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Zhang, Zhao. "Numerical Analysis and Comparison of Gridless Partial Differential Equations." International Journal of Circuits, Systems and Signal Processing 15 (August 31, 2021): 1223–31. http://dx.doi.org/10.46300/9106.2021.15.133.
Повний текст джерелаАнотація:
In the field of science and engineering, partial differential equations play an important role in the process of transforming physical phenomena into mathematical models. Therefore, it is very important to get a numerical solution with high accuracy. In solving linear partial differential equations, meshless solution is a very important method. Based on this, we propose the numerical solution analysis and comparison of meshless partial differential equations (PDEs). It is found that the interaction between the numerical solutions of gridless PDEs is better, and the absolute error and relative error are lower, which proves the superiority of the numerical solutions of gridless PDEs
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Long, Haining, Ting Su, Xianpeng Wang, and Mengxing Huang. "Gridless Multiple Measurements Method for One-Bit DOA Estimation with a Nested Cross-Dipole Array." Wireless Communications and Mobile Computing 2021 (August 31, 2021): 1–10. http://dx.doi.org/10.1155/2021/6635220.
Повний текст джерелаАнотація:
The gridless one-bit direction of arrival (DOA) estimator is proposed to estimate electromagnetic (EM) sources on a nested cross-dipole array, and the multiple measurement vectors (MMV) mode is introduced to improve the reliability of parameter estimation. The gridless method is based on atomic norm minimization, solved by alternating direction multiplier method (ADMM). With gridless method used, sign inconsistency caused by one-bit measurements and basis mismatches by traditional grid-based algorithms can be avoided. Furthermore, the reconstructed denoising measurements with fast convergence and stable recovery accuracy are obtained by ADMM. Finally, spatial smoothing root multiple signal classification (SSRMUSIC) and dual polynomial (DP) methods are used, respectively, to estimate the DOAs on the reconstructed denoising measurements. Numerical results show that our method one-bit ADMM-SSRMUSIC has a better performance than that of one-bit SSRMUSIC used directly. At low signal to noise ratio (SNR) and low snapshot, the one-bit ADMM-DP has an excellent performance which is even better than that of unquantized MUSIC. In addition, the proposed methods are also suitable for both completely polarized (CP) signals and partially polarized (PP) signals.
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Pu, Sai Hu. "Gridless Adaptive Method for Simulating Unsteady Flows with Moving Shocks." Applied Mechanics and Materials 271-272 (December 2012): 948–52. http://dx.doi.org/10.4028/www.scientific.net/amm.271-272.948.
Повний текст джерелаАнотація:
In this paper, the gridless adaptive method is extended to simulate unsteady flows with moving shocks. In order to capture physical features like moving shocks with local high resolution, a technique of dynamic cloud of points is achieved by adopting clouds refinement and clouds coarsening procedures during the evolution of the unsteady flows. The regions for clouds refinement and clouds coarsening are determined at every time step by an indicator, which is defined as a function of the local pressure gradient. Once the regions of cloud of points to be adjusted are located by the indicator, the clouds refinement is carried out by introducing new points based on the existing structure of cloud of points, and the clouds coarsening procedure is also implemented simultaneously in order to control the size of the points distributed in the whole computational domain. The numerical test cases show that the gridless adaptive method presented can capture moving shocks with high resolution successfully in both inviscid and viscous test cases.
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Chhatkuli, Subas, Seiichi Koshizuka, and Mitsuru Uesaka. "Dynamic Tracking of Lung Deformation during Breathing by Using Particle Method." Modelling and Simulation in Engineering 2009 (2009): 1–7. http://dx.doi.org/10.1155/2009/190307.
