A domain decomposition technique based on the multiscale seamless-domain method

Abstract

We present a domain decomposition technique combining the finite-element analysis and a multiscale simulation scheme that is termed the seamless-domain method. This technique is applicable to any type of linear problems and has the below different features from conventional substructuring techniques used for finite-element methods such as the super-elements. Adjacent substructures do not need to have the same finite-element mesh or the same node layout at their interface. Therefore, the proposed technique allows us to connect a substructure having a coarse mesh and another substructure having a fine mesh. Additionally, the neighboring substructures are partially overlapped each other around their interfacial region. The overlapped region attempts to generate continuous dependent-variable distribution(s) at the interfacial region. We present four types of numerical experiments related to linear elasticity to investigate practical feasibility of the proposed technique and evaluate an effect of different finite-element meshes in region shared by two substructures on the computational accuracy.

Higher Order Multiscale Finite Element Method for Heat Transfer Modeling

“…A number of numerical methods are used to model composites. The most frequent applications are based on the finite-element method [ 1 , 11 ], the finite-difference method [ 2 ], the discrete element method [ 12 ] and other methods [ 5 , 13 ]. In our research, we make use of the higher-order, finite-element method.…”

“…State-of-the-art papers devoted to the review and classification of multiscale methods developed for the heat transfer problem are present in the literature [ 25 , 26 , 27 ]. The main distinction refers to the analysis scale [ 27 ]; therefore, one can distinguish: The microscale modeling using molecular dynamics (MD) with the motion analysis of every single atom/molecule in the domain [ 28 , 29 ]; The particle-based mesoscopic modeling based on a coarse-grained analysis, e.g., Monte Carlo method, lattice Boltzmann method [ 30 ]; The macroscale modeling with the assumption of the continuum of the domain [ 2 , 13 , 31 , 32 ]. …”

“…In [ 13 , 31 ], the multiscale seamless-domain method (SDM) is presented. It has some similarities to both the computational homogenization and the multiscale finite-element method used in this paper.…”