = h^2*gamma*H_u*sin(2*phi) + gamma*M_b*sin(2*phi) + 2*(1 – cos(2*phi)) – 2*h*gamma*M_u*cos(2*phi);
D22 = C_psioverI_b + h^2*gamma*H_u*(1 + cos(2*phi)) – gamma*M_b*(1 – cos(2*phi)) + (2 + 2*h*gamma*M_u)*sin(2*phi);
D_matrix = [D11, D12;
D21, D22];
% Define stiffness matrix [K]
K11 = K_theta – h*gamma*V*H_u*(1 – cos(2*phi)) + gamma*V*M_u*sin(2*phi);
K12 = -h*V*gamma*H_u*sin(2*phi) + gamma*V*M_u*(1 + cos(2*phi));
K21 = -h*gamma*V*H_u*sin(2*phi) – gamma*V*M_u*(1 – cos(2*phi));
K22 = K_psi – h*gamma*V*H_u*(1 + cos(2*phi)) – gamma*V*M_u*sin(2*phi);
K_matrix = [K11, K12;
K21, K22];
% Compute the system matrices
M11 = M_matrix(1, 1); M12 = M_matrix(1, 2); M21 = M_matrix(2, 1); M22 = M_matrix(2, 2);
D11 = D_matrix(1, 1); D12 = D_matrix(1, 2); D21 = D_matrix(2, 1); D22 = D_matrix(2, 2);
K11 = K_matrix(1, 1); K12 = K_matrix(1, 2); K21 = K_matrix(2, 1); K22 = K_matrix(2, 2);
% Find the roots of the polynomial equation
P0 = M11*M22-M12*M21;
P1 = (- D11*M22*1j – D22*M11*1j + M12*D21*j + D12*M21*j);
P2 = (D11*D22*(1j)^2 – K22*M11 – K11*M22 – D12*D21*(1j)^2 + M12*K21 + M21*K12);
P3 = (D11*K22*1j – D12*K21*1j – D21*K12*1j + D22*K11*1j);
P4 = K11*K22 – K12*K21;
P = roots([P0, P1, P2, P3, P4]);
r = 1 * P;
%Flutter
for k = 1:length(r)
if (real(r(k)) > 0)
if (imag(r(k)) <= 0)
unstable = [unstable; phi, K_psi, K_theta];
% Proximity check for 1/Ω divergence
if abs(real(r(k)) – freq_1_over_Omega) < 0.1
Rdivergence_map = [Rdivergence_map; phi, K_psi, K_theta];
end
end
end
end
%Divergence
if (real(det(K_matrix)) < 0)
divergence_map = [divergence_map; phi, K_psi, K_theta];
end
end
end
end
% Plotting section
figure;
hold on;
scatter(unstable(:,2), unstable(:,3), ‘filled’);
scatter(divergence_map(:,2), divergence_map(:,3), ‘filled’, ‘r’);
scatter(Rdivergence_map(:,2), Rdivergence_map(:,3), ‘filled’, ‘g’);
xlabel(‘K_psi’);
ylabel(‘K_theta’);
title(‘Whirl Flutter Diagram’);
legend(‘Flutter area’, ‘Divergence area’, ‘1/Ω Divergence area’);
hold off; I’m trying to analyze the stability regions of the equation of motion of a system with periodic coefficients (whirlflutter). I have only written its polynomial equation and examined its roots, but my plot did not match the reference implementation correctly.
If I wanna write the Hill function and use the ode45 code, is it possible for someone to correct my code and my approach to finding the monodromy matrix and calculating the Floquet multipliers?
