Related papers: Enhancing data locality of the conjugate gradient …

The conjugate gradient (CG) method is a classic Krylov subspace method for solving symmetric positive definite linear systems. We introduce an analogous semi-conjugate gradient (SCG) method for unsymmetric positive definite linear systems.…

The simulation of heat flow through heterogeneous material is important for the design of structural and electronic components. Classical analytical solutions to the heat equation PDE are not known for many such domains, even those having…

The performance of graph programs depends highly on the algorithm, the size and structure of the input graphs, as well as the features of the underlying hardware. No single set of optimizations or one hardware platform works well across all…

A current trend in HPC systems is the utilization of architectures with SIMD or vector extensions to exploit data parallelism. There are several ways to take advantage of such modern vector architectures, each with a different impact on the…

In a recent paper, J. Chem. Phys. 162, 214101 (2025), a novel approach for the rigidification of a molecular cluster was proposed, in which starting with an all-atom (AA) potential, a coarse-grained (CG) potential for the associated cluster…

A Command Governor (CG) is an optimization-based add-on scheme to a nominal closed-loop system. It is used to enforce state and control constraints by modifying reference commands. This paper considers the implementation of a CG on embedded…

Conjugated organic molecules play a central role in a wide range of optoelectronic devices, including organic light-emitting diodes, organic field-effect transistors, and organic solar cells. A major bottleneck in the computational design…

In this paper, we consider gradient methods for minimizing smooth convex functions, which employ the information obtained at the previous iterations in order to accelerate the convergence towards the optimal solution. This information is…

Off-lattice agent-based models (or cell-based models) of multicellular systems are increasingly used to create in-silico models of in-vitro and in-vivo experimental setups of cells and tissues, such as cancer spheroids, neural crest cell…

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…

The growing concern for energy efficiency in the Information and Communication Technology (ICT) sector has prompted the exploration of resource management techniques. While hardware architectures, such as single-ISA asymmetric multicore…

The matrix element method utilizes ab initio calculations of probability densities as powerful discriminants for processes of interest in experimental particle physics. The method has already been used successfully at previous and current…

We introduce a simple, accurate, and extremely efficient method for numerically solving the multi-marginal optimal transport (MMOT) problems arising in density functional theory. The method relies on (i) the sparsity of optimal plans [for…

Modeling a high-dimensional Hamiltonian system in reduced dimensions with respect to coarse-grained (CG) variables can greatly reduce computational cost and enable efficient bottom-up prediction of main features of the system for many…

Unfitted finite element methods, like CutFEM, have traditionally been implemented in a matrix-based fashion, where a sparse matrix is assembled and later applied to vectors while solving the resulting linear system. With the goal of…

Collaborative filtering (CF) is widely searched in recommendation with various types of solutions. Recent success of Graph Convolution Networks (GCN) in CF demonstrates the effectiveness of modeling high-order relationships through graphs,…

In this paper we study proximal conditional-gradient (CG) and proximal gradient-projection type algorithms for a block-structured constrained nonconvex optimization model, which arises naturally from tensor data analysis. First, we…

Quantum algorithms are still challenging to solve linear systems of equations on real devices. This challenge arises from the need for deep circuits and numerous ancilla qubits. We introduce the quantum conjugate gradient (QCG) method using…

The Preconditioned Conjugate Gradient method is often employed for the solution of linear systems of equations arising in numerical simulations of physical phenomena. While being widely used, the solver is also known for its lack of…

We present a novel approach to fast on-the-fly low order finite element assembly for scalar elliptic partial differential equations of Darcy type with variable coefficients optimized for matrix-free implementations. Our approach introduces…