Results 41 to 50 of about 27,923 (223)

Cluster-based Generalized Multiscale Finite Element Method for elliptic PDEs with random coefficients

, 2017
We propose a generalized multiscale finite element method (GMsFEM) based on clustering algorithm to study the elliptic PDEs with random coefficients in the multi-query setting. Our method consists of offline and online stages.
Chung, Eric T., Efendiev, Yalchin, Leung, Wing Tat, Zhang, Zhiwen   +3 more
core   +1 more source

Multiscale Partition of Unity [PDF]

, 2013
We introduce a new Partition of Unity Method for the numerical homogenization of elliptic partial differential equations with arbitrarily rough coefficients. We do not restrict to a particular ansatz space or the existence of a finite element mesh.
C.A. Duarte, C.A. Duarte, D.-J. Kim, H. Owhadi, H.W. Alt, I. Babuška, J.M. Melenk, J.T. Oden, N. Moës, T. Belytschko, T.J. Liszka, V. Gupta   +11 more
core   +2 more sources

Mixed Generalized Multiscale Finite Element Method for flow problem in thin domains

Journal of Computational and Applied Mathematics, 2022
In this paper, we construct a class of Mixed Generalized Multiscale Finite Element Methods for the approximation on a coarse grid for an elliptic problem in thin two-dimensional domains. We consider the elliptic equation with homogeneous boundary conditions on the domain walls. For reference solution of the problem, we use a Mixed Finite Element Method
Denis Spiridonov, Maria Vasilyeva, Min Wang, Eric T. Chung   +3 more
openaire   +3 more sources

Universal Electronic‐Structure Relationship Governing Intrinsic Magnetic Properties in Permanent Magnets

Advanced Functional Materials, EarlyView.
Permanent magnets derive their extraordinary strength from deep, universal electronic‐structure principles that control magnetization, anisotropy, and intrinsic performance. This work uncovers those governing rules, examines modern modeling and AI‐driven discovery methods, identifies critical bottlenecks, and reveals electronic fingerprints shared ...
Prashant Singh
wiley   +1 more source

Stabilization arising from PGEM : a review and further developments [PDF]

, 2009
The aim of this paper is twofold. First, we review the recent Petrov-Galerkin enriched method (PGEM) to stabilize numerical solutions of BVP's in primal and mixed forms.
Araya, Araya, Araya, Arnold, Baiocchi, Bank, Barrenechea, Barrenechea, Barrenechea, Brezzi, Brezzi, Brezzi, Brezzi, Brezzi, Brezzi, Brooks, Cangiani, Clément, Ern, Franca, Franca, Franca, Franca, Franca, Franca, Franca, Frédéric Valentin, Gabriel R. Barrenechea, Girault, Hughes, Hughes, Leopoldo P. Franca, Linb, Pierre, Rodolfo Araya, Roos, Stynes, Thomée   +37 more
core   +2 more sources

Bio‐Inspired Molecular Events in Poly(Ionic Liquids)

Advanced Functional Materials, EarlyView.
Originating from dipolar and polar inter‐ and intra‐chain interactions of the building blocks, the topologies and morphologies of poly(ionic liquids) (PIL) govern their nano‐ and micro‐processibility. Modulating the interactions of cation‐anion pairs with aliphatic dipolar components enables the tunability of properties, facilitated by “bottom‐up ...
Jiahui Liu, Marek W. Urban
wiley   +1 more source

Hierarchical multiscale modeling for flows in fractured media using generalized multiscale finite element method [PDF]

GEM - International Journal on Geomathematics, 2015
In this paper, we develop a multiscale finite element method for solving flows in fractured media. Our approach is based on Generalized Multiscale Finite Element Method (GMsFEM), where we represent the fracture effects on a coarse grid via multiscale basis functions.
Efendiev, Yalchin R., Lee, Seong, Li, Guanglian, Yao, Jun, Zhang, Na   +4 more
openaire   +3 more sources

Computational Modeling Meets 3D Bioprinting: Emerging Synergies in Cardiovascular Disease Modeling

Advanced Healthcare Materials, EarlyView.
Emerging advances in three‐dimensional bioprinting and computational modeling are reshaping cardiovascular (CV) research by enabling more realistic, patient‐specific tissue platforms. This review surveys cutting‐edge approaches that merge biomimetic CV constructs with computational simulations to overcome the limitations of traditional models, improve ...
Tanmay Mukherjee, Mehdi Salar Amoli, Sarah Rezapourdamanab, Lama Rita El Shammas, Martin L. Tomov, Emilio A. Mendiola, Vahid Serpooshan, Reza Avazmohammadi   +7 more
wiley   +1 more source

A mixed multiscale spectral generalized finite element method

Numerische Mathematik
We present a multiscale mixed finite element method for solving second order elliptic equations with general $L^{\infty}$-coefficients arising from flow in highly heterogeneous porous media. Our approach is based on a multiscale spectral generalized finite element method (MS-GFEM) and exploits the superior local mass conservation properties of mixed ...
Alber, Christian, Ma, Chupeng, Scheichl, Robert   +2 more
openaire   +2 more sources

A Constraint Energy Minimizing Generalized Multiscale Finite Element Method for Parabolic Equations [PDF]

Multiscale Modeling & Simulation, 2019
In this paper, we present a Constraint Energy Minimizing Generalized Multiscale Finite Element Method (CEM-GMsFEM) for parabolic equations with multiscale coefficients, arising from applications in porous media. We will present the construction of CEM-GMsFEM and rigorously analyze its convergence for the parabolic equations.
Li, Mengnan, Chung, Eric, Jiang, Lijian
openaire   +2 more sources