Search NASA⌕ Search

SEARCH · Search NASA

Results for “level sets”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Delineating Facies Spatial Distribution by Integrating Ensemble Data Assimilation and Indicator Geostatistics with Level-Set Transformation

The facies-based approach has been widely adopted to delineate an aquifer into distinct geological units with unique distributions of hydraulic, physical, and/or chemical properties. The recent development in ensemble-based data assimilation methods allows both the direct and indirect data to be used to improve facies delineation. A major difficulty in those applications is to honor the spatial continuity and avoid overfitting after data assimilation. We introduce a new facies delineation framework to integrate ensemble data assimilation with traditional transition probability-based geostatistics. A level-set concept is used to parametrize discrete facies indicators and for updating facies shape. During the iterative data assimilation process, we impose spatial continuity by conditioning facies field generation on points selected adaptively based on their sensitivity to observation data. This reconditioning step is a key step to maintain spatial continuity and overcome over-fitting problems in inversion. We selected two examples to evaluate the performance of the new framework in estimating facies-based permeability field. The first example is a two-dimensional synthetic system with transient head data induced by pumping tests used for delineating two facies. The second example is a three-dimensional case with three facies, conceptualized from a field tracer experiment within the Columbia River corridor in Washington State, USA. Both examples demonstrate that the new method can adequately capture the spatial pattern of hydrofacies with reconditioning, which leads to the improved prediction of system behaviors.

Song, Xuehang↗
DOE OSTI2022

Minimum feature size control in level set topology optimization via density fields

A level set topology optimization approach that uses an auxiliary density field to nucleate holes during the optimization process and achieves minimum feature size control in optimized designs is explored. The level set field determines the solid-void interface and the density field describes the distribution of a fictitious porous material using the solid isotropic material with penalization. These fields are governed by two sets of independent optimization variables which are initially coupled using a penalty for hole nucleation. The strength of the density field penalization and projection is gradually increased during the optimization process to promote a 0-1 density distribution. In addition, a second penalty regulates the evolution of the density field in the void phase. The treatment of the density field combined with the second penalty mitigate the appearance of small design features. The minimum feature size of optimized designs is controlled by the radius of the linear filter applied to the density optimization variables. The structural response is predicted by the extended finite element method, the sensitivities by the adjoint method, and the optimization variables are updated by a gradient-based optimization algorithm. Numerical examples investigate the robustness of this approach with respect to algorithmic parameters and mesh refinement. The results show the applicability of the combined density level set topology optimization approach for both optimal hole nucleation and for minimum feature size control in 2D and 3D. This comes, however, at the cost of a more complex problem formulation and additional computational cost due to an increased number of optimization variables.

42 ENGINEERING↗
DOE OSTI2017

An arbitrary-order Runge–Kutta discontinuous Galerkin approach to reinitialization for banded conservative level sets

Here, we present a Runge-Kutta discontinuous Galerkin method for solving conservative reinitialization in the context of the conservative level set method. This represents an extension of the method recently proposed by Owkes and Desjardins [21], by solving the level set equations on the refined level set grid and projecting all spatially-dependent variables into the full basis used by the discontinuous Galerkin discretization. By doing so, we achieve the full k+1 order convergence rate in the L1 norm of the level set field predicted for RKDG methods given kth degree basis functions when the level set profile thickness is held constant with grid refinement. Shape and volume errors for the 0.5-contour of the level set, on the other hand, are found to converge between first and second order. We show a variety of test results, including the method of manufactured solutions, reinitialization of a circle and sphere, Zalesak's disk, and deforming columns and spheres, all showing substantial improvements over the high-order finite difference traditional level set method studied for example by Herrmann. We also demonstrate the need for kth order accurate normal vectors, as lower order normals are found to degrade the convergence rate of the method.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2015

Level-Set Topology Optimization with Aeroelastic Constraints

Level-set topology optimization is used to design a wing considering skin buckling under static aeroelastic trim loading, as well as dynamic aeroelastic stability (flutter). The level-set function is defined over the entire 3D volume of a transport aircraft wing box. Therefore, the approach is not limited by any predefined structure and can explore novel configurations. The Sequential Linear Programming (SLP) level-set method is used to solve the constrained optimization problems. The proposed method is demonstrated using three problems with mass, linear buckling and flutter objective and/or constraints. A constraint aggregation method is used to handle multiple buckling constraints in the wing skins. A continuous flutter constraint formulation is used to handle difficulties arising from discontinuities in the design space caused by a switching of the critical flutter mode.

