Abstract:
The interpolation and mosaic-skeleton methods for solving the problem of potential flow of a two-dimensional plate are compared. They compress the dense matrix of the linear system arising from the solution by the collocation method on an irregular grid. The first method is based on fast Fourier transform and linear interpolation with an auxiliary uniform grid. The second one is based on block-majorange approximation of the matrix. Both approaches demonstrate time and memory efficiency, but emphasize different structures in the matrix, which affects the solution of the linear system. For the utilized implementations of the mosaic-matching methods The skeleton method solves the system faster than the interpolation method, but consumes more memory, and its running time grows much more noticeably as the size of the system increases.
