Abstract
The paper describes the use of a computational fragments management automation system called LuNA (Language for Numerical Algorithms) for a fragmented solution for the problem of constructing an adaptive structured grid. The main idea behind LuNA is to use a high-level representation of an application's algorithm to enable it to automatically execute on hybrid node multicomputers without low-level programming by the researcher. The constructed computational grid structure is adapted to the values of the given function by solving the system of differential equations by the finite difference method. The inverse Beltrami equation is used as a differential meshing method. Several tests were carried out on a supercomputer using the described fragmented algorithm, including on a large number of threads for a mesh of 500 million nodes.