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Level Set Methods in Segmentation of SDOCT Retinal Images
Published in Ayman El-Baz, Jasjit S. Suri, Level Set Method in Medical Imaging Segmentation, 2019
N Padmasini, R Umamaheswari, Yacin Sikkandar Mohamed, Manavi D Sindal
The paradigm of the level set is that it is a numerical method for tracking the evolution of contours and surfaces. Instead of manipulating the contour directly, the contour is embedded as the zero level set of a higher dimensional function called the level set function, ψ(X,t). The level set function is then evolved under the control of a differential equation. At any time, the evolving contour can be obtained by extracting the zero level set Γ(X,t)={ψ(X,t)=0} from the output. The main advantages of using level sets is that arbitrarily complex shapes can be modeled and topological changes such as merging and splitting are handled implicitly.
Multiscale topology optimization of pelvic bone for combined walking and running gait cycles
Published in Computer Methods in Biomechanics and Biomedical Engineering, 2023
The sensitivity of Equation (5) is the normal velocity in Equation (4) (Wang et al. 2003; Allaire et al. 2004) and is given by: where is the Lagrange multiplier corresponding to the volume constraint in Equation (5). The advantage of level set over density-based methods like SIMP and homogenization is that the boundary between solid and void is well-defined and there is no problem with checkerboard patterns. On the other hand, some of the drawbacks of the level set method are the inability to generate holes in structures and frequent re-initialization of the level set function. These drawbacks have been overcome by methods like topological derivatives (Novotny et al. 2003), parametric level set functions (Wang and Wang 2006), phase field and reaction-diffusion equations (Takezawa et al. 2010; Yamada et al. 2010). Level set methods in topology optimization is an active area of research and have grown in multifarious directions (Cui et al. 2016; Wang and Kang 2019; Liu et al. 2020; Wei and Paulino 2020; Yaghmaei et al. 2020; Desai et al. 2021; ; Liu et al. 2022; Yu et al. 2022). For an extensive review of the level set method for topology optimization, see (Van Dijk et al. 2013).
A review on development and applications of element-free galerkin methods in computational fluid dynamics
Published in International Journal for Computational Methods in Engineering Science and Mechanics, 2020
Wah Yen Tey, Yutaka Asako, Khai Ching Ng, Wei-Haur Lam
Another possible method to deal with the moving boundaries is the coupling of EFG solvers with Level Set (LS) Method. Instead of tracking the particle movement as in free surface capturing techniques, level set method handles the deforming interface via manipulation of level set function. Indeed, level set method has been well developed by many researchers to be applied in many thermofluidic simulations whenever dynamic interfaces are involved, such as the dynamics of droplets [201], flow dynamics due to deformation particles [202, 203], wave-body interaction [204] and fluid structure interaction of complex moving object [205, 206]. So far, the coupling between EFG and LS Method in CFD applications can only be found on the work of He and Yang [207] who solved heat transfer problem. The applications of the coupling in structural mechanics comprise the simulation on interacting cracks [208] and optimisation of materials’ structure [209].
Zonal Flow Solver (ZFS): a highly efficient multi-physics simulation framework
Published in International Journal of Computational Fluid Dynamics, 2020
Andreas Lintermann, Matthias Meinke, Wolfgang Schröder
In this work, the multi-physics simulation framework ZFS has been presented. The framework unites a whole simulation chain. It starts by processing a geometry file as input for a massively parallel grid generator that can be employed for efficiently solving a variety of multi-physics problems using the solver base implemented in ZFS. Furthermore, parallelised geometries can be generated by this tool. With these inputs at hand quasi-incompressible flow in complex and intricate geometries can be computed by means of a lattice-Boltzmann solver. A finite-volume method is used to compute compressible flow for a whole spectrum of technical applications. A level set solver enables to track moving boundaries, even for arbitrarily shaped interfaces such as flame fronts. A discontinuous Galerkin solver is used to perform aeroacoustic simulations by coupling to a flow solver. With a Lagrangian approach particles can be tracked. ZFS furthermore features dynamic refinement and dynamic load-balancing. Processing of the simulation data can either be performed in-situ at compute time or in a post-processing step.