Improved Feasible-Set Method for Removing Mesh Inversion

2020 ◽  
Vol 20 (4) ◽  
Author(s):  
Soji Yamakawa ◽  
Kenji Shimada
Keyword(s):  
Optimization Techniques ◽  
Computational Method ◽  
Mesh Optimization ◽  
Improved Method ◽  
Smoothing Techniques ◽  
Feasible Set ◽  
Mesh Topology ◽  
Initial Mesh ◽  
Inverted Element ◽  
Nonplanar Surface

Abstract This paper presents a new computational method based on the feasible-set method (Berndt, Kucharik, and Shashkov, 2010, “Using the Feasible Set Method for Rezoning in ALE,” Procedia Comput., 1(1), pp. 1879–1886 and Vachal, Garimella, and Shashkov, 2004, “Untangling of 2D Meshes in ALE Simulations,” J. Comput. Phys., 196, pp. 627–644) for removing inverted elements in surface and volume meshes. The proposed method calculates a region for each node called a “feasible set” in which the node can reside without creating an inverted element. The node is then relocated within the region so that the number of inverted elements is reduced. Unlike the original feasible-set method, it is applicable to nonplanar surface meshes, volume meshes, and also has a step for recovering a feasible set when the set is empty. While various useful mesh optimization techniques have been proposed over several decades, many of them do not work well if the initial mesh has inverted elements. Additionally, some mesh optimizations create new inverted elements when the mesh topology is highly irregular. The goal of the proposed method is to remove mesh inversion without creating a new inverted element. The proposed method is useful for preconditioning for conventional smoothing techniques, which require that the initial mesh be inversion free. It is also useful for correcting inverted elements created by conventional smoothing techniques. The effectiveness of the improved method has been verified by applying it to the facet-repair and the boundary-layer generation problems.

A general framework for analysis and comparison of surface mesh optimization techniques

2005 ◽  
Vol 21 (2) ◽  
pp. 91-100 ◽  
Author(s):  
Irina Semenova ◽  
Nikita Kozhekin ◽  
Vladimir Savchenko ◽  
Ichiro Hagiwara
Keyword(s):  
General Framework ◽  
Optimization Techniques ◽  
Mesh Optimization ◽  
Surface Mesh

Tensor based approach to the numerical treatment of the parameter estimation problems in mathematical immunology

2018 ◽  
Vol 26 (1) ◽  
pp. 51-66 ◽  
Author(s):  
Valeriya V. Zheltkova ◽  
Dmitry A. Zheltkov ◽  
Zvi Grossman ◽  
Gennady A. Bocharov ◽  
Eugene E. Tyrtyshnikov
Keyword(s):  
Global Optimization ◽  
Parameter Estimation ◽  
Optimization Techniques ◽  
Computational Method ◽  
Parameter Estimation Problem ◽  
Multiscale Models ◽  
Computational Tools ◽  
Systems Immunology ◽  
Estimation Problems ◽  
Standard Parameter

AbstractThe development of efficient computational tools for data assimilation and analysis using multi-parameter models is one of the major issues in systems immunology. The mathematical description of the immune processes across different scales calls for the development of multiscale models characterized by a high dimensionality of the state space and a large number of parameters. In this study we consider a standard parameter estimation problem for two models, formulated as ODEs systems: the model of HIV infection and BrdU-labeled cell division model. The data fitting is formulated as global optimization of variants of least squares objective function. A new computational method based on Tensor Train (TT) decomposition is applied to solve the formulated problem. The idea of proposed method is to extract the tensor structure of the optimized functional and use it for optimization. The method demonstrated a better performance in comparison with some other broadly used global optimization techniques.

Truncation Error Based Mesh Optimization

2020 ◽  
Vol 5 (4) ◽  
Author(s):  
Charles W. Jackson ◽  
Christopher J. Roy ◽  
Christopher R. Schrock
Keyword(s):  
Truncation Error ◽  
Optimization Technique ◽  
Optimization Methods ◽  
Discretization Error ◽  
Two Dimensions ◽  
Optimization Techniques ◽  
Local Source ◽  
Mesh Optimization ◽  
Design Variables ◽  
Mesh Equidistribution

