Fast perturbation-based integral equation method with accelerated cartesian expansion

For the IC chips and microelectronic packaging structures, the mesh size of the objects after discretization is usually much smaller than the operating wavelength. Hence, many low-frequency full-wave engines were proposed to simulate this kind of structures with tiny meshes, which can solve the wideband problems from DC to microwave frequencies. An augmented electric field integral equation (A-EFIE) was proposed by introducing charges as additional unknowns to the current densities unknowns. As one of the simplest methods to remedy the low-frequency breakdown, it not only avoids the imbalance between the vector potential and the scalar potential in an easy manner, but also is independent on the selection of basis functions (can be used in Nyström-based algorithms). However, like other integral equation based methods such as Calderón multiplicative preconditioned EFIE (CMP-EFIE), magnetic field integral equation (MFIE), it suffers from the accuracy issue at low frequencies, where the current cannot be captured accurately due to the finite computer precision (Z. G. Qian and W. C. Chew, IEEE T-AP, vol. 58, no. 10, pp. 3256-3264, Oct. 2010). Hence, the perturbation method based on Taylor expansion was proposed as one of effective remedies. It needs to solve multiple equations at different orders, so that more memory usage and CPU time are needed, especially for the complex targets or large-scale real world problems.