An Optimized and Scalable Eigensolver for Sequences of Eigenvalue Problems

In many scientific applications the solution of non-linear differential equations are obtained through the set-up and solution of a number of successive eigenproblems. These eigenproblems can be regarded as a sequence whenever the solution of one problem fosters the initialization of the next. In addition, some eigenproblem sequences show a connection between the solutions of adjacent eigenproblems. Whenever is possible to unravel the existence of such a connection, the eigenproblem sequence is said to be a correlated. When facing with a sequence of correlated eigenproblems the current strategy amounts to solving each eigenproblem in isolation. We propose a novel approach which exploits such correlation through the use of an eigensolver based on subspace iteration and accelerated with Chebyshev polynomials (ChFSI). The resulting eigensolver, is optimized by minimizing the number of matvec multiplications and parallelized using the Elemental library framework. Numerical results shows that ChFSI achieves excellent scalability and is competitive with current dense linear algebra parallel eigensolvers. ∗Article based on research supported by the Excellence Initiative of the German federal and state governments and the Jülich Aachen Research Alliance High-Performance Computing. †School of Mathematics, The University of Manchester, Alan Turing Building, M13 9PL, Manchester, United Kingdom. [email protected]. ‡Institute fo Advanced Simulation and Peter Grünberg Institut, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany. [email protected]. §Jülich Supercomputing Centre, Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, WilhelmJohnen strasse, 52425 Jülich, Germany. [email protected].