Dunning, Peter D.↗
DOE OSTI2018

Identifying arbitrary parameter zonation using multiple level set functions

In this paper, we extended the analytical level set method [1, 2] for identifying a piece-wisely heterogeneous (zonation) binary system to the case with an arbitrary number of materials with unknown material properties. In the developed level set approach, starting from an initial guess, the material interfaces are propagated through iterations such that the residuals between the simulated and observed state variables (hydraulic head) is minimized. We derived an expression for the propagation velocity of the interface between any two materials, which is related to the permeability contrast between the materials on two sides of the interface, the sensitivity of the head to permeability, and the head residual. We also formulated an expression for updating the permeability of all materials, which is consistent with the steepest descent of the objective function. The developed approach has been demonstrated through many examples, ranging from totally synthetic cases to a case where the flow conditions are representative of a groundwater contaminant site at the Los Alamos National Laboratory. These examples indicate that the level set method can successfully identify zonation structures, even if the number of materials in the model domain is not exactly known in advance. Although the evolution of the material zonation depends on the initial guess field, inverse modeling runs starting with different initial guesses fields may converge to the similar final zonation structure. These examples also suggest that identifying interfaces of spatially distributed heterogeneities is more important than estimating their permeability values.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Level set methods for detonation shock dynamics using high-order finite elements

Level set methods are a popular approach to modeling evolving interfaces. We present a level set ad- vection solver in two and three dimensions using the discontinuous Galerkin method with high-order nite elements. During evolution, the level set function is reinitialized to a signed distance function to maintain ac- curacy. Our approach leads to stable front propagation and convergence on high-order, curved, unstructured meshes. The ability of the solver to implicitly track moving fronts lends itself to a number of applications; in particular, we highlight applications to high-explosive (HE) burn and detonation shock dynamics (DSD). We provide results for two- and three-dimensional benchmark problems as well as applications to DSD.

finite element methods↗
DOE OSTI2021

Evaluating Gaussian process metamodels and sequential designs for noisy level set estimation

Abstract We consider the problem of learning the level set for which a noisy black-box function exceeds a given threshold. To efficiently reconstruct the level set, we investigate Gaussian process (GP) metamodels. Our focus is on strongly stochastic simulators, in particular with heavy-tailed simulation noise and low signal-to-noise ratio. To guard against noise misspecification, we assess the performance of three variants: (i) GPs with Student- t observations; (ii) Student- t processes (TPs); and (iii) classification GPs modeling the sign of the response. In conjunction with these metamodels, we analyze several acquisition functions for guiding the sequential experimental designs, extending existing stepwise uncertainty reduction criteria to the stochastic contour-finding context. This also motivates our development of (approximate) updating formulas to efficiently compute such acquisition functions. Our schemes are benchmarked by using a variety of synthetic experiments in 1–6 dimensions. We also consider an application of level set estimation for determining the optimal exercise policy of Bermudan options in finance.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

A high-order discontinuous Galerkin method for level set problems on polygonal meshes

We propose and analyze discontinuous Galerkin schemes for solving level set equations on polygonal meshes. For linear equations, we assume that the velocity is given only on the cell surface. Velocity inside mesh cells is approximated using virtual element projectors on polynomial spaces. For nonlinear equations, we use the Taylor expansion to approximate the normalized solution gradient. Here, we analyze the new schemes for a set of typical level set problems using square and polygonal meshes. The numerical results indicate great potential for using polygonal meshes in applications.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2011

Accurate Adaptive Level Set Method and Sharpening Technique for Three Dimensional Deforming Interfaces

In this paper, we demonstrate improved accuracy of the level set method for resolving deforming interfaces by proposing two key elements: (1) accurate level set solutions on adapted Cartesian grids by judiciously choosing interpolation polynomials in regions of different grid levels and (2) enhanced reinitialization by an interface sharpening procedure. The level set equation is solved using a fifth order WENO scheme or a second order central differencing scheme depending on availability of uniform stencils at each grid point. Grid adaptation criteria are determined so that the Hamiltonian functions at nodes adjacent to interfaces are always calculated by the fifth order WENO scheme. This selective usage between the fifth order WENO and second order central differencing schemes is confirmed to give more accurate results compared to those in literature for standard test problems. In order to further improve accuracy especially near thin filaments, we suggest an artificial sharpening method, which is in a similar form with the conventional re-initialization method but utilizes sign of curvature instead of sign of the level set function. Consequently, volume loss due to numerical dissipation on thin filaments is remarkably reduced for the test problems