Повний текст джерелаАнотація:
To reduce the side effects and to improve the efficiency of radiation therapy in lung cancer, a pinpoint radiation therapy system is under development. In the system, the movement of lung tumor during breathing could be estimated by employing a suitable numerical modeling technique. This paper presents a gridless numerical technique called Moving Particle Semi-implicit (MPS) method to simulate the lung deformation during breathing. The potential of the proposed method to employ in the future pinpoint radiation therapy system has been explored. Deformation of lung during breathing was dynamically tracked and compared against the experimental results at two different locations (upper lobe and lower lobe). Numerical simulations showed that the deformation of lung surface ranged from less than 4 mm to over 20 mm depending on the location at the surface of lung. The simulation showed that the lower section of lung exhibited comparatively large displacement than the upper section. Comparing with the experimental data, the lung surface displacement during inspiration process was predicted reasonably well. Comparison of numerical prediction with experimental observations showed that the root mean squared error was about 2 mm at lower lobe and less than 1 mm at upper lobe at lung surface.
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LANDRINI, M., A. COLAGROSSI, M. GRECO, and M. P. TULIN. "Gridless simulations of splashing processes and near-shore bore propagation." Journal of Fluid Mechanics 591 (October 30, 2007): 183–213. http://dx.doi.org/10.1017/s0022112007008142.
Повний текст джерелаАнотація:
The generation and evolution of two-dimensional bores in water of uniform depth and on sloping beaches are simulated through numerical solution of the Euler equations using the smoothed particle hydrodynamics (SPH) method, wherein particles are followed in Lagrangian fashion, avoiding the need for computational grids. In water of uniform depth, a piston wavemaker produces cyclically breaking bores in the Froude number range 1.37–1.82, which were shown to move at time-averaged speeds in very good agreement with the requirements of global mass and momentum conservation. A single Strouhal number for the breaking period was discovered. Complex repetitive splashing patterns are observed and described, involving forward jet formation growth, impact and ricochet, and similarly, backward jet formation and impact. Observed consequences were the creation of vortical regions of both signs, dipole creation through pairing, large-scale transport of surface water downward and high tangential scouring velocities on the bed, which are quantified. These bores are further allowed to rise on linear slopes to the shoreline, where they are seen to collapse into a tongue-like flow resembling dam-break evolution.This essentially inviscid calculation is able to reproduce the development of a highly vortical flow in excellent agreement with experimental observations and theoretical concepts. The turbulent flow behaviour is partially described by the numerical solution.
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SANJOU, Michio, and Iehisa NEZU. "NUMERICAL SIMULATION OF OPEN-CHANNEL FLOWS INCLUDING BUBBLE PLUMES BY USING A GRIDLESS DISCRETE VORTEX METHOD." PROCEEDINGS OF HYDRAULIC ENGINEERING 49 (2005): 703–8. http://dx.doi.org/10.2208/prohe.49.703.
Повний текст джерела
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Lu, Aihong, Yan Guo, and Sixing Yang. "Gridless Super-Resolution Direction-of-Arrival Estimation with Arbitrary Planar Sparse Array." Frequenz 74, no. 3-4 (March 26, 2020): 103–10. http://dx.doi.org/10.1515/freq-2019-0131.
Повний текст джерелаАнотація:
AbstractTwo-dimensional (2D) direction-of-arrival (DOA) estimation with arbitrary planar sparse array has attracted more interest in massive multiple-input multiple-output application. The research on this issue recently has been advanced with the development of atomic norm technique, which provides super resolution methods for DOA estimation, when the number of snapshots is limited. In this paper, we study the problem of 2D DOA estimation from the sparse array with the sensors randomly selected from uniform rectangular array. In order to identify all azimuth and elevation angles of the incident sources jointly, the 2D atomic norm approach is proposed, which can be solved by semidefinite programming. However, the computational cost of 2D atomic norm is high. To address this issue, our work further reduces the computational complexity of the problem significantly by utilizing the atomic norm approximation method based on the concept of multiple measurement vectors. The numerical examples are provided to demonstrate the practical ability of the proposed method to reduce computational complexity and retain the estimation performance as compared to the competitors.
