The charge simulation method (CSM) was first introduced for field calculation in high-voltage (HV) arrangements involving electrodes and two dielectrics at most. Each electrode is simulated by a set of charges inside it. The interface between the two dielectrics is simulated by two sets of charges, one set in each dielectric. The proposed method aims to extend the CSM for the first time to apply to arrangements with many electrodes and multi-dielectric layers. This represents the novelty of the method. Its intelligence lies in the proper selection of the simulation charges to be used for calculating the electric potential and field anywhere within the HV arrangement, following a systematic procedure. The method predicts potential and field values that coincide with their respective exact values in a single-core cable with multi coaxial-dielectric layers. For a dielectric-barrier discharge (DBD) arrangement having multi parallel-flat-dielectric layers with and without embedded electrodes, the method also predicts potential and field values that agree reasonably with those obtained using COMSOL software. The effectiveness of the embedded electrode in decreasing the field at the edge of the stressed electrode is verified by the proposed method in agreement with the experimental observations recorded for the investigated DBD arrangement.