clc;
clear all;
% Define parameters
N = 2; % Number of blades
I_thetaoverI_b = 2; % Moment of inertia pitch axis over I_b
I_psioverI_b = 2; % Moment of inertia yaw axis over I_b
C_thetaoverI_b = 0.00; % Damping coefficient over I_b
C_psioverI_b = 0.00; % Damping coefficient over I_b
h = 0.3; % rotor mast height, wing tip spar to rotor hub [m]
hoverR = 0.34;
R = h / hoverR; % radius [m]
gamma = 4; % lock number
V_knots = 325; % the rotor forward velocity [knots]
% Convert velocity from [knots] to [meters per second]
% 1 knot = 0.51444 meters per second
V = V_knots * 0.51444;
% Calculate angular velocity in radians per second
omega_rad_s = V / R;
% Convert angular velocity from radians per second to RPM
% 1 radian per second = (60 / (2 * pi)) RPM
Omega = omega_rad_s * (60 / (2 * pi));
freq_1_over_Omega = 1 / Omega;
%the flap moment aerodynamic coefficients for large V
M_b = -(1/10)*V;
M_u = 1/6;
%the propeller aerodynamic coefficients
H_u = V/2;
% Frequency ranges
f_pitch= 5:3:140;
f_yaw= 5:3:140;
divergence_map = [];
Rdivergence_map = [];
unstable = [];
% Modify the loop to iterate over time points
for i = 1:length(f_pitch)
for j = 1:length(f_yaw)
phi_steps = linspace(0, pi, 100); % Time steps within one period
for phi = phi_steps
% Angular frequencies for the current time point
w_omega_pitch = 2 * pi* f_pitch(i);
w_omega_yaw = 2 * pi * f_yaw(j);
K_psi = (w_omega_pitch^2) * I_psioverI_b;
K_theta = (w_omega_yaw^2) * I_thetaoverI_b;
% Define inertia matrix [M]
M_matrix = [I_thetaoverI_b + 1 + cos(2*phi), -sin(2*phi);
-sin(2*phi), I_psioverI_b + 1 – cos(2*phi)];
% Define damping matrix [D]
D11 = C_thetaoverI_b + h^2*gamma*H_u*(1 – cos(2*phi)) – gamma*M_b*(1 + cos(2*phi)) – (2 + 2*h*gamma*M_u)*sin(2*phi);
D12 = h^2*gamma*H_u*sin(2*phi) + gamma*M_b*sin(2*phi) – 2*(1 + cos(2*phi)) – 2*h*gamma*M_u*cos(2*phi);
D21 = h^2*gamma*H_u*sin(2*phi) + gamma*M_b*sin(2*phi) + 2*(1 – cos(2*phi)) – 2*h*gamma*M_u*cos(2*phi);
D22 = C_psioverI_b + h^2*gamma*H_u*(1 + cos(2*phi)) – gamma*M_b*(1 – cos(2*phi)) + (2 + 2*h*gamma*M_u)*sin(2*phi);
D_matrix = [D11, D12;
D21, D22];
% Define stiffness matrix [K]
K11 = K_theta – h*gamma*V*H_u*(1 – cos(2*phi)) + gamma*V*M_u*sin(2*phi);
K12 = -h*V*gamma*H_u*sin(2*phi) + gamma*V*M_u*(1 + cos(2*phi));
K21 = -h*gamma*V*H_u*sin(2*phi) – gamma*V*M_u*(1 – cos(2*phi));
K22 = K_psi – h*gamma*V*H_u*(1 + cos(2*phi)) – gamma*V*M_u*sin(2*phi);
K_matrix = [K11, K12;
K21, K22];
% Compute the system matrices
M11 = M_matrix(1, 1); M12 = M_matrix(1, 2); M21 = M_matrix(2, 1); M22 = M_matrix(2, 2);
D11 = D_matrix(1, 1); D12 = D_matrix(1, 2); D21 = D_matrix(2, 1); D22 = D_matrix(2, 2);
K11 = K_matrix(1, 1); K12 = K_matrix(1, 2); K21 = K_matrix(2, 1); K22 = K_matrix(2, 2);
% Find the roots of the polynomial equation
P0 = M11*M22-M12*M21;
P1 = (- D11*M22*1j – D22*M11*1j + M12*D21*j + D12*M21*j);
P2 = (D11*D22*(1j)^2 – K22*M11 – K11*M22 – D12*D21*(1j)^2 + M12*K21 + M21*K12);
P3 = (D11*K22*1j – D12*K21*1j – D21*K12*1j + D22*K11*1j);
P4 = K11*K22 – K12*K21;
P = roots([P0, P1, P2, P3, P4]);
r = 1 * P;
%Flutter
for k = 1:length(r)
if (real(r(k)) > 0)
if (imag(r(k)) <= 0)
unstable = [unstable; phi, K_psi, K_theta];
% Proximity check for 1/Ω divergence
if abs(real(r(k)) – freq_1_over_Omega) < 0.1
Rdivergence_map = [Rdivergence_map; phi, K_psi, K_theta];
end
end
end
end
%Divergence
if (real(det(K_matrix)) < 0)
divergence_map = [divergence_map; phi, K_psi, K_theta];
end
end
end
end
% Plotting section
figure;
hold on;
scatter(unstable(:,2), unstable(:,3), ‘filled’);
scatter(divergence_map(:,2), divergence_map(:,3), ‘filled’, ‘r’);
scatter(Rdivergence_map(:,2), Rdivergence_map(:,3), ‘filled’, ‘g’);
xlabel(‘K_psi’);
ylabel(‘K_theta’);
title(‘Whirl Flutter Diagram’);
legend(‘Flutter area’, ‘Divergence area’, ‘1/Ω Divergence area’);
hold off; stability theory, floquet theorem, characteristic multiplier, periodic coeffcients MATLAB Answers — New Questions
similarity gives a message something went wrong try again
I have even tried to reinstall office 365. No luck
I have even tried to reinstall office 365. No luck Read More
Reps in Friedman test
