The effective algorithms for solving 2D and 3D boundary problems for elliptical partial differential equations, based on a domain decomposition method have been proposed. Asymptotically optimal multilevel algorithms for solving harmonic and bi-harmonic BVPS on polygonal domains for both quasi-uniform and nested refined meshes are developed . The 2D and 3D calculations of magnetic systems of Nuclotron (LHE) and L3 and dipole magnets for Alice experiment (CERN) have been carried out . The extrapolation methods for magnet data measurement in the EXCHARM set up have been proposed . Computations of the 3D magnetic fields of a spectrometer in the EXCHARM set up have been performed .