Zobrazeno 1 - 10
of 355
pro vyhledávání: '"Olson, Luke"'
Trained neural networks (NN) have attractive features for closing governing equations. There are many methods that are showing promise, but all can fail in cases when small errors consequentially violate physical reality, such as a solution boundedne
Externí odkaz:
http://arxiv.org/abs/2408.03413
This work introduces and assesses the efficiency of a monolithic $ph$MG multigrid framework designed for high-order discretizations of stationary Stokes systems using Taylor-Hood and Scott-Vogelius elements. The proposed approach integrates coarsenin
Externí odkaz:
http://arxiv.org/abs/2407.07253
In recent years, solvers for finite-element discretizations of linear or linearized saddle-point problems, like the Stokes and Oseen equations, have become well established. There are two main classes of preconditioners for such systems: those based
Externí odkaz:
http://arxiv.org/abs/2401.06277
We investigate a novel monolithic algebraic multigrid (AMG) preconditioner for the Taylor-Hood ($\pmb{\mathbb{P}}_2/\mathbb{P}_1$) and Scott-Vogelius ($\pmb{\mathbb{P}}_2/\mathbb{P}_1^{disc}$) discretizations of the Stokes equations. The algorithm is
Externí odkaz:
http://arxiv.org/abs/2306.06795
This work proposes a solution for the problem of training physics-informed networks under partial integro-differential equations. These equations require an infinite or a large number of neural evaluations to construct a single residual for training.
Externí odkaz:
http://arxiv.org/abs/2305.17387
Autor:
Zaman, Tareq, Nytko, Nicolas, Taghibakhshi, Ali, MacLachlan, Scott, Olson, Luke, West, Matthew
Clustering is a commonplace problem in many areas of data science, with applications in biology and bioinformatics, understanding chemical structure, image segmentation, building recommender systems, and many more fields. While there are many differe
Externí odkaz:
http://arxiv.org/abs/2303.01667
Autor:
Taghibakhshi, Ali, Nytko, Nicolas, Zaman, Tareq Uz, MacLachlan, Scott, Olson, Luke, West, Matthew
Domain decomposition methods (DDMs) are popular solvers for discretized systems of partial differential equations (PDEs), with one-level and multilevel variants. These solvers rely on several algorithmic and mathematical parameters, prescribing overl
Externí odkaz:
http://arxiv.org/abs/2301.11378
Autor:
Zaman, Tareq, Nytko, Nicolas, Taghibakhshi, Ali, MacLachlan, Scott, Olson, Luke, West, Matthew
Algebraic Multigrid (AMG) methods are often robust and effective solvers for solving the large and sparse linear systems that arise from discretized PDEs and other problems, relying on heuristic graph algorithms to achieve their performance. Reductio
Externí odkaz:
http://arxiv.org/abs/2212.08371
Autor:
Nytko, Nicolas, Taghibakhshi, Ali, Zaman, Tareq Uz, MacLachlan, Scott, Olson, Luke N., West, Matt
Sparse matrix representations are ubiquitous in computational science and machine learning, leading to significant reductions in compute time, in comparison to dense representation, for problems that have local connectivity. The adoption of sparse re
Externí odkaz:
http://arxiv.org/abs/2212.05159
Supercomputer architectures are trending toward higher computational throughput due to the inclusion of heterogeneous compute nodes. These multi-GPU nodes increase on-node computational efficiency, while also increasing the amount of data to be commu
Externí odkaz:
http://arxiv.org/abs/2209.06141