Kim, Hyoungin↗
DOE OSTI2024

Level-set topology optimization with PDE generated conformal meshes

This paper presents a level-set topology optimization approach that uses conformal meshes for the analysis of the displacement field. The structure’s boundary is represented by the iso-contour of a level-set field discretized on a fixed background design mesh. The conformal mesh is updated for each design iteration via a PDE based mesh morphing process that identifies the set of facets in the background mesh that are homeomorphic to the boundary and relaxes the homeomorphic mesh to conform to the structure’s boundary and ensure high element quality. The conformal mesh allows for a more accurate computation of the response versus density and some level-set based methods which interpolate material properties using the volume fraction. Numerical examples illustrate the proposed approach by optimizing linear-elastic two- and three-dimensional structures, wherein insight into the performance of the mesh morphing process is provided. The examples also highlight the scalability of the approach.

42 ENGINEERING↗
DOE OSTI2019

Learning nonlinear level sets for dimensionality reduction in function approximation

We developed a Nonlinear Level-set Learning (NLL) method for dimensionality reduction in high-dimensional function approximation with small data. This work is motivated by a variety of design tasks in real-world engineering applications, where practitioners would replace their computationally intensive physical models (e.g., high-resolution fluid simulators) with fast-to-evaluate predictive machine learning models, so as to accelerate the engineering design processes. There are two major challenges in constructing such predictive models: (a) high-dimensional inputs (e.g., many independent design parameters) and (b) small training data, generated by running extremely time-consuming simulations. Thus, reducing the input dimension is critical to alleviate the over-fitting issue caused by data insufficiency. Existing methods, including sliced inverse regression and active subspace approaches, reduce the input dimension by learning a linear coordinate transformation; our main contribution is to extend the transformation approach to a nonlinear regime. Specifically, we exploit reversible networks (RevNets) to learn nonlinear level sets of a high-dimensional function and parameterize its level sets in low-dimensional spaces. A new loss function was designed to utilize samples of the target functions' gradient to encourage the transformed function to be sensitive to only a few transformed coordinates. The NLL approach is demonstrated by applying it to three 2D functions and two 20D functions for showing the improved approximation accuracy with the use of nonlinear transformation, as well as to an 8D composite material design problem for optimizing the buckling-resistance performance of composite shells of rocket inter-stages.

Zhang, Guannan↗
DOE OSTI2024

Adaptive immersed isogeometric level-set topology optimization

Here, this paper presents for the first time an adaptive immersed approach for level-set topology optimization using higher-order truncated hierarchical B-spline discretizations for design and state variable fields. Boundaries and interfaces are represented implicitly by the iso-contour of one or multiple level-set functions. An immersed finite element method, the eXtended IsoGeometric Analysis, is used to predict the physical response. The proposed optimization framework affords different adaptively refined higher-order B-spline discretizations for individual design and state variable fields. The increased continuity of higher-order B-spline discretizations together with local refinement enables direct control over the accuracy of the representation of each field while simultaneously reducing computational cost compared to uniformly refined discretizations. A flexible mesh adaptation strategy enables local refinement based on geometric measures or physics-based error indicators. These adaptive discretization and analysis approaches are integrated into gradient-based optimization schemes, evaluating the design sensitivities using the adjoint method. Numerical studies illustrate the features of the proposed framework with static, linear elastic, multi-material, two- and three-dimensional problems. The examples provide insight into the effect of refining the design variable field on the optimization result and the convergence rate of the optimization process. Using coarse higher-order B-spline discretizations for level-set fields promotes the development of smooth designs and suppresses the emergence of small features. Moreover, adaptive mesh refinement for state variable fields results in a reduction of overall computational cost. Higher-order B-spline discretizations are especially interesting when evaluating gradients of state variable fields due to their higher inter-element continuity.

