Zobrazeno 1 - 10
of 209
pro vyhledávání: '"MacLachlan, Scott"'
Unique continuation principles are fundamental properties of elliptic partial differential equations, giving conditions that guarantee that the solution to an elliptic equation must be uniformly zero. Since finite-element discretizations are a natura
Externí odkaz:
http://arxiv.org/abs/2410.08963
Autor:
Rafiei, Amin, MacLachlan, Scott
The numerical analysis of higher-order mixed finite-element discretizations for saddle-point problems, such as the Stokes equations, has been well-studied in recent years. While the theory and practice of such discretizations is now well-understood,
Externí odkaz:
http://arxiv.org/abs/2409.14222
Autor:
Jackaman, James, MacLachlan, Scott
Space-time finite-element discretizations are well-developed in many areas of science and engineering, but much work remains within the development of specialized solvers for the resulting linear and nonlinear systems. In this work, we consider the a
Externí odkaz:
http://arxiv.org/abs/2407.13997
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
Autor:
Kirby, Robert C., MacLachlan, Scott P.
Irksome is a library based on the Unified Form Language (UFL) that enables automated generation of Runge--Kutta methods for time-stepping finite element spatial discretizations of partial differential equations (PDE). Allowing users to express semidi
Externí odkaz:
http://arxiv.org/abs/2403.08084
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
In this paper, we are concerned with efficiently solving the sequences of regularized linear least squares problems associated with employing Tikhonov-type regularization with regularization operators designed to enforce edge recovery. An optimal reg
Externí odkaz:
http://arxiv.org/abs/2306.11067
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
While constraints arise naturally in many physical models, their treatment in mathematical and numerical models varies widely, depending on the nature of the constraint and the availability of simulation tools to enforce it. In this paper, we conside
Externí odkaz:
http://arxiv.org/abs/2306.03210
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