Academic literature on the topic 'Implicit gradient reconstruction'
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Journal articles on the topic "Implicit gradient reconstruction"
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Singh, Manish K., N. Munikrishna, V. Ramesh, and N. Balakrishnan. "Implicit gradient reconstruction (IGR) method for compressible flow simulation." Journal of Physics: Conference Series 822 (April 11, 2017): 012030. http://dx.doi.org/10.1088/1742-6596/822/1/012030.
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Dahlke, Taylor, Biondo Biondi, and Robert Clapp. "Applied 3D salt body reconstruction using shape optimization with level sets." GEOPHYSICS 85, no. 5 (September 1, 2020): R437—R446. http://dx.doi.org/10.1190/geo2019-0352.1.
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As oil and gas extraction becomes more advanced, deep-water exploration becomes increasingly focused on imaging near or under complex salt geology, which necessitates detailed velocity models with strong contrast interfaces. These interfaces can be elegantly tracked using the level sets of an implicit surface. One can invert for the velocity model that best fits the recorded data in a full-waveform inversion (FWI) style objective function by reparameterizing the model in terms of an implicit surface representation of the salt interface. With this parameterization of the FWI objective function, we find the Hessian and solve a conjugate gradient system for the Newton step at every nonlinear iteration. We sparsify the representation of the implicit surface using radial basis functions, which can hasten convergence of the inner inversion by reducing the number of model parameters. We have developed a guided inversion approach that embeds information about the certainty of different salt boundary regions by the initialization of the implicit surface slope at the salt interface. This can help guide the inversion away from perceived local minima. The results of testing this inversion workflow on a 3D Gulf of Mexico data set show that it can be a useful tool for refining salt models because the initial and final seismic images show clearer and more consistent features below the updated salt area.
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Boscheri, Walter, Maurizio Tavelli, and Nicola Paoluzzi. "High order Finite Difference/Discontinuous Galerkin schemes for the incompressible Navier-Stokes equations with implicit viscosity." Communications in Applied and Industrial Mathematics 13, no. 1 (January 1, 2022): 21–38. http://dx.doi.org/10.2478/caim-2022-0003.
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Abstract In this work we propose a novel numerical method for the solution of the incompressible Navier-Stokes equations on Cartesian meshes in 3D. The semi-discrete scheme is based on an explicit discretization of the nonlinear convective flux tensor and an implicit treatment of the pressure gradient and viscous terms. In this way, the momentum equation is formally substituted into the divergence-free constraint, thus obtaining an elliptic equation on the pressure which eventually maintains at the discrete level the involution on the divergence of the velocity field imposed by the governing equations. This makes our method belonging to the class of so-called structure-preserving schemes. High order of accuracy in space is achieved using an efficient CWENO reconstruction operator that is exploited to devise a conservative finite difference scheme for the convective terms. Implicit central finite differences are used to remove the numerical dissipation in the pressure gradient discretization. To avoid the severe time step limitation induced by the viscous eigenvalues related to the parabolic terms in the governing equations, we propose to devise an implicit local discontinuous Galerkin (DG) solver. The resulting viscous sub-system is symmetric and positive definite, therefore it can be efficiently solved at the aid of a matrix-free conjugate gradient method. High order in time is granted by a semi-implicit IMEX time stepping technique. Convergence rates up to third order of accuracy in space and time are proven, and a suite of academic benchmarks is shown in order to demonstrate the robustness and the validity of the novel schemes, especially in the context of high viscosity coefficients.
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Chen, Chong, and Guoliang Xu. "Gradient-flow-based semi-implicit finite-element method and its convergence analysis for image reconstruction." Inverse Problems 28, no. 3 (February 24, 2012): 035006. http://dx.doi.org/10.1088/0266-5611/28/3/035006.
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Zhu, Xiangyuan, Kehua Guo, Hui Fang, Rui Ding, Zheng Wu, and Gerald Schaefer. "Gradient-Based Graph Attention for Scene Text Image Super-resolution." Proceedings of the AAAI Conference on Artificial Intelligence 37, no. 3 (June 26, 2023): 3861–69. http://dx.doi.org/10.1609/aaai.v37i3.25499.
