3 research outputs found
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, in some eigenproblem sequences there is a connection between the
solutions of adjacent eigenproblems. Whenever it is possible to unravel the
existence of such a connection, the eigenproblem sequence is said to be
correlated. When facing with a sequence of correlated eigenproblems the current
strategy amounts to solving each eigenproblem in isolation. We propose a
alternative 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 matrix-vector multiplications and parallelized using the Elemental
library framework. Numerical results show that ChFSI achieves excellent
scalability and is competitive with current dense linear algebra parallel
eigensolvers.Comment: 23 Pages, 6 figures. First revision of an invited submission to
special issue of Concurrency and Computation: Practice and Experienc
Parallel eigensolvers in plane-wave Density Functional Theory
We consider the problem of parallelizing electronic structure computations in
plane-wave Density Functional Theory. Because of the limited scalability of
Fourier transforms, parallelism has to be found at the eigensolver level. We
show how a recently proposed algorithm based on Chebyshev polynomials can scale
into the tens of thousands of processors, outperforming block conjugate
gradient algorithms for large computations
ChASE: Chebyshev Accelerated Subspace iteration Eigensolver for sequences of Hermitian eigenvalue problems
Solving dense Hermitian eigenproblems arranged in a sequence with direct
solvers fails to take advantage of those spectral properties which are
pertinent to the entire sequence, and not just to the single problem. When such
features take the form of correlations between the eigenvectors of consecutive
problems, as is the case in many real-world applications, the potential benefit
of exploiting them can be substantial. We present ChASE, a modern algorithm and
library based on subspace iteration with polynomial acceleration. Novel to
ChASE is the computation of the spectral estimates that enter in the filter and
an optimization of the polynomial degree which further reduces the necessary
FLOPs. ChASE is written in C++ using the modern software engineering concepts
which favor a simple integration in application codes and a straightforward
portability over heterogeneous platforms. When solving sequences of Hermitian
eigenproblems for a portion of their extremal spectrum, ChASE greatly benefits
from the sequence's spectral properties and outperforms direct solvers in many
scenarios. The library ships with two distinct parallelization schemes,
supports execution over distributed GPUs, and it is easily extensible to other
parallel computing architectures.Comment: 33 pages. Submitted to ACM TOM