Intercoupling of an incident electric field in metal nanoparticles causes asymmetric distribution of surface charges, which eventuates in shifting of the surface plasmon resonance frequency. This feature can be used in tuning the surface plasmon resonance and controlling the light absorption in a desired wavelength. This work provides a theoretical study of the plasmonic properties of complex gold nanostructures on a dielectric substrate where the nanoparticles have different morphologies. For analysis, we have developed a discrete dipole approximation with surface interactions-z, which is the third version of the MATLAB-based DDA-SI toolbox. In this version, lower-upper decomposition of the interaction matrix is used as a preconditioning of the LSQR iterative solver. This method accelerates the DDA-SI calculations by decreasing the total number of iteration steps and decreases the relative residual to achieve more accurate results. In the analysis, nanostructures are assumed to be gold dimers, trimers, and quadrumers with different sizes and elongations of cubical or spherical geometries on a BK7 substrate. The results show that absorption spectra exhibit both red- and blueshifted plasmon resonances in array, depending on the particle shape and elongation. The cubic structure of gold array provides the highest absorption efficiency, while the spherical structures give wider bandwidth; the combination of these structures could be used to design a system with intended features. We demonstrate that the geometrical symmetry plays an important role in the plasmon resonance of gold arrays, and it is shifted when the symmetry of the array is broken.