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Scene text image super-resolution (STISR) in the wild has been shown to be beneficial to support improved vision-based text recognition from low-resolution imagery. An intuitive way to enhance STISR performance is to explore the well-structured and repetitive layout characteristics of text and exploit these as prior knowledge to guide model convergence. In this paper, we propose a novel gradient-based graph attention method to embed patch-wise text layout contexts into image feature representations for high-resolution text image reconstruction in an implicit and elegant manner. We introduce a non-local group-wise attention module to extract text features which are then enhanced by a cascaded channel attention module and a novel gradient-based graph attention module in order to obtain more effective representations by exploring correlations of regional and local patch-wise text layout properties. Extensive experiments on the benchmark TextZoom dataset convincingly demonstrate that our method supports excellent text recognition and outperforms the current state-of-the-art in STISR. The source code is available at https://github.com/xyzhu1/TSAN.
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Strauss, Thilo, and Taufiquar Khan. "Implicit Solutions of the Electrical Impedance Tomography Inverse Problem in the Continuous Domain with Deep Neural Networks." Entropy 25, no. 3 (March 13, 2023): 493. http://dx.doi.org/10.3390/e25030493.
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Electrical impedance tomography (EIT) is a non-invasive imaging modality used for estimating the conductivity of an object Ω from boundary electrode measurements. In recent years, researchers achieved substantial progress in analytical and numerical methods for the EIT inverse problem. Despite the success, numerical instability is still a major hurdle due to many factors, including the discretization error of the problem. Furthermore, most algorithms with good performance are relatively time consuming and do not allow real-time applications. In our approach, the goal is to separate the unknown conductivity into two regions, namely the region of homogeneous background conductivity and the region of non-homogeneous conductivity. Therefore, we pose and solve the problem of shape reconstruction using machine learning. We propose a novel and simple jet intriguing neural network architecture capable of solving the EIT inverse problem. It addresses previous difficulties, including instability, and is easily adaptable to other ill-posed coefficient inverse problems. That is, the proposed model estimates the probability for a point of whether the conductivity belongs to the background region or to the non-homogeneous region on the continuous space Rd∩Ω with d∈{2,3}. The proposed model does not make assumptions about the forward model and allows for solving the inverse problem in real time. The proposed machine learning approach for shape reconstruction is also used to improve gradient-based methods for estimating the unknown conductivity. In this paper, we propose a piece-wise constant reconstruction method that is novel in the inverse problem setting but inspired by recent approaches from the 3D vision community. We also extend this method into a novel constrained reconstruction method. We present extensive numerical experiments to show the performance of the architecture and compare the proposed method with previous analytic algorithms, mainly the monotonicity-based shape reconstruction algorithm and iteratively regularized Gauss–Newton method.
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Zang, Miao, Huimin Xu, and Yongmei Zhang. "Kernel-Based Multiview Joint Sparse Coding for Image Annotation." Mathematical Problems in Engineering 2017 (2017): 1–11. http://dx.doi.org/10.1155/2017/6727105.
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It remains a challenging task for automatic image annotation problem due to the semantic gap between visual features and semantic concepts. To reduce the gap, this paper puts forward a kernel-based multiview joint sparse coding (KMVJSC) framework for image annotation. In KMVJSC, different visual features as well as label information are considered as distinct views and are mapped to an implicit kernel space, in which the original nonlinear separable data become linearly separable. Then, all the views are integrated into a multiview joint sparse coding framework aiming to find a set of optimal sparse representations and discriminative dictionaries adaptively, which can effectively employ the complementary information of different views. An optimization algorithm is presented by extending K-singular value decomposition (KSVD) and accelerated proximal gradient (APG) algorithms to the kernel multiview framework. In addition, a label propagation scheme using the sparse reconstruction and weighted greedy label transfer algorithm is also proposed. Comparative experiments on three datasets have demonstrated the competitiveness of proposed approach compared with other related methods.
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Bates, Oscar, Lluis Guasch, George Strong, Thomas Caradoc Robins, Oscar Calderon-Agudo, Carlos Cueto, Javier Cudeiro, and Mengxing Tang. "A probabilistic approach to tomography and adjoint state methods, with an application to full waveform inversion in medical ultrasound." Inverse Problems 38, no. 4 (March 14, 2022): 045008. http://dx.doi.org/10.1088/1361-6420/ac55ee.
