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We provide a preliminary study on utilizing GPU (Graphics Processing Unit) to accelerate computation for three simulation optimization tasks with either first-order or second-order algorithms. Compared to the implementation using only CPU…
Clawpack is a library for solving nonlinear hyperbolic partial differential equations using high-resolution finite volume methods based on Riemann solvers and limiters. It supports Adaptive Mesh Refinement (AMR), which is essential in…
In this paper, we introduce a quasi-Newton method optimized for efficiently solving quasi-linear elliptic equations and systems, with a specific focus on GPU-based computation. By approximating the Jacobian matrix with a combination of…
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…
We discuss the development, verification, and performance of a GPU accelerated discontinuous Galerkin method for the solutions of two dimensional nonlinear shallow water equations. The shallow water equations are hyperbolic partial…
This research proposes a practical method for detecting featureless objects by using image alignment approach with a robust similarity measure in industrial applications. This similarity measure is robust against occlusion, illumination…
Closed combustion devices like gas turbines and rockets are prone to thermoacoustic instabilities. Design engineers in the industry need tools to accurately identify and remove instabilities early in the design cycle. Many different…
We propose a solution strategy for linear systems arising in interior method optimization, which is suitable for implementation on hardware accelerators such as graphical processing units (GPUs). The current gold standard for solving these…
Two approaches for approximating the solution of large-scale Lyapunov equations are considered: the alternating direction implicit (ADI) iteration and projective methods by Krylov subspaces. A link between them is presented by showing that…
The conservative Post-Newtonian (PN) Hamiltonian formulation of spinning compact binaries has six integrals of motion including the total energy, the total angular momentum and the constant unit lengths of spins. The manifold correction…
With the emergence of mixed precision capabilities in hardware, iterative refinement schemes for solving linear systems $Ax=b$ have recently been revisited and reanalyzed in the context of three or more precisions. These new analyses show…
In recent years, GPU-accelerated optimization solvers based on second-order methods (e.g., interior-point methods) have gained momentum with the advent of mature and efficient GPU-accelerated direct sparse linear solvers, such as cuDSS.…
Many computer vision and human-computer interaction applications developed in recent years need evaluating complex and continuous mathematical functions as an essential step toward proper operation. However, rigorous evaluation of this kind…
We present a computational method for extreme-scale simulations of incompressible turbulent wall flows at high Reynolds numbers. The numerical algorithm extends a popular method for solving second-order finite differences Poisson/Helmholtz…
Matrix multiplication is fundamental in the backpropagation algorithm used to train deep neural network models. Libraries like Intel's MKL or NVIDIA's cuBLAS implemented new and optimized matrix multiplication techniques that increase…
Bivariate matrix functions provide a unified framework for various tasks in numerical linear algebra, including the solution of linear matrix equations and the application of the Fr\'echet derivative. In this work, we propose a novel…
Memory bound applications such as solvers for large sparse systems of equations remain a challenge for GPUs. Fast solvers should be based on numerically efficient algorithms and implemented such that global memory access is minimised. To…
Krylov subspace methods are a powerful tool for efficiently solving high-dimensional linear algebra problems. In this work, we study the approximation quality that a Krylov subspace provides for estimating the numerical range of a matrix.…
Advancements in AI have greatly enhanced the medical imaging process, making it quicker to diagnose patients. However, very few have investigated the optimization of a multi-model system with hardware acceleration. As specialized edge…
We describe the GPU implementation of shifted or multimass iterative solvers for sparse linear systems of the sort encountered in lattice gauge theory. We provide a generic tool that can be used by those without GPU programming experience…