Mixed-Dimensional Coupling via an Extended Dirichlet-to-Neumann Method

Ofir, Yoav; Rabinovich, Daniel; Givoli, Dan

doi:10.1615/intjmultcompeng.2016018551

Cited by 5 publications

(1 citation statement)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Partial differential equations in domains containing thin cylindrical parts are used in modelling of processes in industrial installations such as rod structures and pipelines, as well as in some biological applications (blood circulation). For unions of thin cylinders  called rod structures or tube structures, such problems were studied in Panasenko, 1,2 where asymptotic expansions were constructed and the method of asymptotic partial decomposition of the domain (MAPDD) [3][4][5][6][7][8][9][10] was justified and tested numerically. In these papers, the small parameter was the ratio of the diameter of a cylinder and its length, so that all cylinders had diameters of the same order.…”

Section: Introductionmentioning

confidence: 99%

Partial dimension reduction for the heat equation in a domain containing thin tubes

Амосов

Panasenko

2018

Math Methods in App Sciences

View full text Add to dashboard Cite

The heat equation in considered in a domain containing thin cylindrical tubes with Neumann's boundary condition at the lateral boundary of these tubes. This problem is reduced to a hybrid dimension problem keeping the initial dimension out of thin tubes and reducing it to the one-dimensional heat equation within the tubes at some distance from the bases of the cylinders. Junction of models of different dimensions is done according to the method of asymptotic partial decomposition of domain. The difference of solutions of the original and partially reduced problems is estimated. This result generalizes the method of partial dimension reduction for the case when the domain has only one restriction that it contains several thin cylinders possibly of different orders of diameters. KEYWORDS asymptotic partial decomposition of domain, dimension reduction, domain containing thin tubes, estimates of the error, heat equation Math Meth Appl Sci. 2018;41:9529-9545.wileyonlinelibrary.com/journal/mma

show abstract

Section: Introductionmentioning

confidence: 99%

Partial dimension reduction for the heat equation in a domain containing thin tubes

Амосов

Panasenko

2018

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

Partial Decomposition of a Domain Containing Thin Tubes for Solving the Diffusion Equation

Амосов

Panasenko

2022

J Math Sci

View full text Add to dashboard Cite

In a domain containing thin cylindrical tubes, we consider the diffusion equation with the Neumann boundary condition on the lateral surface of the tubes. The problem is reduced to a problem of hybrid dimension so that the reduced problem has the original dimension outside the tubes, but is reduced to the one-dimensional diffusion equation inside the tubes. The docking of models of different dimensions is carried out according to the method of asymptotic partial decompositions of domains. We estimate the difference between the solutions to the initial problem and the problem of different dimension. Bibliography: 14 titles. Illustrations: 3 figures.

show abstract

Hybrid 3D-plane finite element modeling for elastodynamics

Efrati

Givoli²

2022

Finite Elements in Analysis and Design

View full text Add to dashboard Cite

Mixed-Dimensional Coupling via an Extended Dirichlet-to-Neumann Method

Cited by 5 publications

References 0 publications

Partial dimension reduction for the heat equation in a domain containing thin tubes

Partial dimension reduction for the heat equation in a domain containing thin tubes

Partial Decomposition of a Domain Containing Thin Tubes for Solving the Diffusion Equation

Hybrid 3D-plane finite element modeling for elastodynamics

Contact Info

Product

Resources

About