Hi, I want to do Friedman test on a test data where data from an individual has been collected for 18 days. I have 4 groups with 5, 7, 8, and 6 individuals in each group. If I am understanding correctly, then the data should be in the following format:
[D11 D11
D21 D21
D31 D31
D12 D12];
So basically , each column would have 18*n group individuals and each column would represent different group. I want to make sure I am understanding the reqs correctly. Also, how would I represent the reps in this case? The code gives me bad rep number.
Thank you.Hi, I want to do Friedman test on a test data where data from an individual has been collected for 18 days. I have 4 groups with 5, 7, 8, and 6 individuals in each group. If I am understanding correctly, then the data should be in the following format:
[D11 D11
D21 D21
D31 D31
D12 D12];
So basically , each column would have 18*n group individuals and each column would represent different group. I want to make sure I am understanding the reqs correctly. Also, how would I represent the reps in this case? The code gives me bad rep number.
Thank you. Hi, I want to do Friedman test on a test data where data from an individual has been collected for 18 days. I have 4 groups with 5, 7, 8, and 6 individuals in each group. If I am understanding correctly, then the data should be in the following format:
[D11 D11
D21 D21
D31 D31
D12 D12];
So basically , each column would have 18*n group individuals and each column would represent different group. I want to make sure I am understanding the reqs correctly. Also, how would I represent the reps in this case? The code gives me bad rep number.
Thank you. friedman test, non-parametric, statistics MATLAB Answers — New Questions
Windows 11 Insider Preview 10.0.26120.1330 Not
I cannot seem to get this update and the other update along with this caused one of my 2 displays not to work and any video software like AMD, filmora, and adobe not to work anymore on my computer. Something is off and I worked with one of the tech guys with no luck.
I cannot seem to get this update and the other update along with this caused one of my 2 displays not to work and any video software like AMD, filmora, and adobe not to work anymore on my computer. Something is off and I worked with one of the tech guys with no luck. Read More
Combined Discrete-Continuous Simulation In SIMULINK
I am not even sure if that is the right title for this question.
Here’s the question:
How to implement the following dynamic system in Simulink?
Here’s the problem:
Time points are used to establish a uniform time grid on the interval , where the constant step size is . The solver is assumed to be at the beginning of the time step , where the state at the current time , is known, and the objective is to compute the next state through the relation , where is described as follows:
is first transformed to through some algebraic functions,
an IVP is set up with its initial condition set to . This IVP is then solved using a variable step ODE solver from to ,
the solution at time , is then mapped to the next state by some other algebraic mappings.
The following figure shows how the state is propagated thorugh time, in a single step:
In the output, I need the intermediate solutions (denoted by x) in each step, as well as the state variables .This can be easily done in a script, but I am looking for a way to do it in Simulink; which may be trivial problem, but I am really confused at this moment and I can’t really find a way to do it.
In some ways, in each step, the continuous-time subsystem waits for the input to be available, and once it is there, the external solver "waits" for the continuous-time subsystem to locally solve the continuous-time dynamical equations using an adaptive step-size solver, then the external solver receives this subsystem’s output and continuous to perform the remaining functions to produce . I feel like this should be logical workflow of the simulation, but I am not sure how Simulink treats problems of this type.I am not even sure if that is the right title for this question.
