MMMFEM swMATH ID: 12715 Software Authors: B. Ganis; I. Yotov Description: Implementation of a mortar mixed finite element method using a Multiscale Flux Basis. This paper provides a new implementation of a multiscale mortar mixed finite element method for second order elliptic problems. The algorithm uses non-overlapping domain decomposition to reformulate a fine scale problem as a coarse scale mortar interface problem, which is then solved using an iterative method. The original implementation by T. Arbogast et al. [Simul. 6, No. 1, 319–346 (2007; Zbl 05255539)]. Multiscale model required solving one local Dirichlet problem on each subdomain per interface iteration. We alter this implementation by forming a Multiscale Flux Basis. This basis consists of mortar functions representing the individual flux responses for each mortar degree of freedom, on each subdomain independently. The computation of these basis functions requires solving a fixed number of Dirichlet subdomain problems. Taking linear combinations of the Multiscale Flux Basis functions replaces the need to solve any Dirichlet subdomain problems during the interface iteration. This new implementation yields the same solution as the original implementation, and is computationally more efficient in cases where the number of interface iterations is greater than the number of mortar degrees of freedom per subdomain. The gain in computational efficiency increases with the number of subdomains. Homepage: http://www.sciencedirect.com/science/article/pii/S0045782509003077 Related Software: CutFEM; PorePy; ShaPo; DuMuX; drp-benchmarks; SciPy; p4est; hypre; FreeFem++; Thrust; XMOF2D; Jali; GitHub; FLAG; IPARS; ML; KELLEY; PARCEL; Nike2D Cited in: 39 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year Implementation of a mortar mixed finite element method using a multiscale flux basis. Zbl 1231.76145Ganis, Benjamin; Yotov, Ivan 2009 all top 5 Cited by 60 Authors 13 Yotov, Ivan 10 Wheeler, Mary Fanett 7 Ganis, Benjamin 6 Pencheva, Gergina V. 6 Wildey, Tim M. 3 Khattatov, Eldar 3 Kikinzon, Evgeny 3 Park, Eun-Jae 3 Shashkov, Mikhail J. 2 Ahmed, Elyes 2 Ambartsumyan, Ilona 2 Arbogast, Todd 2 Ausas, Roberto Federico 2 Budiša, Ana 2 Buscaglia, Gustavo Carlos 2 Chung, Tsz Shun Eric 2 Fu, Shubin 2 Fumagalli, Alessio 2 Girault, Vivette 2 Guiraldello, Rafael T. 2 Shin, Dongwook 2 Sousa, Fabrício S. 2 Tavener, Simon J. 2 Vassilev, Danail 2 Wang, Changqing 2 Xue, Guangri 1 Amanbek, Yerlan 1 Bischoff, Manfred 1 Boon, Wietse M. 1 Castelletto, Nicola 1 Cichosz, Thomas 1 Estep, Donald J. 1 Garimella, Rao V. 1 Ginting, Victor 1 Gläser, Dennis 1 Helmig, Rainer 1 Jabeen, Rukhsana 1 Juntunen, Mika 1 Keilegavlen, Eirik 1 Khan, Suliman 1 Kumar, Kundan 1 Kuznetsov, Yurii Alekseevich 1 Lipnikov, Konstatin 1 Mehmani, Yashar 1 Nordbotten, Jan Martin 1 Olshanskii, Maxim A. 1 Qu, Dong 1 Radu, Florin Adrian 1 Rigelo, Joyce C. 1 Singh, Gurpreet 1 Svyatsky, Daniil 1 Tchelepi, Hamdi A. 1 van Duijn, Cornelis Johannes 1 Vohralík, Martin 1 Xiao, Hailong 1 Xu, Chuanju 1 Yang, Yanfang 1 Zhiliakov, Alexander 1 Zhong, Ming 1 Zunino, Paolo all top 5 Cited in 16 Serials 7 Journal of Computational Physics 6 Computer Methods in Applied Mechanics and Engineering 4 SIAM Journal on Numerical Analysis 3 Mathematics and Computers in Simulation 3 SIAM Journal on Scientific Computing 2 Computers and Fluids 2 Computers & Mathematics with Applications 2 Numerische Mathematik 2 Multiscale Modeling & Simulation 2 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 1 Applied Mathematics and Computation 1 Journal of Computational and Applied Mathematics 1 Numerical Linear Algebra with Applications 1 Computational Geosciences 1 Communications in Computational Physics 1 SIAM/ASA Journal on Uncertainty Quantification Cited in 4 Fields 32 Numerical analysis (65-XX) 22 Fluid mechanics (76-XX) 13 Partial differential equations (35-XX) 5 Mechanics of deformable solids (74-XX) Citations by Year