Related papers: Development of Krylov and AMG linear solvers for l…
Sparse General Matrix Multiply (SpGEMM) is key for various High-Performance Computing (HPC) applications such as genomics and graph analytics. Using the semiring abstraction, many algorithms can be formulated as SpGEMM, allowing…
This paper presents a heterogeneous adaptive mesh refinement (AMR) framework for efficient simulation of moderately stiff reactive problems. This framework features an elaborate subcycling-in-time algorithm along with a specialized…
GPUs are uniquely suited to accelerate (SQL) analytics workloads thanks to their massive compute parallelism and High Bandwidth Memory (HBM) -- when datasets fit in the GPU HBM, performance is unparalleled. Unfortunately, GPU HBMs remain…
Fueled by the ability to mine real-world graph data, GNN applications have experienced phenomenal growth. Sparse Matrix-Matrix Multiplication (SpMM) is a critical operator in GNNs. However, existing SpMM designs for GNNs struggle to adapt…
It is well known that for general linear systems, only optimal Krylov methods with long recurrences exist. For special classes of linear systems it is possible to find optimal Krylov methods with short recurrences. In this paper we consider…
The main objective of this work consists in analyzing sub-structuring method for the parallel solution of sparse linear systems with matrices arising from the discretization of partial differential equations such as finite element, finite…
We present the design and optimization of a linear solver on General Purpose GPUs for the efficient and high-throughput evaluation of the marginalized graph kernel between pairs of labeled graphs. The solver implements a preconditioned…
An alternating direction method of multipliers (ADMM) solver is described for optimal resource allocation problems with separable convex quadratic costs and constraints and linear coupling constraints. We describe a parallel implementation…
A High Performance Computing alternative to traditional Krylov subspace methods, pipelined Krylov subspace solvers offer better scalability in the strong scaling limit compared to standard Krylov subspace methods for large and sparse linear…
Sparse triangular solve (SpTRSV) is widely used in various domains. Numerous studies have been conducted using CPUs, GPUs, and specific hardware accelerators, where dataflows can be categorized into coarse and fine granularity. Coarse…
Answer Set Programming (ASP) has become, the paradigm of choice in the field of logic programming and non-monotonic reasoning. Thanks to the availability of efficient solvers, ASP has been successfully employed in a large number of…
Krylov subspace methods are among the most efficient solvers for large scale linear algebra problems. Nevertheless, classic Krylov subspace algorithms do not scale well on massively parallel hardware due to synchronization bottlenecks.…
Support for lower precision computation is becoming more common in accelerator hardware due to lower power usage, reduced data movement and increased computational performance. However, computational science and engineering (CSE) problems…
I present HPRMAT, a high-performance solver library for the linear systems arising in R-matrix coupled-channel scattering calculations in nuclear physics. Designed as a drop-in replacement for the linear algebra routines in existing…
Preconditioning is at the heart of iterative solutions of large, sparse linear systems of equations in scientific disciplines. Several algebraic approaches, which access no information beyond the matrix itself, are widely studied and used,…
Parallel multigrid is widely used as preconditioners in solving large-scale sparse linear systems. However, the current multigrid library still needs more satisfactory performance for structured grid problems regarding speed and…
Sparse matrix-vector multiplication (SpMV) is a fundamental operation with a wide range of applications in scientific computing and artificial intelligence. However, the large scale and sparsity of sparse matrix often make it a performance…
Linear Programming (LP) is a foundational optimization technique with widespread applications in finance, energy trading, and supply chain logistics. However, traditional Central Processing Unit (CPU)-based LP solvers often struggle to meet…
In the present paper we consider numerical methods to solve the discrete Schr\"odinger equation with a time dependent Hamiltonian (motivated by problems encountered in the study of spin systems). We will consider both short-range…
Developing efficient solvers for large-scale multi-term linear matrix equations remains a central challenge in numerical linear algebra and is still largely unresolved. This paper introduces a methodology leveraging CUR decomposition for…