The island dynamics model on parallel quadtree grids

Mistani, Pouria; Guittet, Arthur; Bochkov, Daniil; Schneider, Joshua P.; Margetis, Dionisios; Rätsch, Christian; Gibou, Frédéric

doi:10.1016/j.jcp.2018.01.054

Cited by 19 publications

(6 citation statements)

References 44 publications

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“…During the second pass, isolated pools of liquid created as a result of such "bridging" procedure (if any) are identified and "solidified" as well. The identification of isolated pools on distributed computational grids is done using the parallel "island counting" algorithm described in [18].…”

Section: Appendix D Removing Extremely Underresolved Regionsmentioning

confidence: 99%

Sharp-Interface Simulations of Multicomponent Alloy Solidification

Bochkov¹,

Pollock²,

Gibou³

2021

Preprint

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We present a computational method for the simulation of the solidification of multicomponent alloys. Contrary to the case of binary alloys where a fixed point iteration is adequate, we hereby propose a Newton-type approach to solve the non-linear system of coupled PDEs arising from the time discretization of the governing equations. A combination of spatially adaptive quadtree grids, Level-Set Method, and sharp-interface numerical methods for imposing boundary conditions is used to accurately and efficiently resolve the complex behavior of the solidification front. We validate the proposed computational method on the case of axisymmetric radial solidification admitting an analytical solution and show that the overall method's accuracy is close to second order. Finally, we perform numerical experiments for the directional solidification of a Co-Al-W ternary alloy with a phase diagram obtained from the PANDAT™database and analyze the solutal segregation dependence on the processing conditions and alloy properties.

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Section: Appendix D Removing Extremely Underresolved Regionsmentioning

confidence: 99%

Sharp-Interface Simulations of Multicomponent Alloy Solidification

Bochkov¹,

Pollock²,

Gibou³

2021

Preprint

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“…High resolution data-sets describing temporal evolution of complex systems at multiple length scales are increasingly accessible from advanced multi-scale numerical simulations (see e.g. [48,47]). These advances have become possible partly due to recent developments in discretization techniques for nonlinear partial differential equations with sharp boundaries (see e.g.…”

Section: Bipdes For Dynamic Problemsmentioning

confidence: 99%

Solving inverse-PDE problems with physics-aware neural networks

Pakravan,

Mistani,

Aragon-Calvo

et al. 2020

Preprint

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We propose a novel composite framework that enables finding unknown fields in the context of inverse problems for partial differential equations (PDEs). We blend the high expressibility of deep neural networks as universal function estimators with the accuracy and reliability of existing numerical algorithms for partial differential equations. Our design brings together techniques of computational mathematics, machine learning and pattern recognition under one umbrella to seamlessly incorporate any domain-specific knowledge and insights through modeling. The network is explicitly aware of the governing physics through a hard-coded PDE solver layer in contrast to existing methods that incorporate the governing equations in the loss function; this subsequently focuses the computational load to only the discovery of the hidden fields and enables incorporating more sophisticated neural network architectures in the scientific computing domain. In addition, techniques of pattern recognition and surface reconstruction are used to further represent the unknown fields in a straightforward fashion. Most importantly, our inverse-PDE solver enables effortless integration of domain-specific knowledge about the physics of the underlying fields, such as symmetries and proper basis functions. We call this architecture Blended inverse-PDE networks (hereby dubbed BiPDE networks) and demonstrate its applicability on recovering the variable diffusion coefficient in Poisson problems in one and two spatial dimensions, as well as the diffusion coefficient in the time-dependent and nonlinear Burgers' equation in one dimension. We also show that this approach is robust to noise.

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“…This introduces a significant reduction in the size of the grid from ≈ 2 30 nodes to 194, 666, 253 nodes in this example. We refer the interested reader to [31] for a quantitative study of this enhancement. This consequently advances the limits of the possible simulation scales with the current state-ofthe-art available resources.…”

Section: Performance and Scalability Of The Approachmentioning

confidence: 99%

A parallel Voronoi-based approach for mesoscale simulations of cell aggregate electropermeabilization

Mistani

Guittet

Poignard

et al. 2019

Journal of Computational Physics

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We introduce a numerical framework that enables unprecedented direct numerical studies of the electropermeabilization effects of a cell aggregate at the meso-scale. Our simulations qualitatively replicate the shadowing effect observed in experiments and reproduce the time evolution of the impedance of the cell sample in agreement with the trends observed in experiments. This approach sets the scene for performing homogenization studies for understanding the effect of tissue environment on the efficiency of electropermeabilization. We employ a forest of Octree grids along with a Voronoi mesh in a parallel environment that exhibits excellent scalability. We exploit the electric interactions between the cells through a nonlinear phenomenological model that is generalized to account for the permeability of the cell membranes. We use the Voronoi Interface Method (VIM) to accurately capture the sharp jump in the electric potential on the cell boundaries. The case study simulation covers a volume of (1 mm) 3 with more than 27, 000 well-resolved cells with a heterogeneous mix of morphologies that are randomly distributed throughout a spheroid region.

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The island dynamics model on parallel quadtree grids

Cited by 19 publications

References 44 publications

Sharp-Interface Simulations of Multicomponent Alloy Solidification

Sharp-Interface Simulations of Multicomponent Alloy Solidification

Solving inverse-PDE problems with physics-aware neural networks

A parallel Voronoi-based approach for mesoscale simulations of cell aggregate electropermeabilization

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