Abstract <p>In the article, interpolation-based and mosaic-skeleton approaches for solving the problem of the potential flow of a plate are compared. They compress a dense matrix of a linear system, arising in the collocation method on the non-uniform grid. The first method relies on Fast Fourier Transform and linear interpolation from an additional uniform grid. The second uses block low-rank approximation of a matrix. Both techniques demonstrate effectiveness in time and memory but distinguish different structures in a matrix, which affects the solution of a linear system. In our implementation, the mosaic-skeleton method solves the problem quicker than its competitor. Still, it consumes more memory, and its duration grows more significantly with an increase in the size of a system.</p>