相关论文: Hybrid Numerical Solvers for Massively Parallel Ei…

Quadratic eigenvalue problems (QEP) and more generally polynomial eigenvalue problems (PEP) are among the most common types of nonlinear eigenvalue problems. Both problems, especially the QEP, have extensive applications. A typical approach…

Message-passing graph neural network interatomic potentials (GNN-IPs), particularly those with equivariant representations such as NequIP, are attracting significant attention due to their data efficiency and high accuracy. However,…

The last ten years have witnessed fast spreading of massively parallel computing clusters, from leading supercomputing facilities down to the average university computing center. Many companies in the private sector have undergone a similar…

We describe a parallel solver for the discretized weakly singular space-time boundary integral equation of the spatially two-dimensional heat equation. The global space-time nature of the system matrices leads to improved parallel…

Heterogeneous systems are becoming more common on High Performance Computing (HPC) systems. Even using tools like CUDA and OpenCL it is a non-trivial task to obtain optimal performance on the GPU. Approaches to simplifying this task include…

This paper advocates for an intertwined design of the dense linear algebra software stack that breaks down the strict barriers between the high-level, blocked algorithms in LAPACK (Linear Algebra PACKage) and the low-level,…

Large-scale eigenvalue computations on sparse matrices are a key component of graph analytics techniques based on spectral methods. In such applications, an exhaustive computation of all eigenvalues and eigenvectors is impractical and…

As we rapidly approach the frontiers of ultra large computing resources, software optimization is becoming of paramount interest to scientific application developers interested in efficiently leveraging all available on-Node computing…

In this paper, we propose a hybrid parallel programming approach for a numerical solution of a two-dimensional acoustic wave equation using an implicit difference scheme for a single computer. The calculations are carried out in an implicit…

We present a new implementation of the numerical integration of the classical, gravitational, N-body problem based on a high order Hermite's integration scheme with block time steps, with a direct evaluation of the particle-particle forces.…

We present a parallel computing strategy for a hybridizable discontinuous Galerkin (HDG) nested geometric multigrid (GMG) solver. Parallel GMG solvers require a combination of coarse-grain and fine-grain parallelism to improve time to…

Numerical studies of shock waves in large scale systems via kinetic simulations with millions of particles are too computationally demanding to be processed in serial. In this work we focus on optimizing the parallel performance of a…

The Hypergraph Partitioning (HGP) problem is a well-studied problem that finds applications in a variety of domains. The literature on the HGP problem has heavily focused on developing fast heuristic approaches. In several application…

The Traveling Salesman Problem (TSP) is a well-known NP-hard combinatorial optimization problem with wide-ranging applications in logistics, routing, and intelligent systems. Due to its factorial complexity, solving large-scale instances…

Current algorithms for large-scale industrial optimization problems typically face a trade-off: they either require exponential time to reach optimal solutions, or employ problem-specific heuristics. To overcome these limitations, we…

In this work, we consider the reformulation of hierarchical ($\mathcal{H}$) matrix algorithms for many-core processors with a model implementation on graphics processing units (GPUs). $\mathcal{H}$ matrices approximate specific dense…

Iterative methods for solving large sparse systems of linear equations are widely used in many HPC applications. Extreme scaling of these methods can be difficult, however, since global communication to form dot products is typically…

Prior work on Automatically Scalable Computation (ASC) suggests that it is possible to parallelize sequential computation by building a model of whole-program execution, using that model to predict future computations, and then…

The functional renormalisation group (fRG) has evolved into a versatile tool in condensed matter theory for studying important aspects of correlated electron systems. Practical applications of the method often involve a high numerical…

The Variational Quantum Eigensolver (VQE) is a hybrid quantum-classical algorithm for computing ground state energies of molecular systems. We implement VQE to calculate the potential energy surface of the hydrogen molecule (H$_2$) across…