A new approach to the solution of electromagnetic problems with the impedance method

We propose a new approach based on the use of interpolation which provides a significant increase in the accuracy of electric potential calculation using the impedance method. In a rectangular three-dimensional grid, we use a first order interpolation function to describe the distribution of electric potential within each voxel of the mesh. The electric field obtained analytically from this function is used as a solution of the continuity equation applied to each node of the mesh. The system of node equations is then solved to obtain the potential distribution. The obtained results show that this technique provides better accuracy than the conventional impedance method. This approach is exemplified in this article in problems involving high dielectric constant and low conductivity media similar to biological materials.