The transport of charged particles, which can be described by the Maxwell-Ampere Nernst-Planck (MANP) framework, is essential in various applications including ion channels and semiconductors. We propose a decoupled structure-preserving numerical scheme for the MANP model in this work. The Nernst-Planck equations are treated by the implicit exponential time differencing method associated with the Slotboom transform to preserve the positivity of the concentrations. In order to be effective with the Fast Fourier Transform, additional diffusive terms are introduced into Nernst-Planck equations. Meanwhile, the correction is introduced in the Maxwell-Ampere equation to fulfill Gauss's law. The curl-free condition for electric displacement is realized by a local curl-free relaxation algorithm whose complexity is O(N). We present sufficient restrictions on the time and spatial steps to satisfy the positivity and energy dissipation law at a discrete level. Numerical experiments are conducted to validate the expected numerical accuracy and demonstrate the structure-preserving properties of the proposed method.

翻译：带电粒子的输运在离子通道和半导体等多种应用中至关重要，可由Maxwell-Ampère Nernst-Planck (MANP) 框架描述。本文中，我们为MANP模型提出了一种解耦的结构保持数值格式。Nernst-Planck方程采用与Slotboom变换相结合的隐式指数时间差分方法处理，以保持浓度的正性。为了与快速傅里叶变换有效结合，在Nernst-Planck方程中引入了额外的扩散项。同时，在Maxwell-Ampère方程中引入修正项以满足高斯定律。电位移的无旋条件通过一种计算复杂度为O(N)的局部无旋松弛算法实现。我们给出了时间和空间步长的充分限制条件，以确保在离散层面上满足正性定律和能量耗散定律。数值实验验证了所提方法具有预期的数值精度，并展示了其结构保持特性。