On the application of mosaic-skeleton approximations of matrices for the acceleration of computations in the vortex method for the three-dimensional Euler equations

Abstract

We study the possibility of using fast matrix multiplication methods for the approximation of the velocity field when solving the system of differential equations describing the vorticity transport in an ideal incompressible fluid in Lagrangian coordinates. We suggest a numerical scheme that permits effectively using the fast matrix multiplication (the method of mosaic-skeleton approximations). We show that the functions used for the computation of the velocity field and moving grids appearing in the solution of the problem permit one to use the above-mentioned method. We prove the convergence of the resulting numerical solution to the exact solution with regard of the error contributed by the use of the algorithm for approximate fast multiplication of matrices by vectors.