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pro vyhledávání: '"Farrell, Patrick"'
We derive and analyze a broad class of finite element methods for numerically simulating the stationary, low Reynolds number flow of concentrated mixtures of several distinct chemical species in a common thermodynamic phase. The underlying partial di
Externí odkaz:
http://arxiv.org/abs/2408.17390
We address the solution of the distributed control problem for the steady, incompressible Navier--Stokes equations. We propose an inexact Newton linearization of the optimality conditions. Upon discretization by a finite element scheme, we obtain a s
Externí odkaz:
http://arxiv.org/abs/2408.05095
Autor:
Andrews, Boris D., Farrell, Patrick E.
Numerical methods for the simulation of transient systems with structure-preserving properties are known to exhibit greater accuracy and physical reliability, in particular over long durations. These schemes are often built on powerful geometric idea
Externí odkaz:
http://arxiv.org/abs/2407.11904
Nematic ordering describes the phenomenon where anisotropic molecules tend to locally align, like matches in a matchbox. This ordering can arise in solids (as nematic elastomers), liquids (as liquid crystals), and in gases. In the 1940s, Onsager desc
Externí odkaz:
http://arxiv.org/abs/2312.15210
Autor:
Bueler, Ed, Farrell, Patrick E.
Publikováno v:
SIAM Journal on Scientific Computing, 2024, Vol. 46, No. 4, pp. A2421--A2444
We present the full approximation scheme constraint decomposition (FASCD) multilevel method for solving variational inequalities (VIs). FASCD is a common extension of both the full approximation scheme (FAS) multigrid technique for nonlinear partial
Externí odkaz:
http://arxiv.org/abs/2308.06888
Autor:
Wittmann, René, Monderkamp, Paul A., Xia, Jingmin, Cortes, Louis B. G., Grobas, Iago, Farrell, Patrick E., Aarts, Dirk G. A. L., Löwen, Hartmut
Publikováno v:
Phys. Rev. Research 5, 033135 (2023)
Liquid crystals can self-organize into a layered smectic phase. While the smectic layers are typically straight forming a lamellar pattern in bulk, external confinement may drastically distort the layers due to the boundary conditions imposed on the
Externí odkaz:
http://arxiv.org/abs/2303.01425
Autor:
Peterson, Brian C.1 (AUTHOR) casey.schoenebeck@state.mn.us, Farrell, Patrick D.2 (AUTHOR) farrellp@headwaterscorp.com, Schoenebeck, Casey W.1,3 (AUTHOR)
Publikováno v:
Symmetry (20738994). Oct2024, Vol. 16 Issue 10, p1301. 13p.
Autor:
Brubeck, Pablo D., Farrell, Patrick E.
The Riesz maps of the $L^2$ de Rham complex frequently arise as subproblems in the construction of fast preconditioners for more complicated problems. In this work we present multigrid solvers for high-order finite element discretizations of these Ri
Externí odkaz:
http://arxiv.org/abs/2211.14284
We present a method to embed local electroneutrality within Onsager-Stefan-Maxwell electrolytic-transport models, circumventing their formulation as differential systems with an algebraic constraint. Flux-explicit transport laws are formulated for ge
Externí odkaz:
http://arxiv.org/abs/2211.13505
Publikováno v:
SIAM SISC 46(2):A629-A644 (2024)
In recent years a great deal of attention has been paid to discretizations of the incompressible Stokes equations that exactly preserve the incompressibility constraint. These are of substantial interest because these discretizations are pressure-rob
Externí odkaz:
http://arxiv.org/abs/2211.05494