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Abstract Bayesian methods are a popular research direction for inverse problems. There are a variety of techniques available to solve Bayes’ equation, each with their own strengths and limitations. Here, we discuss stochastic variational inference (SVI), which solves Bayes’ equation using gradient-based methods. This is important for applications which are time-limited (e.g. medical tomography) or where solving the forward problem is expensive (e.g. adjoint methods). To evaluate the use of SVI in both these contexts, we apply it to ultrasound tomography of the brain using full-waveform inversion (FWI). FWI is a computationally expensive adjoint method for solving the ultrasound tomography inverse problem, and we demonstrate that SVI can be used to find a no-cost estimate of the pixel-wise variance of the sound-speed distribution using a mean-field Gaussian approximation. In other words, we show experimentally that it is possible to estimate the pixel-wise uncertainty of the sound-speed reconstruction using SVI and a common approximation which is already implicit in other types of iterative reconstruction. Uncertainty estimates have a variety of uses in adjoint methods and tomography. As an illustrative example, we focus on the use of uncertainty for image quality assessment. This application is not limiting; our variance estimator has effectively no computational cost and we expect that it will have applications in fields such as non-destructive testing or aircraft component design where uncertainties may not be routinely estimated.
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Bi, Sheng, Jianzhong Zhou, Yi Liu, and Lixiang Song. "A Finite Volume Method for Modeling Shallow Flows with Wet-Dry Fronts on Adaptive Cartesian Grids." Mathematical Problems in Engineering 2014 (2014): 1–20. http://dx.doi.org/10.1155/2014/209562.
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A second-order accurate, Godunov-type upwind finite volume method on dynamic refinement grids is developed in this paper for solving shallow-water equations. The advantage of this grid system is that no data structure is needed to store the neighbor information, since neighbors are directly specified by simple algebraic relationships. The key ingredient of the scheme is the use of the prebalanced shallow-water equations together with a simple but effective method to track the wet/dry fronts. In addition, a second-order spatial accuracy in space and time is achieved using a two-step unsplit MUSCL-Hancock method and a weighted surface-depth gradient method (WSDM) which considers the local Froude number is proposed for water depths reconstruction. The friction terms are solved by a semi-implicit scheme that can effectively prevent computational instability from small depths and does not invert the direction of velocity components. Several benchmark tests and a dam-break flooding simulation over real topography cases are used for model testing and validation. Results show that the proposed model is accurate and robust and has advantages when it is applied to simulate flow with local complex topographic features or flow conditions and thus has bright prospects of field-scale application.
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PADOVANI, E., E. PRIOLO, and G. SERIANI. "LOW AND HIGH ORDER FINITE ELEMENT METHOD: EXPERIENCE IN SEISMIC MODELING." Journal of Computational Acoustics 02, no. 04 (December 1994): 371–422. http://dx.doi.org/10.1142/s0218396x94000233.
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The finite element method (FEM) is a numerical technique well suited to solving problems of elastic wave propagation in complex geometries and heterogeneous media. The main advantages are that very irregular grids can be used, free surface boundary conditions can be easily taken into account, a good reconstruction is possible of irregular surface topography, and complex geometries, such as curved, dipping and rough interfaces, intrusions, cusps, and holes can be defined. The main drawbacks of the classical approach are the need for a large amount of memory, low computational efficiency, and the possible appearance of spurious effects. In this paper we describe some experience in improving the computational efficiency of a finite element code based on a global approach, and used for seismic modeling in geophysical oil exploration. Results from the use of different methods and models run on a mini-superworkstation APOLLO DN10000 are reported and compared. With Chebyshev spectral elements, great accuracy can be reached with almost no numerical artifacts. Static condensation of the spectral element's internal nodes dramatically reduces memory requirements and CPU time. Time integration performed with the classical implicit Newmark scheme is very accurate but not very efficient. Due to the high sparsity of the matrices, the use of compressed storage is shown to greatly reduce not only memory requirements but also computing time. The operation which most affects the performance is the matrix-by-vector product; an effective programming of this subroutine for the storage technique used is decisive. The conjugate gradient method preconditioned by incomplete Cholesky factorization provides, in general, a good compromise between efficiency and memory requirements. Spectral elements greatly increase its efficiency, since the number of iterations is reduced. The most efficient and accurate method is a hybrid iterative-direct solution of the linear system arising from the static condensation of high order elements. The size of 2D models that can be handled in a reasonable time on this kind of computer is nowadays hardly sufficient, and significant 3D modeling is completely unfeasible. However the introduction of new FEM algorithms coupled with the use of new computer architectures is encouraging for the future.
