PFEAST: a high performance sparse eigenvalue solver using distributed-memory linear solvers
James Kestyn,Vasileios Kalantzis,Eric Polizzi,Yousef Saad +3 more
- 13 Nov 2016
- pp 178-189
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TL;DR: This paper highlights a recent development within the software package that allows the dominant computational task, solving a set of complex linear systems, to be performed with a distributed memory solver.
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Abstract: The FEAST algorithm and eigensolver for interior eigenvalue problems naturally possesses three distinct levels of parallelism. The solver is then suited to exploit modern computer architectures containing many interconnected processors. This paper highlights a recent development within the software package that allows the dominant computational task, solving a set of complex linear systems, to be performed with a distributed memory solver. The software, written with a reverse-communication-interface, can now be interfaced with any generic MPI linear-system solver using a customized data distribution for the eigenvector solutions. This work utilizes two common "black-box" distributed memory linear-systems solvers (Cluster-MKL-Pardiso and MUMPS), as well as our own application-specific domain-decomposition MPI solver, for a collection of 3-dimensional finite-element systems. We discuss and analyze how parallel resources can be placed at all three levels simultaneously in order to achieve good scalability and optimal use of the computing platform.
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Citations
SMASH: Co-designing Software Compression and Hardware-Accelerated Indexing for Efficient Sparse Matrix Operations
Konstantinos Kanellopoulos,Nandita Vijaykumar,Christina Giannoula,Roknoddin Azizi,Skanda Koppula,Nika Mansouri Ghiasi,Taha Shahroodi,Juan Gómez Luna,Onur Mutlu +8 more
- 12 Oct 2019
TL;DR: In this article, the authors propose a hardware-software cooperative mechanism that enables highly efficient indexing and storage of sparse matrices by explicitly enabling the hardware to recognize and exploit sparsity in data.
63
All-electron density functional theory and time-dependent density functional theory with high-order finite elements
TL;DR: In this article, an all-electron method which employs high-order hierarchical finite element bases is presented for static density functional theory and time-dependent density functional analysis calculations, in which structured atomic meshes are merged to an unstructured molecular mesh, allowing a highly nonuniform discretization of the space.
Complex Moment-Based Supervised Eigenmap for Dimensionality Reduction
Akira Imakura,Momo Matsuda,Xiucai Ye,Tetsuya Sakurai +3 more
- 17 Jul 2019
TL;DR: This work proposes a novel complex moment-based supervised eigenmap including multiple eigenvectors for dimensionality reduction and provides a general formulation for matrix trace optimization methods to incorporate with ridge regression, which models the linear dependency between covariate variables and univariate labels.
Beyond Automated Multilevel Substructuring: Domain Decomposition with Rational Filtering
TL;DR: This paper proposes a rational filtering domain decomposition technique for the solution of large and sparse symmetric generalized eigenvalue problems and integrates only a part of the matrix resolvent while it applies any orthogonalization necessary to vectors whose length is equal to the number of interface variables.
17
Block SS–CAA: A complex moment-based parallel nonlinear eigensolver using the block communication-avoiding Arnoldi procedure
Akira Imakura,Tetsuya Sakurai +1 more
- 01 May 2018
TL;DR: Numerical experiments indicate that the proposed block SS-CAA method has higher performance compared with traditional complex moment-based nonlinear eigensolvers, i.e., the block SS–Hankel and Beyn methods.
17
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