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The space radiation environment comprises all of the nuclei in the periodic table with energies that extend from a fraction of an MeV/n to TeV/n. The vast range of projectile-target and energy combinations necessitates highly efficient and accurate cross section codes for use in radiation transport codes. As particles in the space radiation environment impinge on shielding materials, nuclear reactions, such as nuclear fragmentation, occur. One way of estimating nuclear fragmentation cross sections is to use an abrasion-ablation model, which describes how nucleons are dislodged from the nuclei as a result of nuclear collisions and the mechanism by which excited pre-fragments decay via particle emission to more stable states. The well-known partial wave solution method cannot be used directly for the computation of abrasion cross sections. Instead, abrasion cross sections may be computed by slightly altering the Eikonal solution method, which is a high energy (small scattering angle) approximation that depends on the nucleus-nucleus optical potential. The aim of the current work is to present two efficient methods for the computation of the Eikonal phase shift function. Analytic formulas of the optical potential are presented in the position-space representation for nuclei that are well-represented by harmonic-well nuclear matter densities ( A < 20), which reduces the Eikonal phase factor to an integration over a single dimension. Next, the Eikonal phase function is presented in the momentum-space representation, which is particularly useful when the Fourier transform of the position-space optical potential is known. These new methods increase the computational efficiency by three orders of magnitude and allow for rapid prediction of elastic differential, total, elastic, and reaction cross sections in the Eikonal approximation. [ABSTRACT FROM AUTHOR]