the basis set is increased until the relevant eigenvalues χ$_{k}$ and their corresponding weights p$_{k}$ have acquired the desired accuracy. A necessary test for convergence is the fulfillment of the sum rules ∑ k P$_{k,i}$ = 1 and ∑ i,k χ$_{k}$P$_{k,i}$ = 1 / 2 with sufficient accuracy [18, 19]. Usually the convergence is fast in both the number of quadrature points and the size of basis, unless the system has a tight junction where some care must be considered in order to achieve the required accuracy of the eigenmodes with the eigenvalues close to 1 / 2. For a sphere there is just one dipole-active eigenmode which has eigenvalue χ = 1 / 6 and weight p = 1, while for an ellipsoid there is one dipole-active eigenmode along each axis. Fast and accurate solutions are achieved for spheroids with a basis size of NB =20 and with NQ = 64 quadrature points. In general, the size of the basis and the number of the quadrature points increase with the number of cells in the cluster and with the decreasing of the junction size. Thus, for our numerical examples a basis with NB =35-40 and NQ = 128 quadrature points are enough for a converged solution in the case of the dimers and NB =50 and NQ = 200 quadrature points in the case of the clusters with up to four cells. The equation r ( θ ) = ( h +cos 2 θ ) / (1 − a cos 2 θ ) describes the shape of a two-particle cluster. Parameter h controls the tightness of the inter-particle junction and parameter a measures the deviation from a spherical shape. More precisely, h is the radius of the smallest circle at around the thinnest part of the junction. Figure 1 shows the effective permittivity for a suspension of particles with the following parameters: ε$_{1}$ = 70, σ$_{1}$ = 0 . 25 S/m, ε$_{S}$ = 6, σ$_{S}$ = 0, ε$_{0}$ = 81, σ$_{0}$ = 0 . 374 S/m, volume fraction f = 0 . 05, membrane thickness δ = 0 . 00947275, and a = 0 . 2. The effective per- mittivity does not depend on the thickness parameter h when the stimulus electric field is perpendicular to the cluster axis. However, a new relaxation becomes apparent as h → 0, for parallel fields [3, 25]. Figure 2 presents the first 7 eigenvalues χ$_{k}$ and their weights P$_{k,}$$_{1}$ for a field parallel to the z axis. As the junction become tighter ( h → 0) more eigenvalues become dipole- active. While all eigenvalues are important in shaping the dielectric spectrum, the second largest eigenvalue χ$_{2}$ is crucial to explaining the occurrence of an additional relaxation at low frequencies, as observed for small h in [3, 25]. Although its weight P$_{2}$$_{,}$$_{1}$ also decreases for 14 B. Two cells joined by tight junction