The LuNA library of parallel numerical fragmented subroutines is now under development. It is aimed at automated treatment of a range of important and stubborn properties of numerical subroutines. The method of algorithm and program fragmentation is used. The library is being developed with the LuNA fragmented programming system. It provides all the necessary properties of subroutines and their high portability.

The paper presents the design and the first stage of implementation of the NumGRID middleware that is devoted to the development of the multicomputer grid software for the large scale numerical simulation. Global addressing of the NumGRID computational resources and MPI programs execution is provided. This stage is the basis for the development of supporting system that automatically provides the dynamic properties of MPI applications.

With evolution of mathematical modeling and creation of high-performance computer systems, many scientific applications have appeared, demanding an increase in computational performance higher than any of available supercomputers can provide. In this connection, it seems necessary to integrate several supercomputers, i.e., to create a grid. Not every application can effectively be solved on grids because of low capacity of communications networks. However, such applications as the search for alien civilizations and decoding the human genome were successfully run on grids (http://setiathome.berkeley.edu). In recent years, many large-scale problems have appeared in numerical modeling (evolution of a proto-planetary disk, evolution of galaxies, problems of plasma physics). Their solution demands integration of several multicomputers. Another problem is the fast progress in microprocessor development which forces to use heterogeneous computer systems for solution of the largescale problems. In particular, in 2005, the ICM&MG (Siberian Branch of the Russian Academy of Sciences) is planning to exploit the following multicomputers: a cluster of MVS-1000 type based on 3L Alpha EV68 microprocessors (833 MHz), another MVS-1000 cluster based on 128 Alpha EV67 microprocessors (633 MHz), and a multicomputer based on 32 Intel Itanium processors. Therefore, there is a necessity to create the software, which should provide the large-scale simulation in such heterogeneous environments. In 2003, the co-operative project NumGRID intended for the creation of the necessary grid system software, started in Novosibirsk (ICM&MG) and Marseille (L3M CNRS).

A digital electromagnetic model of electric power system is suggested. The parallel and the sequential algorithms to solve the equation set are described. Implementation of the parallel algorithm on k processors provides more then k times speedup.