Here’s the question:
How to implement the following dynamic system in Simulink?
Here’s the problem:
Time points are used to establish a uniform time grid on the interval , where the constant step size is . The solver is assumed to be at the beginning of the time step , where the state at the current time , is known, and the objective is to compute the next state through the relation , where is described as follows:
is first transformed to through some algebraic functions,
an IVP is set up with its initial condition set to . This IVP is then solved using a variable step ODE solver from to ,
the solution at time , is then mapped to the next state by some other algebraic mappings.
The following figure shows how the state is propagated thorugh time, in a single step:
In the output, I need the intermediate solutions (denoted by x) in each step, as well as the state variables .This can be easily done in a script, but I am looking for a way to do it in Simulink; which may be trivial problem, but I am really confused at this moment and I can’t really find a way to do it.
In some ways, in each step, the continuous-time subsystem waits for the input to be available, and once it is there, the external solver "waits" for the continuous-time subsystem to locally solve the continuous-time dynamical equations using an adaptive step-size solver, then the external solver receives this subsystem’s output and continuous to perform the remaining functions to produce . I feel like this should be logical workflow of the simulation, but I am not sure how Simulink treats problems of this type. I am not even sure if that is the right title for this question.
Here’s the question:
How to implement the following dynamic system in Simulink?
Here’s the problem:
Time points are used to establish a uniform time grid on the interval , where the constant step size is . The solver is assumed to be at the beginning of the time step , where the state at the current time , is known, and the objective is to compute the next state through the relation , where is described as follows:
is first transformed to through some algebraic functions,
an IVP is set up with its initial condition set to . This IVP is then solved using a variable step ODE solver from to ,
the solution at time , is then mapped to the next state by some other algebraic mappings.
The following figure shows how the state is propagated thorugh time, in a single step:
In the output, I need the intermediate solutions (denoted by x) in each step, as well as the state variables .This can be easily done in a script, but I am looking for a way to do it in Simulink; which may be trivial problem, but I am really confused at this moment and I can’t really find a way to do it.
In some ways, in each step, the continuous-time subsystem waits for the input to be available, and once it is there, the external solver "waits" for the continuous-time subsystem to locally solve the continuous-time dynamical equations using an adaptive step-size solver, then the external solver receives this subsystem’s output and continuous to perform the remaining functions to produce . I feel like this should be logical workflow of the simulation, but I am not sure how Simulink treats problems of this type. simulink, simulation MATLAB Answers — New Questions
PivotBy & GroupBy
When will these functions be available in Excel 365? I keep seeing YouTube videos on how to use, but still not available in my version of Excel. I am not part of beta group.
When will these functions be available in Excel 365? I keep seeing YouTube videos on how to use, but still not available in my version of Excel. I am not part of beta group. Read More
شـيخـ روحاني شهير 🔴00.966.540966.983🟢 طلاسم التحصين & المحبة
شـيخـ روحاني شهير :red_circle:00.966.540966.983🟢 طلاسم التحصين & المحبة
، فك السحر ،
رد المطلقة ،
جلب الحبيب،
خواتم روحانية،
عرق السواحل،
فرج الضبعة،
تزويج البائر،
تسهيل الزواج ،
علاج العقم،
تفريق وطلاق ،
طاعة عمياء،
عقد لسان الظالم ،
جلب الحبيب السعودية ،
خ روحاني،
شيخة،
روحانية،
ساحر،
مشعوذ،
سحر أسود،
سحر تفريق،
سحر علوي ،
جلب الحبيب البحرين،
جلب الحبيب عُمان
السعودية
الكويت
قطر
البحرين
الامارات
شـيخـ روحاني شهير :red_circle:00.966.540966.983🟢 طلاسم التحصين & المحبة، فك السحر ،رد المطلقة ،جلب الحبيب،خواتم روحانية،عرق السواحل،فرج الضبعة،تزويج البائر،تسهيل الزواج ،علاج العقم،تفريق وطلاق ،طاعة عمياء،عقد لسان الظالم ،جلب الحبيب السعودية ،خ روحاني،شيخة،روحانية،ساحر،مشعوذ،سحر أسود،سحر تفريق،سحر علوي ،جلب الحبيب البحرين،جلب الحبيب عُمانالسعوديةالكويتقطرالبحرينالامارات Read More
جـلب الــحبيب ايطاليا /🟠00.973.343289.55 🟠 / تنزيل الأموال الروحي الآمن ألمانيا السويد
جـلب الــحبيب ايطاليا /🟠00.973.343289.55 🟠 / تنزيل الأموال الروحي الآمن ألمانيا السويد
