A combination of the mesh-based finite integration technique with a modal expansion is proposed for the solution of the eddy-current induction problem in geometries involving workpieces with translational or rotational symmetry and an arbitrary 3-D current excitation. The solution is expanded in a series of modes along the symmetry axis, and thus, the reduced Helmholtz equation is discretized and solved independently for each mode in the transversal plane. Finally, the impedance variation of the eddy-current probe is evaluated by means of the reciprocity theorem. The main advantage of the proposed decomposition relies on the use of a 2-D instead of the 3-D grid with the consequent reduction of the numerical noise and the smaller size of the resulting linear system, which allows the simultaneous treatment of different sources.

中文翻译：

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具有一个对称轴的零件的混合空间光谱涡流公式

建议将基于网格的有限积分技术与模态扩展相结合，以解决涉及具有平移或旋转对称性和任意 3-D 电流激励的工件的几何结构中的涡流感应问题。该解沿对称轴在一系列模式中展开，因此，简化的亥姆霍兹方程被离散化并针对横向平面中的每个模式独立求解。最后，通过互易定理评估涡流探头的阻抗变化。所提出的分解的主要优点依赖于使用 2-D 而不是 3-D 网格，随之而来的是数值噪声的减少和所得线性系统的更小尺寸，这允许同时处理不同来源。