Dissertations / Theses on the topic "Implicit gradient reconstruction"
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De, Santis Dante. "Development of a high-order residual distribution method for Navier-Stokes and RANS equations." Phd thesis, Université Sciences et Technologies - Bordeaux I, 2013. http://tel.archives-ouvertes.fr/tel-00946171.
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The construction of compact high-order Residual Distribution schemes for the discretizationof steady multidimensional advection-diffusion problems on unstructuredgrids is presented. Linear and non-linear scheme are considered. A piecewise continuouspolynomial approximation of the solution is adopted and a gradient reconstructionprocedure is used in order to have a continuous representation of both thenumerical solution and its gradient. It is shown that the gradient must be reconstructedwith the same accuracy of the solution, otherwise the formal accuracy ofthe numerical scheme is lost in applications in which diffusive effects prevail overthe advective ones, and when advection and diffusion are equally important. Thenthe method is extended to systems of equations, with particular emphasis on theNavier-Stokes and RANS equations. The accuracy, efficiency, and robustness of theimplicit RD solver is demonstrated using a variety of challenging aerodynamic testproblems.
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De, Santis Dante. "Schémas d'ordre élevé distribuant le résidu pour la résolution des équations de Navier-Stokes et Navier-Stokes moyennées (RANS)." Phd thesis, Université Sciences et Technologies - Bordeaux I, 2013. http://tel.archives-ouvertes.fr/tel-00935419.
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Cette thèse présente la construction de schémas distribuant le résidu (RD) d'ordre très élevés, pour la discrétisation d'équations d'advection-diffusion multidimensionnelles et stationnaires sur maillages non structurés. Des schémas linéaires ainsi que des schémas non linéaires sont considérés. Une approximation de la solution polynomiale par morceaux et continue sur chaque élément est adoptée, de plus une procédure de reconstruction du gradient que celle de la solution numérique est utilisée afin d'avoir une représentation continue de la solution numérique et de son gradient. Il est montré que le gradient doit être reconstruit avec la même précision de la solution, sans quoi la précision formel du schéma numérique est perdue dans les cas où les effets de diffusion prévalent sur les effets d'advection, et aussi quand l'advection et la diffusion sont également importants. Ensuite, la méthode est étendue à des systèmes d'équations, en particulier aux équations de Navier-Stokes et aux équations RANS. La précision, l'efficacité et la robustesse du solveur RD implicite sont démontrées sur plusieurs cas tests.
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Singh, Manish Kumar. "Implicit Gradient Reconstruction for Unstructured Mesh Finite Volume Method." Thesis, 2022. https://etd.iisc.ac.in/handle/2005/5934.
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In the present work, an Implicit Gradient Reconstruction (IGR) method is proposed in the
context of Finite Volume Methodology (FVM). There are three computationally intensive steps
involved in a typical finite volume framework for a spatially second-order accurate upwind
scheme. These are solution reconstruction, solution limiting and flux finding. Solution re-
construction involves determination of gradients while solution limiting requires comparison
of double precision numbers. Further, computation of gradient and solution limiting is cell
based procedure while flux finding is edge/face based procedure. The proposed IGR procedure,
which is edge/face based procedure, integrates all these steps obviating explicit reconstruction
and limiting steps resulting in a considerable reduction in computational effort and associated
memory footprint.
In the modified CIR (MCIR) scheme of linear convection equation, a parameter φ is in-
troduced to control dissipation. The IGR procedure is derived from the MCIR scheme. The
relation between the φ parameter and solution reconstruction in a finite volume procedure is
systematically established. The methodology is extended to multidimensions, where the use of
φ implicitly represents a reconstruction step. Hence, this procedure is referred to as Implicit
Gradient Reconstruction. In addition, it is brought out that the use of φ also serves the purpose
of solution limiting. The spatial accuracy of this procedure is demonstrated by computing the
2-D circular convection problem.
The methodology, when extended to the Euler equations of Gas dynamics, results in the
reconstruction of the characteristic variables. Consequently, three steps in the computation of
explicit residual, namely, solution reconstruction, limiting and flux computation, are seamlessly
merged into a single step. Owing to its significantly smaller memory footprint, the procedure
is particularly relevant to large scale parallel computing. This procedure can be effortlessly
incorporated into any of the existing finite volume solvers where inviscid flux formulation is
based on characteristic decomposition. The capability of IGR procedure is established through
several test cases involving inviscid and viscous flow computations in one and two dimensions.