جـلب الــحبيب ايطاليا /🟠00.973.343289.55 🟠 / تنزيل الأموال الروحي الآمن ألمانيا السويد Read More
جـلب الــحبيب سويسرا ” 🟡00.973.33766.836🟡 ” تنزيل الأموال المستمر
جـلب الــحبيب سويسرا ” 🟡00.973.33766.836🟡 ” تنزيل الأموال المستمر
جـلب الــحبيب سويسرا ” 🟡00.973.33766.836🟡 ” تنزيل الأموال المستمر Read More
how can i make a parent – children hierarchy
Hello
i have two column one is number of hiarachy the second is the name of that hiarachy like this :
can you help make a code that will generate what is manually wrote in the third column , note that the file is large and contain long WBS path like this (2.2.3.5.4.5.7)
RegardsHello
i have two column one is number of hiarachy the second is the name of that hiarachy like this :
can you help make a code that will generate what is manually wrote in the third column , note that the file is large and contain long WBS path like this (2.2.3.5.4.5.7)
Regards Hello
i have two column one is number of hiarachy the second is the name of that hiarachy like this :
can you help make a code that will generate what is manually wrote in the third column , note that the file is large and contain long WBS path like this (2.2.3.5.4.5.7)
Regards data, excel, matlab, matrix, importing excel data, code MATLAB Answers — New Questions
MS Word Create Table of Contents (TOC)
Been following directions to have MS Word create a Table of Contents (TOC) for chapters in a book. Table does appear, but with only one item in it: the table itself with its page #. But I can’t get it to “see” all the chapters.
The chapter titles have their own style which is supposed to cause the “automatic” TOC function to be able to include them in the TOC.
I gave the TOC itself that same chapter style, so that may be why it listed itself, but it won’t list any other chapters.
Thanks for any clues
Been following directions to have MS Word create a Table of Contents (TOC) for chapters in a book. Table does appear, but with only one item in it: the table itself with its page #. But I can’t get it to “see” all the chapters. The chapter titles have their own style which is supposed to cause the “automatic” TOC function to be able to include them in the TOC. I gave the TOC itself that same chapter style, so that may be why it listed itself, but it won’t list any other chapters. Thanks for any clues Read More
License needed for access to Planner as an individual
What are the opportunities to use Planner for a family plan of O365?
I have been a user of ToDo and previous user of Planner – in a previous corporate position.
I now have a small consulting business, with multiple clients/multiple projects and manage a non-profit – as well as general home based projects. The features of Planner will be very useful for me – but I cannot seem to find a way to gain access to Planner.
Any help will be appreciated.
What are the opportunities to use Planner for a family plan of O365?I have been a user of ToDo and previous user of Planner – in a previous corporate position.I now have a small consulting business, with multiple clients/multiple projects and manage a non-profit – as well as general home based projects. The features of Planner will be very useful for me – but I cannot seem to find a way to gain access to Planner. Any help will be appreciated. Read More
معالج جلب الحبيب♻️ -٩ِ٦ِ٦ِْ٥ِ٥٥ِْ٨ِْ٤ِ٩ِ٢ِِ٦ِ٤ ٠َ٠ -♻️رقم شيخ روحاني بالــســعـوديـة
معالج جلب الحبيب:recycling_symbol: -٩ِ٦ِ٦ِْ٥ِ٥٥ِْ٨ِْ٤ِ٩ِ٢ِِ٦ِ٤ ٠َ٠ -:recycling_symbol:رقم شيخ روحاني بالــســعـوديـة
فك السحر
رد المطلقة
رقم معالج روحاني
الكويت
قطر
الامارات
عُمان
البحرين
معالج جلب الحبيب:recycling_symbol: -٩ِ٦ِ٦ِْ٥ِ٥٥ِْ٨ِْ٤ِ٩ِ٢ِِ٦ِ٤ ٠َ٠ -:recycling_symbol:رقم شيخ روحاني بالــســعـوديـةفك السحر رد المطلقةرقم معالج روحانيالكويتقطرالاماراتعُمانالبحرين Read More
جـلبـ الـحـبيبـ بالنور الأبرق (849264 00966555 )
جـلبـ الـحـبيبـ بالنور الأبرق (849264 00966555 )
رقم شيخ روحاني
رقم معالج روحاني
رد المطلقة
فك السحر
خواتم روحانية
سحر الطلاق
سحر التفريق
السعودية ، الكويت ، قطر ، الإمارات ، البحرين ، عُمان
جـلبـ الـحـبيبـ بالنور الأبرق (849264 00966555 )رقم شيخ روحانيرقم معالج روحانيرد المطلقةفك السحرخواتم روحانيةسحر الطلاقسحر التفريقالسعودية ، الكويت ، قطر ، الإمارات ، البحرين ، عُمان Read More
Trying to create Graph connector, can’t see menu options
I am trying to follow this microsoft tutuorial to create a graph connector: https://github.com/microsoftgraph/msgraph-sample-github-connector-python
I am a global admin in my own personal tenant (it is a paid subscription). The code in this repo creates a connection in azure, and I have no problem following the first part of it (the code successfully creates the connection, and I am able to create the schema for the connection.
