Nonlinear boundary element method for two-dimensional magnetostatics

An interface formulation, successfully used for the solution of magnetostatic fields in piecewise homogeneous media, is extended to nonlinear media problems. The advantage of boundary integral techniques, in the reduction of problem dimensionality, is retained. This nonlinear boundary element method (BEM) algorithm alternates solution of the augmented interface equation with satisfaction of the constitutive media relations. Use of the M̄-B̄ chararteristics is shown to guarantee iteration stability because the slope approaches unity as μ tends to infinity. Isoparametric elements of second order are used for both geometry and sources to ensure high solution fidelity. Galerkin’s method is employed for discretization to matrix form. Each iteration requires only the product of the inverted system matrix with the augmented RHS. Examples include saturation of square and circular cylinders of high permeability in a uniform field. It is shown that with an optimal relaxation factor of 0.65, only 3–6 iterations are needed for convergence to 3% error tolerance in both magnetization and surface currents.