Abstract Truncation error is used to drive mesh adaptation in order to reduce the discretization error in solutions to a variety of 1D and 2D flow problems. The adaptation is performed using r-adaptation to move the mesh nodes in the domain in an attempt to reduce the truncation error since it is the local source of discretization error. Here, we present a new set of r-adaptation methods called mesh optimization along with three different ways of performing this type of adaptation. Each of these techniques uses a finite difference gradient-based local optimization technique with different sets of design variables to create a mesh that minimizes a functional based on truncation error. These new truncation error based mesh optimization techniques are compared to a more common truncation error based mesh equidistribution technique. Some observations on the performance and behavior of the different adaptation methods and best practices for their use are presented. All of the optimization methods are shown to reduce the truncation error one or two orders of magnitude and the discretization error by roughly one order of magnitude for the 1D problems tested. In two dimensions, the optimization-based adaptation methods are able to reduce the discretization error by up to a factor of seven. Mesh equidistribution achieved similar levels of improvement for much less cost compared to the mesh optimization techniques.

scholarly journals Ecology-guided prediction of cross-feeding interactions in the human gut microbiome

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Akshit Goyal ◽  
Tong Wang ◽  
Veronika Dubinkina ◽  
Sergei Maslov
Keyword(s):  
Gut Microbiome ◽  
Experimental Testing ◽  
Mechanistic Model ◽  
Optimization Techniques ◽  
Computational Method ◽  
Large Network ◽  
Human Gut ◽  
Human Gut Microbiome ◽  
Microbial Species ◽  
Feeding Interactions

AbstractUnderstanding a complex microbial ecosystem such as the human gut microbiome requires information about both microbial species and the metabolites they produce and secrete. These metabolites are exchanged via a large network of cross-feeding interactions, and are crucial for predicting the functional state of the microbiome. However, till date, we only have information for a part of this network, limited by experimental throughput. Here, we propose an ecology-based computational method, GutCP, using which we predict hundreds of new experimentally untested cross-feeding interactions in the human gut microbiome. GutCP utilizes a mechanistic model of the gut microbiome with the explicit exchange of metabolites and their effects on the growth of microbial species. To build GutCP, we combine metagenomic and metabolomic measurements from the gut microbiome with optimization techniques from machine learning. Close to 65% of the cross-feeding interactions predicted by GutCP are supported by evidence from genome annotations, which we provide for experimental testing. Our method has the potential to greatly improve existing models of the human gut microbiome, as well as our ability to predict the metabolic profile of the gut.

scholarly journals Ecology-guided prediction of cross-feeding interactions in the human gut microbiome

2020 ◽  
Author(s):  
Akshit Goyal ◽  
Tong Wang ◽  
Veronika Dubinkina ◽  
Sergei Maslov
Keyword(s):  
Gut Microbiome ◽  
Metabolic Profile ◽  
Mechanistic Model ◽  
Optimization Techniques ◽  
Computational Method ◽  
Large Network ◽  
Human Gut ◽  
Human Gut Microbiome ◽  
Microbial Species ◽  
Feeding Interactions

Understanding a complex microbial ecosystem such as the human gut microbiome requires information about both microbial species and the metabolites they produce and secrete. These metabolites are exchanged via a large network of cross-feeding interactions, and are crucial for predicting the functional state of the microbiome. However, till date, we only have information for a part of this network, limited by experimental throughput. Here, we propose an ecology-based computational method, GutCP, using which we predict hundreds of new experimentally untested cross-feeding interactions in the human gut microbiome. GutCP utilizes a mechanistic model of the gut microbiome with the explicit exchange of metabolites and their effects on the growth of microbial species. To build GutCP, we combined metagenomic and metabolomic measurements from the gut microbiome with optimization techniques from machine learning. Close to 65% of the cross-feeding interactions predicted by GutCP are supported by evidence from genome annotation; we provide these predictions for experimentally testing. Our method has the potential to greatly improve existing models of the human gut microbiome, as well as our ability to predict the metabolic profile of the gut.

scholarly journals LEVELS-OF-DETAIL GENERATION METHOD FOR SKELETAL MESHES

2019 ◽  
Vol 6 (125) ◽  
pp. 3-14
Author(s):  
Yevgeniya Sulema ◽  
Ihor Los
Keyword(s):  
Real World ◽  
Mesh Simplification ◽  
Level Of Detail ◽  
Mesh Optimization ◽  
Improved Method ◽  
Object A ◽  
Virtual Camera ◽  
Levels Of Detail ◽  
Visual Models ◽  
Digital Twins