36 MATERIALS SCIENCE↗
DOE OSTI2023

A Level Set Model for Structured Mesh Representation of Fibrous Preforms used in Composites Manufacturing

Here, a model for implicit representation of fibrous and woven preforms used for composites manufacturing is described. The method is based on a level set function defined on a structured mesh to implicitly capture the complex fiber and weave geometries. Since most software packages used to model woven preforms are based on unstructured mesh, a numerical model for transforming a discretized surface to a structured mesh representation and vice-a-versa is presented. Specific emphasis is on scalable computation of a level set function for large and complex 3D woven structures from a triangulated surface of the smallest unit (yarn). The model is applied to capture a periodic 3D layered 5-harness satin (5HS) weave geometry on a structured mesh. Geometric transformations needed to efficiently compute the level set function for the 3D structure on a high resolution mesh are described. Effects of mesh resolution on the geometric features such as number of resolved fibers, effective fiber size, and the surface area to volume ratio of the iso-surface are analyzed. Using the distance property of the level set function, an approach to evaluate the structure function resulting from transient evolving topology representing densification due to matrix phase depositions is also presented. The approach captures transition of the geometric characteristic from fiber governed at early stages of densification to yarn governed at the terminal stage.

36 MATERIALS SCIENCE↗
NASA NTRS2014

Aerostructural Level Set Topology Optimization for a Common Research Model Wing

The purpose of this work is to use level set topology optimization to improve the design of a representative wing box structure for the NASA common research model. The objective is to minimize the total compliance of the structure under aerodynamic and body force loading, where the aerodynamic loading is coupled to the structural deformation. A taxi bump case was also considered, where only body force loads were applied. The trim condition that aerodynamic lift must balance the total weight of the aircraft is enforced by allowing the root angle of attack to change. The level set optimization method is implemented on an unstructured three-dimensional grid, so that the method can optimize a wing box with arbitrary geometry. Fast matching and upwind schemes are developed for an unstructured grid, which make the level set method robust and efficient. The adjoint method is used to obtain the coupled shape sensitivities required to perform aerostructural optimization of the wing box structure.

Dunning, Peter D.↗
DOE OSTI2023

A level-set immersed boundary method for reactive transport in complex topologies with moving interfaces

A simulation framework based on the level-set and the immersed boundary methods (LS-IBM) has been developed for reactive transport problems in porous media involving a moving solid-fluid interface. The interface movement due to surface reactions is tracked by the level-set method, while the immersed boundary method captures the momentum and mass transport at the interface. The proposed method is capable of accurately modeling transport near evolving boundaries in Cartesian grids. The framework formulation guarantees second order accuracy in space. Since the interface velocity is only defined at the moving boundary, an interface velocity propagation method is also proposed. The method can be applied to other moving interface problems of the “Stefan” type. Here, we validate the proposed LS-IBM both for flow and transport close to an immersed object with reactive boundaries as well as for crystal growth. Lastly, the proposed method provides a powerful tool to model more realistic problems involving moving reactive interfaces in complex domains.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2003

A Cartesian Adaptive Level Set Method for Two-Phase Flows

In the present contribution we develop a level set method based on local anisotropic Cartesian adaptation as described in Ham et al. (2002). Such an approach should allow for the smallest possible Cartesian grid capable of resolving a given flow. The remainder of the paper is organized as follows. In section 2 the level set formulation for free surface calculations is presented and its strengths and weaknesses relative to the other free surface methods reviewed. In section 3 the collocated numerical method is described. In section 4 the method is validated by solving the 2D and 3D drop oscilation problem. In section 5 we present some results from more complex cases including the 3D drop breakup in an impulsively accelerated free stream, and the 3D immiscible Rayleigh-Taylor instability. Conclusions are given in section 6.

Ham, F.↗
DOE OSTI2021

Hierarchical median narrow band for level set segmentation of cervical cell nuclei

This paper presents a novel hierarchical nuclei segmentation algorithm for isolated and overlapping cervical cells based on a narrow band level set implementation. Our method applies a new multiscale analysis algorithm to estimate the number of clusters in each image region containing cells, which turns into the input to a narrow band level set algorithm. We assess the nuclei segmentation results on three public cervical cell image databases. Overall, our segmentation method outperformed six state-of-the-art methods concerning the number of correctly segmented nuclei and the Dice coefficient reached values equal to or higher than 0.90. We also carried out classification experiments using features extracted from our segmentation results and the proposed pipeline achieved the highest average accuracy values equal to 0.89 and 0.77 for two-class and three-class problems, respectively. Furthermore, these results demonstrated the suitability of the proposed segmentation algorithm to integrate decision support systems for cervical cell screening.

47 OTHER INSTRUMENTATION↗