The many-body problem in quantum mechanics is well-known for its complexity, but with the aid of supercomputers it should be possible to increase the accuracy of calculations by several orders of magnitude. The use of supercomputers, however, presents many problems - new methods and new approaches need to be developed. The long-range goal of this project is to develop parallel algorithms for atomic structure calculations, based on the proven multiconfiguration Hartree-Fock method (MCHF), that execute efficiently on vector/concurrent architectures such as the shared memory Cray Y-MP and the distributed memory Intel iPSC-RX hypercube. The first task is the revision of the finite difference methods used by MCHF to spline based methods for which higher accuracy and better vectorization properties have been achieved. The use of splines in MCHF atomic structure calculations, leads to large, sparse, generalized eigenvalue problems for which only a few eigenvalues and eigenvectors are needed. Often the problem is a non-linear, generalized eigenvalue problem. Another frequently occurring problem is the solution of large, sparse, structured systems of equations where parts of the matrix are dense. Vector/concurrent algorithms for these problems will be developed and incorporated into an atomic structure package based on the MCHF method.