The problem I have is that I can’t see the “Data Options” tab in my tenant.
Here is what the instructor sees:
here is what I see in my tenant:
Once again, I was able to create the schema for the connector via code, so I know it is there:
I am trying to follow this microsoft tutuorial to create a graph connector: https://github.com/microsoftgraph/msgraph-sample-github-connector-pythonI am a global admin in my own personal tenant (it is a paid subscription). The code in this repo creates a connection in azure, and I have no problem following the first part of it (the code successfully creates the connection, and I am able to create the schema for the connection. The problem I have is that I can’t see the “Data Options” tab in my tenant. Here is what the instructor sees:here is what I see in my tenant: Once again, I was able to create the schema for the connector via code, so I know it is there: Read More
Add a new Partition to a running CycleCloud SLURM cluster
Overview
Azure CycleCloud (CC) is a user-friendly platform that orchestrates High-Performance Computing (HPC) environments on Azure, enabling admins to set up infrastructure, job schedulers, filesystems and scale resources efficiently at any size. It’s designed for HPC administrators intent on deploying environments with specific schedulers.
SLURM, a widely-used HPC job scheduler, is notable for its open-source, scalable, fault-tolerant design, suitable for Linux clusters of any scale. SLURM manages user resources, workloads, accounting, monitoring, and supports parallel/distributed computing, organizing compute nodes into partitions.
This blog will specifically explain how to integrate a new partition into an active SLURM cluster within CycleCloud, without the need to terminate or restart the entire cluster.
Requirements/Versions:
CycleCloud Server (CC version used is 8.6.2)
Cyclecloud cli initialized on the CycleCloud VM
A Running Slurm Cluster
CycleCloud project used is 3.0.7
Slurm version used is 23.11.7-1
SSH and HTTPS access to CycleCloud VM
High Level Overview
Git clone the CC SLURM repo (not required if you already have a slurm template file)
Edit the Slurm template to add a new partition
Export parameters from the running SLURM cluster
Import the updated template file to the running cluster
Activate the new nodearray(s)
Update the cluster settings (VM size, core count, Image, etc)
Scale the cluster to create the nodes
Step 1: Git clone the CC SLURM repo
SSH into the CC VM and run the following commands:
sudo yum install -y git
git clone https://github.com/Azure/cyclecloud-slurm.git
cd cyclecloud-slurm/templates
ll
Step 2: Edit the SLURM template to add new partition(s)
Use your editor of choice (ie. vi, vim, Nano, VSCode remote, etc) to edit the “slurm.txt” template file:
cp slurm.txt slurm-part.txt
vim slurm-part.txt
The template file nodearray is the CC configuration unit that associates to a SLURM partition. There are 3 nodearrays defined in the default template:
hpc: tightly coupled MPI workloads with Infiniband (slurm.hpc = true)
htc: massively parallel throughput jobs w/o Infiniband (slurm.hpc = false)
dynamic: enables multiple VM types in the same partition
Choose the nodearray type for the new partition (hpc or htc) and duplicate the [[[nodearray …]]] config section. For example, to create a new nodearray named “GPU” based on the hpc nodearray (NOTE: hpc nodearray configs included for reference):
[[nodearray hpc]]
Extends = nodearraybase
