Figure 13 shows that the proposed multiscale model closely matches the experimental force–displacement curve, with the numerical band oscillating around the experimental results. In contrast, the defect-free model significantly overpredicts the compressive response, particularly in terms of absorbed energy (area under the force–displacement curve). The multiscale model more accurately predicts the first peak force, with the experimental value at 13.5 kN (46.7 MPa), the defect-free model at 14.7 kN (51 MPa, 9% error), and the multiscale model ranging between 13.3–13.7 kN (46—47.5 MPa).

• However, many studies rely on simplified approaches, such as equivalent diameters 9, 51, 53 or defect-based corrections 39, 43, while computationally efficient, lack the integration of detailed defect data into multiscale frameworks.
• There is probably a performance benefit to using a single data structure, but separating the submodels provides more clarity and provides a path to directing parallelization efforts towards only parts of a code.
• The framework also introduces variable-step algorithms to simulate both micro-state and macro-state efficiently.
• Otherwise, the submodels have different or slightly overlapping computational domains.
• Then, the new geometry of the cells induces a new boundary condition for the flow, which must be recomputed ().

Infrared and visible image fusion based on nonlinear enhancement and NSST decomposition

We believe that MMSF will contribute to exploring these highly relevant issues. An early example is the work we did on finding multi-scale modelling errors in a reaction–diffusion model 16. It is clear that a well-established methodology is quite important when developing an interdisciplinary application within a group of researchers with different scientific backgrounds and different geographical locations.

II-A Introduction of a generic HMM

A good match between the application design and its implementation on a computer is central for incremental development and its long-term sustainability. This is done by introducing fast-scale and slow-scale variables for an independent variable, and subsequently treating these variables, fast and slow, as if they are independent. In the solution process of the perturbation problem thereafter, the resulting additional freedom – introduced by the new independent variables – is used to remove (unwanted) secular Software quality assurance terms.

Multiple-Scale Analysis

The vegetation submodel keeps running, while the forest fire submodel is restarted at each iteration. However, the runtime environment will determine whether this is actually possible, or if they have to modify separate data structures which are combined after each iteration (see figure 6 for a number of execution options). The latter option is necessary if the submodels are executed on different machines, or if the forest fire and vegetation submodels use different resolutions. If they have different resolutions, a mapper may run between the vegetation and forest fire submodel to map a grid of https://wizardsdev.com/en/vacancy/middle-business-analyst/ one resolution to another. Alternatively, multiple vegetation submodels might be run concurrently, and a single forest fire submodel might run on the combined domain.

This separation of scales is likely to affect the quality of the result, when compared with a fully resolved (yet unaffordable) computation. The art of multi-scale modelling is then to propose a good compromise between CPU performance and accuracy by selecting the most relevant parts of the domain at an appropriate scale. Finding a proper accuracy metrics and the right balance between precision and CPU requirements is a wide open question 9.

• The RVE size is determined through a sensitivity analysis of homogenized stiffness and yield stress (Sect. 4.1).
• This paper presents a multiscale strategy for modeling the degrading influence of internal defects on the compressive mechanical response of an octet truss lattice structure produced by Powder Bed Fusion and made of AlSi10Mg alloy.
• Operations that are finer than this temporal scale and operations that are not time dependent may be placed inside the S or B operations instead of being represented explicitly in the SEL.
• The new simulation method is illustrated using a two-area system and is then tested on a detailed EMT model of the IEEE 39-bus system.
• Focusing on the splitting and single-scale models gives the benefit of using proven models (and code) for each part of a multi-scale model.
• Our framework assumes that a multi-scale model can be formulated in terms of a collection of coupled single-scale submodels.

Methodology

The latter puts constraints on the approximate solution, which are called solvability conditions. However, the multiscale model shows a less-pronounced plastic deformation before the first force drop compared to the experimental curve, indicating earlier failure. This brittle behavior is attributed to the failure criterion used in RVE analyses, where beams fail when at least 10% of the RVE volume reaches the ultimate strain. Developing a more refined failure criterion at the microscopic level is Multi-scale analysis beyond the scope of this work. The load drops observable in the numerical results are due to the progressive failure of the beams, which lead to contact loss with the rigid wall and consequent numerical fluctuations.