Requires thousands of Newton Iterations in some configurations.

[coreqode]

Hello,

I’ve implemented the IPC algorithm using IPCToolkit with the convergent formulation, friction disabled, and adaptive stiffness enabled. In one of my demos—a cloth with approximately 20,000 vertices colliding against a mesh—the solver stalls in a slowly converging state. The Newton iterations climb past 1,000, while the inf-norm barely decreases (for example, at iteration 1167 the inf-norm is 0.00454121 and at iteration 1170 it’s only 0.00452964), and the maximum barrier stiffness remains fixed at 288,285.

I’ve attached a screenshot of the configuration where this occurs. Have you ever encountered a similar behavior, or might there be something I’m overlooking in my implementation?

Thanks for any insights.

timestep: 1 / 100
DMin: 0
DHat: 1e-2
InfNorm Threshold: 1e-4

Newton Iteration: 1167 infNorm: 0.00454121 max_barrier_stiffness: 288285 
Newton Iteration: 1168 infNorm: 0.00453734 max_barrier_stiffness: 288285
Newton Iteration: 1169 infNorm: 0.00453349 max_barrier_stiffness: 288285
Newton Iteration: 1170 infNorm: 0.00452964 max_barrier_stiffness: 288285 

[zfergus]

You are correct, that many iterations is not expected. Typically, for challenging steps, it can take 100–200 iterations to converge, but not 1000 unless some parameters are incorrect.

The most likely culprit is the barrier stiffness:

• Too small can result in small distances which make it challenging to perform collision detection reliably and efficiently.
• Too large can make the problem overly stiff and cause the solver to take too many iterations.

Here are some steps and questions to help debug:

1. What other energies are involved in the simulation?
2. The max_barrier_stiffness=288285, but what is the barrier stiffness in use?
3. Typically for the convergent formulation we use a fixed stiffness relative to the elastic material stiffness. For example, 0.1 * Young's modulus works well in many scenarios. This requires setting use_physical_barrier in BarrierPotential to true.
4. Are you using a direct or iterative linear solver? Direct solvers are typically the best choice because IPC has stiff barrier energies.
5. Inf-norm can be overly challenging to converge because it is a discontinuous measure. A better alternative might be an area-weighted L2-norm. E.g., $g^\top M g$ where $g$ is the gradient and $M$ is the mass matrix. You might also want to multiply by the time-step to remove that dependence, too.