MachineType = $HPCMachineType
ImageName = $HPCImageName
MaxCoreCount = $MaxHPCExecuteCoreCount
Azure.MaxScalesetSize = $HPCMaxScalesetSize
AdditionalClusterInitSpecs = $HPCClusterInitSpecs
EnableNodeHealthChecks = $EnableNodeHealthChecks
[[[configuration]]]
slurm.default_partition = true
slurm.hpc = true
slurm.partition = hpc
[[nodearray GPU]]
Extends = nodearraybase
MachineType = $GPUMachineType
ImageName = $GPUImageName
MaxCoreCount = $MaxGPUExecuteCoreCount
Azure.MaxScalesetSize = $HPCMaxScalesetSize
AdditionalClusterInitSpecs = $GPUClusterInitSpecs
EnableNodeHealthChecks = $EnableNodeHealthChecks
[[[configuration]]]
slurm.default_partition = false
slurm.hpc = true
slurm.partition = gpu
slurm.use_pcpu = false
NOTE: there can only be 1 “slurm.default_partition” and by default it is the HPC nodearray. Set the new one to false, or if you set it to true then change the HPC nodearray to false.
The “variables” in the nodearray config (ie. $GPUMachineType) are referred to as “Parameters” in CC. The Parameters are attributes exposed in the CC GUI to enable per cluster customization. Further down in the template file begins the Parameters configuration beginning with [parameters About] section. We need to add several configuration blocks throughout this section to correspond to the Parameters defined in the nodearray (ie. $GPUMachineType).
Add the GPUMachineType from HPCMachineType:
[[[parameter HPCMachineType]]]
Label = HPC VM Type
Description = The VM type for HPC execute nodes
ParameterType = Cloud.MachineType
DefaultValue = Standard_F2s_v2
[[[parameter GPUMachineType]]]
Label = GPU VM Type
Description = The VM type for GPU execute nodes
ParameterType = Cloud.MachineType
DefaultValue = Standard_F2s_v2
Add the GPUExecuteCoreCount from HPCExecuteCoreCount:
[[[parameter MaxHPCExecuteCoreCount]]]
Label = Max HPC Cores
Description = The total number of HPC execute cores to start
DefaultValue = 100
Config.Plugin = pico.form.NumberTextBox
Config.MinValue = 1
Config.IntegerOnly = true
[[[parameter MaxGPUExecuteCoreCount]]]
Label = Max GPU Cores
Description = The total number of GPU execute cores to start
DefaultValue = 100
Config.Plugin = pico.form.NumberTextBox
Config.MinValue = 1
Config.IntegerOnly = true
Add the GPUImageName from HPCImageName:
[[[parameter HPCImageName]]]
Label = HPC OS
ParameterType = Cloud.Image
Config.OS = linux
DefaultValue = almalinux8
Config.Filter := Package in {“cycle.image.centos7”, “cycle.image.ubuntu20”, “cycle.image.ubuntu22”, “cycle.image.sles15-hpc”, “almalinux8”}
[[[parameter GPUImageName]]]
Label = GPU OS
ParameterType = Cloud.Image
Config.OS = linux
DefaultValue = almalinux8
Config.Filter := Package in {“cycle.image.centos7”, “cycle.image.ubuntu20”, “cycle.image.ubuntu22”, “cycle.image.sles15-hpc”, “almalinux8”}
Add the GPUClusterInitSpecs from HPCClusterInitSpecs:
[[[parameter HPCClusterInitSpecs]]]
Label = HPC Cluster-Init
DefaultValue = =undefined
Description = Cluster init specs to apply to HPC execute nodes
ParameterType = Cloud.ClusterInitSpecs
[[[parameter GPUClusterInitSpecs]]]
Label = GPU Cluster-Init
DefaultValue = =undefined
Description = Cluster init specs to apply to GPU execute nodes
ParameterType = Cloud.ClusterInitSpecs
NOTE: Keep in mind that you can customize the “DefaultValue” for parameters as per your requirements, or alternatively, you can make changes directly within the CycleCloud graphical user interface.
Save the template file and exit (ie. :wq for vi/vim).
