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A multi-domain spectral method for computing very high precision 3-D stellarmodels is presented. The boundary of each domain is chosen in order to coincidewith a physical discontinuity (e.g. the star's surface). In addition, aregularization procedure is introduced to deal with the infinite derivatives onthe boundary that may appear in the density field when stiff equations of stateare used. Consequently all the physical fields are smooth functions on eachdomain and the spectral method is absolutely free of any Gibbs phenomenon,which yields to a very high precision. The power of this method is demonstratedby direct comparison with analytical solutions such as MacLaurin spheroids andRoche ellipsoids. The relative numerical error reveals to be of the order of$10^{-10}$. This approach has been developed for the study of relativisticinspiralling binaries. It may be applied to a wider class of astrophysicalproblems such as the study of relativistic rotating stars too.Comment: Minor changes, Phys. Rev. D in pres

Numerical approach for high precision 3D relativistic star models