The results obtained from IGR procedure are compared with reconstruction based solvers and wind tunnel data wherever available. The IGR procedure produces results comparable to the
classical reconstruction based procedure.
The aforementioned IGR procedure is applicable to any flux formulation involving charac-
teristic decomposition. An Edge Based Reconstruction Limiting (EBRL) is proposed for flux
formulation not involving characteristic decomposition. This procedure is very simple and does
not require classical diamond path reconstruction. The results obtained from EBRL based Roe
and AUSM Plus flux formulation on transonic viscous flow over RAE 2822 airfoil are very good
and compare well with wind tunnel experiments.
Conference papers on the topic "Implicit gradient reconstruction"
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Sommer, Christiane, Lu Sang, David Schubert, and Daniel Cremers. "Gradient-SDF: A Semi-Implicit Surface Representation for 3D Reconstruction." In 2022 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). IEEE, 2022. http://dx.doi.org/10.1109/cvpr52688.2022.00618.
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Veyrat, A., J. F. Carrotte, A. D. Walker, C. Hall, and H. Simpson. "A Rapid Viscous-Inviscid Interaction Method for the Preliminary Design of S-Shaped Transition Ducts." In ASME Turbo Expo 2021: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/gt2021-59515.
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Abstract For preliminary design of compressor transition ducts, knowledge-based tools for the rapid assessment of aerodynamic performance of S-shaped ducts are not currently available in the open literature. This is due to the highly complex flow developing under the combined influence of pressure gradients and streamline curvature. This paper presents a new approach enabling an agile design process avoiding premature use of time-consuming high-fidelity CFD calculations. The features of a 2D axisymmetric incompressible steady flow field are captured with a semi-analytical viscous inviscid interaction method. A potential core, based on streamline curvature and implicit velocity profile by parametric spline reconstruction, is coupled to an integral method predicting the turbulent boundary layer growth up to separation. The shear stress distribution is generated by a modified mixing length model for strongly curved flows and wall shear stress closure is performed by inverse calculation of a composite law-of-the-wall. When compared to CFD, the aerodynamic loading is generally predicted to within ±3% but convergence is achieved 20 times faster.
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Schilling, Oleg. "Reynolds-Averaged Navier-Stokes Modeling of Turbulent Rayleigh-Taylor, Richtmyer-Meshkov, and Kelvin-Helmholtz Mixing Using a Higher-Order Shock-Capturing Method." In ASME-JSME-KSME 2019 8th Joint Fluids Engineering Conference. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/ajkfluids2019-5235.
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Abstract A numerical implementation of a large number of Reynolds-averaged Navier–Stokes (RANS) models based on two-, three-, four-equation, and Reynolds stress turbulence models (using either the turbulent kinetic energy dissipation rate or the turbulent lengthscale) in an Eulerian, finite-difference shock-capturing code is described. The code uses third-order weighted essentially nonoscillatory (WENO) reconstruction of the advective fluxes, and second- or fourth-order central difference derivatives for the computation of spatial gradients. A third-order TVD Runge–Kutta time-evolution scheme is used to evolve the fields in time. Improved closures for the turbulence production terms, compressibility corrections, mixture transport coefficients, and a consistent initialization methodology for the turbulent fields are briefly summarized. The code framework allows for systematic comparisons of detailed predictions from a variety of turbulence models of increasing complexity. Applications of the code with selected K–ε based models are illustrated for each of the three instabilities. Simulations of Rayleigh–Taylor unstable flows for Atwood numbers 0.1–0.9 are shown to be consistent with previous implicit LES (ILES) results and with the expectation of increased asymmetry in the mixing layer characteristics with increasing stratification. Simulations of reshocked Richtmyer–Meshkov turbulent mixing corresponding to experiments with light-to-heavy transition in air/sulfur hexafluoride and incident shock Mach number Mas = 1.50, and heavy-to-light transition in sulfur hexafluoride/air with Mas = 1.45 are shown to be in generally good agreement with both pre- and post-reshock mixing layer widths. Finally, simulations of the seven Brown–Roshko Kelvin–Helmholtz experiments with various velocity and density ratios using nitrogen, helium, and air are shown to give mixing layer predictions in good agreement with data. The results indicate that the numerical algorithms and turbulence models are suitable for simulating these classes of inhomogeneous turbulent flows.