COMSOL Multiphysics Approach

Broadly there are two: fully coupled (monolithic) and segregated. Fully coupled solving gathers every unknown — potential, temperature, displacement — into one system and solves it with Newton's method including how each affects the others. Convergence is fast and robust, but the matrix grows, raising memory and per-iteration time. Segregated solving solves each physics in turn and repeats: each pass is light, but strong coupling increases iterations and can prevent convergence. The choice depends on coupling strength and problem size. Here we compare both on a strongly coupled case — a device that conducts better as it warms.

Exactly. When a coupled calculation won't converge, many people first change relaxation factors or shrink time steps, but if physically no steady solution exists, no setting will converge it — and a forced answer would be more dangerous. To tell, tighten conditions gradually while tracking the solution (continuation) and see whether peak temperature shoots up and then ends. Here peak temperature rose 38 K between 22 and 23 V and ended about 0.3 V later. With that shape, the design should keep ample margin below it. A sudden rise in segregated iterations is also a warning that you are near the limit. The fully coupled method's advantage is tracking solutions right up to the edge with few iterations, so the limit is located correctly.

Related pages include convergence of coupled analysis, staggered coupling, co-simulation coupling, reduced-order models for coupled problems and Joule heating.