Related papers: A Parallel Direct Eigensolver for Sequences of Her…
We consider the problem of selecting the best variable-value strategy for solving a given problem in constraint programming. We show that the recent Embarrassingly Parallel Search method (EPS) can be used for this purpose. EPS proposes to…
Deep neural networks with large model sizes achieve state-of-the-art results for tasks in computer vision (CV) and natural language processing (NLP). However, these large-scale models are too compute- or memory-intensive for…
We consider multi-value expansion planning (MEP), a general bilevel optimization model in which a planner optimizes arbitrary functions of the dispatch outcome in the presence of a partially controllable, competitive electricity market. The…
The paper describes a sparse direct solver for the linear systems that arise from the discretization of an elliptic PDE on a two dimensional domain. The scheme decomposes the domain into thin subdomains, or ``slabs'' and uses a two-level…
It is customary to identify sparse matrices with the corresponding adjacency or incidence graph. For the solution of linear systems of equations using Gaussian elimination, the representation by its adjacency graph allows a symbolic…
Over the past decades, transformations between different classes of eigenvalue problems have played a central role in the development of numerical methods for eigenvalue computations. One of the most well-known and successful examples of…
This paper addresses the problem of parallelizing computations to study non-linear dynamics in large networks of non-locally coupled oscillators using heterogeneous computing resources. The proposed approach can be applied to a variety of…
This work studies the problem of maximizing a higher degree real homogeneous multivariate polynomial over the unit sphere. This problem is equivalent to finding the leading eigenvalue of the associated symmetric tensor of higher order,…
We propose a new parallel-in-time algorithm for solving optimal control problems constrained by discretized partial differential equations. Our approach, which is based on a deeper understanding of ParaExp, considers an overlapping…
The Helmholtz equation is related to seismic exploration, sonar, antennas, and medical imaging applications. It is one of the most challenging problems to solve in terms of accuracy and convergence due to the scalability issues of the…
In this paper, we propose a decomposition approach for eigenvalue problems with spatial symmetries, including the formulation, discretization as well as implementation. This approach can handle eigenvalue problems with either Abelian or…
We present an efficient and scalable algorithm for performing matrix-vector multiplications ("matvecs") for block Toeplitz matrices. Such matrices, which are shift-invariant with respect to their blocks, arise in the context of solving…
We consider PDE eigenvalue problems as they occur in two-dimensional photonic crystal modeling. If the permittivity of the material is frequency-dependent, then the eigenvalue problem becomes nonlinear. In the lossless case, linearization…
In this article, we introduce a fast and memory efficient solver for sparse matrices arising from the finite element discretization of elliptic partial differential equations (PDEs). We use a fast direct (but approximate) multifrontal…
We propose a two-sided Lanczos method for the nonlinear eigenvalue problem (NEP). This two-sided approach provides approximations to both the right and left eigenvectors of the eigenvalues of interest. The method implicitly works with…
We present the capabilities and results of the Parallel Edge-based Tool for Geophysical Electromagnetic modeling (PETGEM), as well as the physical and numerical foundations upon which it has been developed. PETGEM is an open-source and…
We develop a new parallel algorithm for minimizing Lipschitz, convex functions with a stochastic subgradient oracle. The total number of queries made and the query depth, i.e., the number of parallel rounds of queries, match the prior…
We introduce a fast direct solver for variable-coefficient elliptic partial differential equations on surfaces based on the hierarchical Poincar\'e-Steklov method. The method takes as input an unstructured, high-order quadrilateral mesh of…
In this study, we develop a new parallel algorithm for solving systems of linear algebraic equations with the same block-tridiagonal matrix but with different right-hand sides. The method is a generalization of the parallel dichotomy…
The central importance of large scale 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…