Towards a taxonomy for multiscale methods in computational mechanics: building blocks of existing methods

Gravemeier, V.; Lenz, Stefan; Wall, Wolfgang A.

doi:10.1007/s00466-007-0185-7

Cited by 21 publications

(14 citation statements)

References 52 publications

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“…Other approaches include multi-scale algorithms driven by microscopic numerical solution data, e.g., database look-up or regression fit [12,13] and sub-grid modeling [14] approaches. A recent article in this journal summarizes various techniques proposed in the solid and fluid mechanics community for addressing multi-scale problems in general [15].…”

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confidence: 99%

Multi-scale homogenization of moving interface problems with flux jumps: application to solidification

Lee

Sundararaghavan

2009

Comput Mech

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In this paper, a multi-scale analysis scheme for solidification based on two-scale computational homogenization is discussed. Solidification problems involve evolution of surfaces coupled with flux jump boundary conditions across interfaces. We provide consistent macro-micro transition and averaging rules based on Hill's macrohomogeneity condition. The overall macro-scale behavior is analyzed with solidification at the micro-scale modeled using an enthalpy formulation. The method is versatile in the sense that two different models can be employed at the macroand micro-scales. The micro-scale model can incorporate all the physics associated with solidification including moving interfaces and flux discontinuities, while the macro-scale model needs to only model thermal conduction using continuous (homogenized) fields. The convergence behavior of the tightly coupled macro-micro finite element scheme with respect to decreasing element size is analyzed by comparing with a known analytical solution of the Stefan problem.

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confidence: 99%

Multi-scale homogenization of moving interface problems with flux jumps: application to solidification

Lee

Sundararaghavan

2009

Comput Mech

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“…As a matter of principle, these methods aim to integrate fine-scale effects in a coarse-scale model while obviating a direct numerical simulation of the completely resolved micro-structure. A variety of different multi-scale approaches has been developed in the past (confer [64] for a comprehensive review and taxonomy). For our particular application, multiscale procedures based on the nested solution of the boundary value problems (BVP) on both scales-the parenchymal and the alveolar level-are most suitable (see, e.g.…”

Section: Multi-scale Approach For Lung Parenchymamentioning

confidence: 99%

Towards a comprehensive computational model for the respiratory system

Wall

Wiechert

Comerford

et al. 2010

Numer Methods Biomed Eng

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SUMMARYThis paper is concerned with computational modeling of the respiratory system against the background of acute lung diseases and mechanical ventilation. Conceptually, we divide the lung into two major subsystems, namely the conducting airways and the respiratory zone represented by lung parenchyma. Owing to their respective complexity, both parts are themselves out of range for a direct numerical simulation resolving all relevant length scales. Therefore, we develop detailed individual models for parts of the subsystems as a basis for novel multi-scale approaches taking into account the unresolved parts appropriately. In the tracheobronchial region, CT-based geometries up to a maximum of approximately seven generations are employed in fluid-structure interaction simulations, considering not only airway wall deformability but also the influence of surrounding lung tissue. Physiological outflow boundary conditions are derived by considering the impedance of the unresolved parts of the lung in a fully coupled 3D-1D approach. In the respiratory zone, an ensemble of alveoli representing a single ventilatory unit is modeled considering not only soft tissue behavior but also the influence of the covering surfactant film. Novel nested multi-scale procedures are then employed to simulate the dynamic behavior of lung parenchyma as a whole and local alveolar ensembles simultaneously without resolving the alveolar micro-structure completely.

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“…Both multiscale and multigrid methods have become important tools in the analysis of a wide range of physical phenomena, including problems in solid and fluid mechanics [3][4][5]. Increases in computational power and refinements in programming tools and concepts have enabled researchers to develop conceptually complex but highly efficient algorithms in a systematic way, providing diverse methods with a potentially wide range of applications [6].…”

Section: Introductionmentioning

confidence: 99%

Meshing Highly Regular Structures: The Case of Super Carbon Nanotubes of Arbitrary Order

Schröppel

Wackerfuß

2015

Journal of Nanomaterials

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Mesh generation is an important step in many numerical methods. We present the “Hierarchical Graph Meshing” (HGM) method as a novel approach to mesh generation, based on algebraic graph theory. The HGM method can be used to systematically construct configurations exhibiting multiple hierarchies and complex symmetry characteristics. The hierarchical description of structures provided by the HGM method can be exploited to increase the efficiency of multiscale and multigrid methods. In this paper, the HGM method is employed for the systematic construction of super carbon nanotubes of arbitrary order, which present a pertinent example of structurally and geometrically complex, yet highly regular, structures. The HGM algorithm is computationally efficient and exhibits good scaling characteristics. In particular, it scales linearly for super carbon nanotube structures and is working much faster than geometry-based methods employing neighborhood search algorithms. Its modular character makes it conducive to automatization. For the generation of a mesh, the information about the geometry of the structure in a given configuration is added in a way that relates geometric symmetries to structural symmetries. The intrinsically hierarchic description of the resulting mesh greatly reduces the effort of determining mesh hierarchies for multigrid and multiscale applications and helps to exploit symmetry-related methods in the mechanical analysis of complex structures.

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Towards a taxonomy for multiscale methods in computational mechanics: building blocks of existing methods

Cited by 21 publications

References 52 publications

Multi-scale homogenization of moving interface problems with flux jumps: application to solidification

Multi-scale homogenization of moving interface problems with flux jumps: application to solidification

Towards a comprehensive computational model for the respiratory system

Meshing Highly Regular Structures: The Case of Super Carbon Nanotubes of Arbitrary Order

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