This paper is devoted to the development of an algorithm for Levels-Of-Detail generation from skinned meshes. Animated meshes, unlike static ones, cannot be simplified without redistributing or recalculation bone weights. In some cases, objects of rendered scene have redundant details. It happens when their size on a screen, the distance from a virtual camera and other factors are such that there is no sense to display these objects in their full complexity, as it may significantly impact time for rendering one frame. One of the solutions is to create a set of Levels-Of-Detail for each object – a set of meshes and/or texture which represent same object, but with lower level of detail – and change the original object with them, when it is necessary. The simplification of visual models is especially important for visualisation of digital twins of real-world objects, subjects, or processes within the digital twin technology. An analysis of existing algorithms for Levels-Of-Detail generation for animated meshes is presented and discussed. An improved method for Levels-Of-Detail generation is introduced and discussed. The proposed method is based on Houle and Poulin animated mesh simplification. However, there are the following core differences in the proposed method: weights of resulting vertices are interpolated, not just copied; multiple poses are used for simplification input. These new features allow to achieve the animated meshes simplification without significant drawbacks in animation quality and mesh optimization.

scholarly journals ANISOTROPIC TRIANGULATION OF PARAMETRIC SURFACES VIA CLOSE PACKING OF ELLIPSOIDS

2000 ◽  
Vol 10 (04) ◽  
pp. 417-440 ◽  
Author(s):  
KENJI SHIMADA ◽  
ATSUSHI YAMADA ◽  
TAKAYUKI ITOH
Keyword(s):  
Tensor Field ◽  
Close Packing ◽  
Computational Method ◽  
Parametric Surface ◽  
Parametric Surfaces ◽  
New Approach ◽  
Anisotropic Mesh ◽  
Mesh Topology ◽  
Principal Axes ◽  
The Given

This paper describes a new computational method of fully automated anisotropic triangulation of a trimmed parametric surface. Given as input: (1) a domain geometry and (2) a 3×3 tensor field that specifies a desired anisotropic node-spacing, this new approach first packs ellipsoids closely in the domain by defining proximity-based interacting forces among the ellipsoids and finding a force-balancing configuration using dynamic simulation. The centers of the ellipsoids are then connected by anisotropic Delaunay triangulation for a complete mesh topology. Since a specified tensor field controls the directions and the lengths of the ellipsoids' principal axes, the method generates a graded anisotropic mesh whose elements conform precisely to the given tensor field.

scholarly journals Ecology-guided prediction of cross-feeding interactions in the human gut microbiome

2020 ◽  
Author(s):  
Akshit Goyal ◽  
Tong Wang ◽  
Veronika Dubinkina ◽  
Sergei Maslov
Keyword(s):  
Gut Microbiome ◽  
Metabolic Profile ◽  
Mechanistic Model ◽  
Optimization Techniques ◽  
Computational Method ◽  
Large Network ◽  
Human Gut ◽  
Human Gut Microbiome ◽  
Microbial Species ◽  
Feeding Interactions

Abstract Understanding a complex microbial ecosystem such as the human gut microbiome requires information about both microbial species and the metabolites they produce and secrete. These metabolites are exchanged via a large network of cross-feeding interactions, and are crucial for predicting the functional state of the microbiome. However, till date, we only have information for a part of this network, limited by experimental throughput. Here, we propose an ecology-based computational method, GutCP, using which we predict hundreds of new experimentally untested cross-feeding interactions in the human gut microbiome. GutCP utilizes a mechanistic model of the gut microbiome with the explicit exchange of metabolites and their effects on the growth of microbial species. To build GutCP, we combined metagenomic and metabolomic measurements from the gut microbiome with optimization techniques from machine learning. Close to 65% of the cross-feeding interactions predicted by GutCP are supported by evidence from genome annotation; we provide these predictions for experimentally testing. Our method has the potential to greatly improve existing models of the human gut microbiome, as well as our ability to predict the metabolic profile of the gut.

A Self-Organizing Mesh Generation Program

1974 ◽  
Vol 96 (3) ◽  
pp. 193-199 ◽  
Author(s):  
R. E. Jones
Keyword(s):  
Mesh Generation ◽  
User Interaction ◽  
Two Dimensional ◽  
Mesh Smoothing ◽  
Smoothing Techniques ◽  
Quadrilateral Elements ◽  
Initial Mesh ◽  
Automatic Mesh ◽  
Self Organizing

A two-dimensional mesh generation program producing quadrilateral elements is presented. It uses a modular, flexible input scheme, and incorporates some existing techniques of initial mesh generation. Some new, more powerful mesh smoothing techniques are developed, and automatic mesh restructuring techniques are coupled with smoothing techniques to produce improved meshes without user interaction.

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