SIPs: Tailored parallelization of the generalized symmetric eigenproblem

Michael Sternberg, Materials Science Division, Argonne National Laboratory, 9700
S. Cass Ave., Argonne, IL 60439, Hong Zhang, Computer Science Department,
Illinois Institute of Technology, 10 West 31st Street, Chicago, IL 60616, Barry
Smith, Mathematics and Computer Science Division, Argonne National Laboratory,
9700 S. Cass Ave., Argonne, IL 60439, and Peter Zapol, Materials Science and
Chemistry Divisions, Argonne National Laboratory, 9700 S. Cass Ave., Argonne, IL
60439.

We present the development and initial applications of SIPs, a software package
created to compute large fractions of eigenpairs for sparse symmetric
generalized eigenvalue problems, such as those posed by DFTB. The
characteristics of typical eigenspectra include densely clustered eigenvalues
and wide gaps, which challenge the efficiency and robustness of the solver. The
package implements multiple shift-and-invert spectral transformations on
parallel computers and uses the existing software packages SLEPc and PETSc. We
describe the object-oriented design and implementation in SIPs, and demonstrate
numerical performance on an advanced distributed computer.