Step 3: Export parameters from the running SLURM cluster
You now have an updated SLURM template file to add a new GPU partition. The template will need to be “imported” into CycleCloud to overwrite the existing cluster definition. Before doing that, however, we need to export all the current cluster GUI parameter configs from the cluster into a local json file to use in the import process. Without this json file the cluster configs are all reset to the default values specified in the template file (and overwriting any customizations applied to the cluster in the GUI).
From the CycleCloud VM run the following command format:
cyclecloud export_parameters cluster_name > file_name.json
For my cluster the specific command is:
cyclecloud export_parameters jm-slurm-test > jm-slurm-test-params.json
cat jm-slurm-test-params.json
{
“UsePublicNetwork” : false,
“configuration_slurm_accounting_storageloc” : null,
“AdditionalNFSMountOptions” : null,
“About shared” : null,
“NFSSchedAddress” : null,
“loginMachineType” : “Standard_D8as_v4”,
“DynamicUseLowPrio” : false,
“configuration_slurm_accounting_password” : null,
“Region” : “southcentralus”,
“MaxHPCExecuteCoreCount” : 240,
“NumberLoginNodes” : 0,
“HTCImageName” : “cycle.image.ubuntu22”,
“MaxHTCExecuteCoreCount” : 10,
“AdditionalNFSExportPath” : “/data”,
“DynamicClusterInitSpecs” : null,
“About shared part 2” : null,
“HPCImageName” : “cycle.image.ubuntu22”,
“SchedulerClusterInitSpecs” : null,
“SchedulerMachineType” : “Standard_D4as_v4”,
“NFSSchedDiskWarning” : null,
…<truncated>
}
If the cyclecloud command does not work you may need to initialize the cli tool as described in the docs: https://learn.microsoft.com/en-us/azure/cyclecloud/how-to/install-cyclecloud-cli?view=cyclecloud-8#initialize-cyclecloud-cli
Step 4: Import the updated template file to the running cluster
To import the updated template to the running cluster in CycleCloud run the following command format:
cyclecloud import_cluster <cluster_name> -c Slurm -f <template file name> txt -p <parameter file name> –force
For my cluster the specific command is:
cyclecloud import_cluster jm-slurm-test -c Slurm -f slurm-part.txt -p jm-slurm-test-params.json –force
In the CycleCloud GUI we can now see the “gpu” nodearray has been added. Click on the “Arrays” tab in the middle panel as shown in the following screen capture:
The gpu nodearray is added to the cluster but it is not yet “Activated,” which means it is not yet available for use.
Step 5: Activate the new nodearray(s)
The cyclecloud start_cluster command will now kickstart the new nodearray activation using the following format:
cyclecloud start_cluster <cluster_name>
For my cluster the command is:
cyclecloud start_cluster jm-slurm-test
From the CycleCloud GUI we will see the gpu nodearray status will move to “Activation” and finally “Activated:”
Step 6: Update the cluster settings
Edit the cluster settings in the CycleCloud GUI to pick the “GPU VM Type” and “Max GPU Cores” in the “Required Settings” section:
Update the “GPU OS” and “GPU Cluster-Init” as needed in the “Advanced Settings” section:
Step 7: Scale the cluster to create the nodes
To this point we added the new nodearray to CycleCloud but SLURM does not yet know about the new GPU partition. We can see this from the scheduler VM with the sinfo command:
The final step is to “scale” the cluster to “pre-define” the compute nodes as needed by SLURM. The CycleCloud azslurm scale command will accomplish this:
Your cluster is now ready to use the new GPU partition.
SUMMARY
Adding a new partition to SLURM with Azure CycleCloud is a flexible and efficient way to update your cluster and leverage different types of compute nodes. You can follow the steps outlined in this article to create a new nodearray, configure the cluster settings, and scale the cluster to match the SLURM partition. By using CycleCloud and SLURM, you can optimize your cluster performance and resource utilization.
References:
CycleCloud Documentation
CycleCloud-SLURM Github repository
Microsoft Training for SLURM on Azure CycleCloud
Microsoft Tech Community – Latest Blogs –Read More
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for i=1:Time
while water_tank_soc(i-1) < Water_tank_capacity_max
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for i=1:Time
while water_tank_soc(i-1) < Water_tank_capacity_max
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