swMATH ID: 
42180

Software Authors: 
WilliamsYoung, David B.; Beckman, Paul G.; Yang, Chao

Description: 
A shift selection strategy for parallel shiftinvert spectrum slicing in symmetric selfconsistent eigenvalue computation. The central importance of largescale eigenvalue problems in scientific computation necessitates the development of massively parallel algorithms for their solution. Recent advances in dense numerical linear algebra have enabled the routine treatment of eigenvalue problems with dimensions on the order of hundreds of thousands on the world’s largest supercomputers. In cases where dense treatments are not feasible, Krylov subspace methods offer an attractive alternative due to the fact that they do not require storage of the problem matrices. However, demonstration of scalability of either of these classes of eigenvalue algorithms on computing architectures capable of expressing massive parallelism is nontrivial due to communication requirements and serial bottlenecks, respectively. In this work, we introduce the SISLICE method: a parallel shiftinvert algorithm for the solution of the symmetric selfconsistent field (SCF) eigenvalue problem. The SISLICE method drastically reduces the communication requirement of current parallel shiftinvert eigenvalue algorithms through various shift selection and migration techniques based on density of states estimation and kmeans clustering, respectively. This work demonstrates the robustness and parallel performance of the SISLICE method on a representative set of SCF eigenvalue problems and outlines research directions that will be explored in future work. 
Homepage: 
https://arxiv.org/abs/1908.06043

Keywords: 
eigenvalues;
parallel eigenvalue algorithms;
selfconsistent field;
shiftinvert spectrum slicing

Related Software: 
SIESTA;
NWChemEx;
EVSL;
kmeans++;
ELPA;
SparseMatrix;
ARPACK;
METIS;
MUMPS;
ScaLAPACK;
PARDISO;
LAPACK

Cited in: 
1 Publication
