A PARALLEL EIGENSOLVER USING CONTOUR INTEGRATION FOR GENERALIZED EIGENVALUE PROBLEMS IN MOLECULAR SIMULATION

In the present paper, we consider a parallel method for computing interior eigenvalues and corresponding eigenvectors of generalized eigenvalue problems arisen from molecular orbital computation in biochemistry applications. Matrices in such applications are sparse but often have a relatively large number of nonzero elements, and we may require some eigenpairs in a specific part of the spectrum. We use contour integration to construct a desired subspace. Properties of the subspace obtained by numerical integration are discussed, and a parallel implementation is then presented. We report the numerical aspects and parallel performance of the proposed method with matrices derived from molecular orbital computation.