How to change the Jacobian settings (full, fixed, lumped) when using solvepde?

Anyone knows how to change the Jacobian setting (full, fixed, lumped) when using solvepde. The legacy pdenonlin allows you to change the setting, but it appears that solvepde does not have the option.

Thank you.

Answer 1

[J Philps]

You are right, Jacobian selection option is no longer supported in the new workflow introduced since R2016a. Note that even in pdenonlin, the Jacobian selection was limited to 2-D problems. Approximate Jacobian, by specifying ‘fixed’ or ‘lumped’ options, often results in convergence issues.

Could you please share your workflow and any possible reason to not use the default full Jacobian?

[Hassan Baji]

Thanks Philps,

Here is my a simple code I am trying to solve. My actual problem is 3D. It is actually a water seepage problem, which is very similar to heat transfer.

clc clear clf

tic

B = 10; H = 10; a = 2; km = 0.01; ki = 0.10; ti = 0.02;

ht = 100; hb = 0; grad = (ht - hb)/H;

model = createpde;

R = [3 4 -B/2 B/2 B/2 -B/2 -H/2 -H/2 H/2 H/2]';

C = [1, 0, 0, a]'; C = [C; zeros(length® - length(C), 1)];

gd = [R, C];

ns = char('R', 'C'); ns = ns';

sf = 'R-C';

[g, bt] = decsg(gd, sf, ns);

pdegplot(g,'EdgeLabels','on','FaceLabels','on') xlim(1.5*[-B/2, B/2]) ylim(1.5*[-H/2, H/2]) axis equal

pg = geometryFromEdges(model, g);

applyBoundaryCondition(model, 'dirichlet', 'edge', 2, 'u', ht); applyBoundaryCondition(model, 'dirichlet', 'edge', 4, 'u', hb); applyBoundaryCondition(model, 'neumann', 'edge', [1, 3], 'g', 0, 'q', 0);

g = @(region, state) gpdenonlin(region, state, ki, ti, a);

applyBoundaryCondition(model, 'neumann','edge', 5:8, 'g', g, 'q', 0, 'Vectorized', 'on');

specifyCoefficients(model,'m', 0, 'd', 0, 'c', -km, 'a', 0,'f', 0);

generateMesh(model, 'GeometricOrder','linear', 'Hmax', 0.5);

u = pdenonlin(model, -km, 0, 0,'Report','on', 'Jacobian', 'fixed'); results = createPDEResults(model, u);

[gcxu, gcyu] = evaluateCGradient(results); pdeplot(model,'XYData', u, 'Mesh', 'off', 'Contour', 'on', 'FlowData', [gcxu, gcyu]) axis equal

n = 20; xq = linspace(-B/2, B/2, n); yq = (-H/2)*ones(1, n); [qx, qy] = evaluateCGradient(results, xq, yq);

[p, e, t] = model.Mesh.meshToPet();

Qy = -trapz(xq, qy);

disp(Qy)

toc

The Neumann boundary condition is a function with the following code:

function gcoeff = gpdenonlin(region, state, ki, ti, a)

[theta, ~] = cart2pol(region.x, region.y);

hh = 4*del2(state.u, theta);

gcoeff(1, :) = -(ki*ti./a^2)*hh;

end

The problem is that, when you change the setting to "full", it does not converge.