Library Subscription: Guest
Begell Digital Portal Begell Digital Library eBooks Journals References & Proceedings Research Collections
International Journal for Multiscale Computational Engineering
IF: 1.016 5-Year IF: 1.194 SJR: 0.554 SNIP: 0.82 CiteScore™: 2

ISSN Print: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.2016018551
pages 489-513

MIXED-DIMENSIONAL COUPLING VIA AN EXTENDED DIRICHLET-TO-NEUMANN METHOD

Yoav Ofir
Interdepartmental Program of Applied Mathematics, Technion−Israel Institute of Technology, Haifa 32000, Israel
Daniel Rabinovich
Department of Aerospace Engineering, Technion−Israel Institute of Technology, Haifa 32000, Israel
Dan Givoli
Department of Aerospace Engineering, Technion−Israel Institute of Technology, Haifa 32000, Israel; Faculty of Civil Engineering & Geosciences, Technical University of Delft, 2600 GA Delft, The Netherlands

ABSTRACT

Recently, a Dirichlet-to-Neumann (DtN) coupling method was proposed for mixed-dimensional modeling of time-harmonic wave problems. The original two-dimensional (2D) problem's domain in this multiscale scenario is assumed to consist of two regions: a bulky one and a slender one. In a previous publication on the DtN coupling method, the problems considered were such that in the slender region, the exact solution approximately behaved in a one-dimensional (1D) way, namely its lateral variation decayed rapidly away from the wave source. In the present paper, a more general class of problems is considered. The computational domain still includes a slender region ("a long tail" or "a tree"), but the solution in that region does not necessarily behave in a 1D way. Such a persistent 2D behavior occurs for sufficiently large wave numbers, as is shown here. The DtN coupling method is extended for this more general situation. The problem in the slender part is reduced to a sequence of 1D problems. In the hybrid model, the bulky and slender regions are discretized by using 2D and 1D finite element formulations, respectively, which are then coupled together by employing on the interface the numerically calculated DtN maps associated with the 1D problems. To enhance the accuracy of the calculated DtN map, a boundary flux recovery technique is applied on the interface. The hybrid model is more efficient than the standard 2D model taken for the entire problem, yet its accuracy is not significantly lower. The performance of the method is demonstrated via numerical examples.


Articles with similar content:

A WEIGHT-BOUNDED IMPORTANCE SAMPLING METHOD FOR VARIANCE REDUCTION
International Journal for Uncertainty Quantification, Vol.9, 2019, issue 3
Linjun Lu, Tenchao Yu, Jinglai Li
COMPUTATION OF THE EFFECTIVE CONDUCTIVITY OF THREE-DIMENSIONAL ORDERED COMPOSITES WITH A THERMALLY-CONDUCTING DISPERSED PHASE
International Heat Transfer Conference 11, Vol.19, 1998, issue
Manuel Ernani C. Cruz
Multiscale Modeling for Planar Lattice Microstructures with Structural Elements
International Journal for Multiscale Computational Engineering, Vol.4, 2006, issue 4
Ken Ooue, Isao Saiki, Kenjiro Terada, Akinori Nakajima
ITERATIVE GLOBAL-LOCAL APPROACH TO CONSIDER THE EFFECTS OF LOCAL ELASTO-PLASTIC DEFORMATIONS IN THE ANALYSIS OF THIN-WALLED MEMBERS
International Journal for Multiscale Computational Engineering, Vol.15, 2017, issue 2
Ali Saleh, R. Emre Erkmen
Stabilised Meshless Local Petrov Galerkin Method for Heat Conduction
Proceedings of the 25th National and 3rd International ISHMT-ASTFE Heat and Mass Transfer Conference (IHMTC-2019), Vol.0, 2019, issue
Krishna Mohan Singh, Rituraj Singh, Abhishek Kumar Singh