Active Plasma Resonance Spectroscopy (APRS) denotes a class of industry-compatible plasma diagnostic methods which utilize the natural ability of plasmas to resonate on or near the electron plasma frequency ωpe. The Multipole Resonance Probe (MRP) is a particular realization of APRS with a high degree of geometric and electric symmetry. The Ideal MRP(IMRP) is an even more symmetric idealization of that probe which is particularly suited for theoretical investigations. It consists of two hemispherical electrodes which dielectrically shielded from the plasma. In this contribution, a spectral kinetic scheme is presented to investigate the behavior of the IMRP in the low pressure regime. The scheme consists of two modules, the particle pusher and the field solver. The particle pusher integrates the equations of motion for the studied particle ensemble over a suitable time interval Δt. The Poisson solver, unlike the well-known particle-in-cell (PIC), determines the electric field at each particle position without employing a numerical grid. The proposed method overcomes the limitations of the cold plasma model and covers kinetic effects like collision-less damping.