Due to the modern telescopes, we found that the Universe is filled with a cosmic web which is composed of interconnected filaments of galaxies separated by giant voids. The emergence of this large-scale structure is one of the major challenges of modern cosmology. We study this phenomenon with the help of relativistic N-body cosmological simulation based on General Relativity. It is well known that gravity is the main force responsible for the structure formation in the Universe. In the first part of my talk, I demonstrate that in the cosmological setting gravitational interaction undergoes an exponential cutoff at large cosmological scales. This effect is called cosmic screening. It arises due to the interaction of the gravitational field with the background matter. Then, I compare two competing relativistic approaches to the N-body simulation of the Universe large-scale structure: “gevolution” vs. “screening”. To this end, employing the corresponding alternative computer codes, I demonstrate that the corresponding power spectra are in very good agreement between the compared schemes. However, since the perturbed Einstein equations have much simpler form in the “screening” approach, the simulation with this code consumes less computational time, saving almost 40% of CPU (central processing unit) hours.