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Convergence problems for magnetic circuit

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I am quite new in using Comsol and currently facing convergence problems in the following situation:

I want to solve the magnetic field in a magnetic circuit where I put a coil of a rectangular cross section modelled by addition of an External Current Density node. Properties of magnetic material are given by HB curve. I think everything is properly defined because for common magnetic materials the solution is converged without any significant problems and looks as expected. However, the convergence problems arise when the HB curve is quite steep for higher B. The solution hardly converges for quite rough mesh and for denser mesh which I need to use for further calculations it does not converge at all.

I was trying to solve the problem for lower excitation current density, where the solution converges, and use the converged solution as initial values in following study for higher excitation. However, it seems that such an approach does not help and I am looking for another hints how to overcome such problems. Has anybody faced anything like this?

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