Multigrid method: Difference between revisions

Revision as of 19:01, 17 March 2021

Revision as of 19:05, 7 September 2021

Line 26:

<syntaxhighlight lang="matlab">

function phi = V_Cycle(phi,f,h)

% Recursive V-Cycle Multigrid for solving the Poisson equation (\nabla^2 phi = f) on a uniform grid of spacing h

% Pre-Smoothing

phi = smoothing(phi,f,h);

% Compute Residual Errors

r = residual(phi,f,h);

% Restriction

rhs = restriction(r);

% Compute Residual Errors

eps = zeros(size(rhs));

r = residual(phi,f,h);

% Restriction

% stop recursion at smallest grid size, otherwise continue recursion

rhs = restriction(r);

if smallest_grid_size_is_achieved

eps = smoothing(eps,rhs,2*h);

else

eps = V_Cycle(eps,rhs,2*h);

end

% Prolongation and Correction

phi = phi + prolongation(eps);

% Post-Smoothing

phi = smoothing(phi,f,h);

end

eps = zeros(size(rhs));

% stop recursion at smallest grid size, otherwise continue recursion

if smallest_grid_size_is_achieved

eps = smoothing(eps,rhs,2*h);

else

eps = V_Cycle(eps,rhs,2*h);

end

% Prolongation and Correction

phi = phi + prolongation(eps);

% Post-Smoothing

phi = smoothing(phi,f,h);

end

</syntaxhighlight>

||

Line 59 ⟶ 58:

<syntaxhighlight lang="matlab">

function phi = F_Cycle(phi,f,h)

% Recursive F-cycle multigrid for solving the Poisson equation (\nabla^2 phi = f) on a uniform grid of spacing h

% Pre-smoothing

phi = smoothing(phi,f,h);

% Compute Residual Errors

r = residual(phi,f,h);

% Restriction

rhs = restriction(r);

% Compute Residual Errors

eps = zeros(size(rhs));

r = residual(phi,f,h);

% Restriction

% stop recursion at smallest grid size, otherwise continue recursion

rhs = restriction(r);

if smallest_grid_size_is_achieved

eps = smoothing(eps,rhs,2*h);

else

eps = F_Cycle(eps,rhs,2*h);

end

% Prolongation and Correction

phi = phi + prolongation(eps);

% Re-smoothing

phi = smoothing(phi,f,h);

eps = zeros(size(rhs));

% Compute residual errors

r = residual(phi,f,h);

% Restriction

rhs = restriction(r);

% stop recursion at smallest grid size, otherwise continue recursion

if smallest_grid_size_is_achieved

eps = smoothing(eps,rhs,2*h);

else else

eps = V_CycleF_Cycle(eps,rhs,2*h);
end

end

% Prolongation and Correction

phi = phi + prolongation(eps);

% Prolongation and Correction

phi = phi + prolongation(eps);

% Re-smoothing

% Post- phi = smoothing(phi,f,h);

phi = smoothing(phi,f,h);

% Compute residual errors

r = residual(phi,f,h);

% Restriction

rhs = restriction(r);

% stop recursion at smallest grid size, otherwise continue recursion

if smallest_grid_size_is_achieved

eps = smoothing(eps,rhs,2*h);

else

eps = V_Cycle(eps,rhs,2*h);

end

% Prolongation and Correction

phi = phi + prolongation(eps);

% Post-smoothing

phi = smoothing(phi,f,h);

end

</syntaxhighlight>

Line 110 ⟶ 109:

<syntaxhighlight lang="matlab">

function phi = W_cycle(phi,f,h)

% Recursive W-cycle multigrid for solving the Poisson equation (\nabla^2 phi = f) on a uniform grid of spacing h

% Pre-smoothing

phi = smoothing(phi,f,h);

% Compute Residual Errors

r = residual(phi,f,h);

% Restriction

rhs = restriction(r);

eps = zeros(size(rhs));

% stop recursion at smallest grid size, otherwise continue recursion

if smallest_grid_size_is_achieved

eps = smoothing(eps,rhs,2*h);

else

eps = W_cycle(eps,rhs,2*h);

end

% Prolongation and correction

phi = phi + prolongation(eps);

% Re-smoothing

phi = smoothing(phi,f,h);

% Compute residual errors

% Pre-smoothing

phi r = smoothingresidual(phi,f,h);

% Compute Residual Errors

r = residual(phi,f,h);

% Restriction

rhs = restriction(r);

% Restriction

eps = zeros(size(rhs));

rhs = restriction(r);

% stop recursion at smallest grid size, otherwise continue recursion

if smallest_grid_size_is_achieved

eps = smoothing(eps,rhs,2*h);

else else

eps = W_cycle(eps,rhs,2*h);
end

end

% Prolongation and correction

phi = phi + prolongation(eps);

% Re-smoothing

phi = smoothing(phi,f,h);

% Prolongation and correction

% Compute residual errors

phi = phi + prolongation(eps);

r = residual(phi,f,h);

% Restriction

rhs = restriction(r);

% Post-smoothing

% stop recursion at smallest grid size, otherwise continue recursion

phi = smoothing(phi,f,h);

if smallest_grid_size_is_achieved

eps = smoothing(eps,rhs,2*h);

else

eps = W_cycle(eps,rhs,2*h);

end

% Prolongation and correction

phi = phi + prolongation(eps);

% Post-smoothing

phi = smoothing(phi,f,h);

end

</syntaxhighlight>