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Alabideen, Lama Zien, Oumayma Al-Dakkak, and Khaldoun Khorzom. "Hybrid Reweighted Optimization Method for Gridless Direction of Arrival Estimation in Heteroscedastic Noise Environment." Mathematical Modelling of Engineering Problems 8, no. 1 (February 28, 2021): 125–33. http://dx.doi.org/10.18280/mmep.080116.
Повний текст джерелаАнотація:
In this paper, we present a hybrid optimization framework for gridless sparse Direction of Arrival (DoA) estimation under the consideration of heteroscedastic noise scenarios. The key idea of the proposed framework is to combine global and local minima search techniques that offer a sparser optimizer with boosted immunity to noise variation. In particular, we enforce sparsity by means of reformulating the Atomic Norm Minimization (ANM) problem through applying the nonconvex Schatten-p quasi-norm (0<p<1) relaxation. In addition, to enhance the adaptability of the relaxed ANM in more practical noise scenarios, it is combined with a covariance fitting (CF) criterion resulting in a locally convergent reweighted iterative approach. This combination forms a hybrid optimization framework and offers the advantages of both optimization approaches while balancing their drawbacks. Numerical simulations are performed taking into account the configuration of co-prime array (CPA). The simulations have demonstrated that the proposed method can maintain a high estimation resolution even in heteroscedastic noise environments, a low number of snapshots, and correlated sources.
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Alabideen, Lama Zien, Oumayma Al-Dakkak, and Khaldoun Khorzom. "Reweighted Covariance Fitting Based on Nonconvex Schatten-p Minimization for Gridless Direction of Arrival Estimation." Mathematical Problems in Engineering 2020 (April 27, 2020): 1–11. http://dx.doi.org/10.1155/2020/3012952.
Повний текст джерелаАнотація:
In this paper, we reformulate the gridless direction of arrival (DoA) estimation problem in a novel reweighted covariance fitting (CF) method. The proposed method promotes joint sparsity among different snapshots by means of nonconvex Schatten-p quasi-norm penalty. Furthermore, for more tractable and scalable optimization problem, we apply the unified surrogate for Schatten-p quasi-norm with two-factor matrix norms. Then, a locally convergent iterative reweighted minimization method is derived and solved efficiently via a semidefinite program using the optimization toolbox. Finally, numerical simulations are carried out in the background of unknown nonuniform noise and under the consideration of coprime array (CPA) structure. The results illustrate the superiority of the proposed method in terms of resolution, robustness against nonuniform noise, and correlations of sources, in addition to its applicability in a limited number of snapshots.
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Tan, Weijie, and Xi’an Feng. "Covariance Matrix Reconstruction for Direction Finding with Nested Arrays Using Iterative Reweighted Nuclear Norm Minimization." International Journal of Antennas and Propagation 2019 (March 18, 2019): 1–13. http://dx.doi.org/10.1155/2019/7657898.
Повний текст джерелаАнотація:
In this paper, we address the direction finding problem in the background of unknown nonuniform noise with nested array. A novel gridless direction finding method is proposed via the low-rank covariance matrix approximation, which is based on a reweighted nuclear norm optimization. In the proposed method, we first eliminate the noise variance variable by linear transform and utilize the covariance fitting criteria to determine the regularization parameter for insuring robustness. And then we reconstruct the low-rank covariance matrix by iteratively reweighted nuclear norm optimization that imposes the nonconvex penalty. Finally, we exploit the search-free DoA estimation method to perform the parameter estimation. Numerical simulations are carried out to verify the effectiveness of the proposed method. Moreover, results indicate that the proposed method has more accurate DoA estimation in the nonuniform noise and off-grid cases compared with the state-of-the-art DoA estimation algorithm.
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Zhang, Yu, Yinan Sun, Gong Zhang, Xinhai Wang, and Yu Tao. "Crosscorrelation and DOA Estimation for L-Shaped Array via Decoupled Atomic Norm Minimization." Wireless Communications and Mobile Computing 2021 (March 29, 2021): 1–11. http://dx.doi.org/10.1155/2021/6659679.
Повний текст джерелаАнотація:
A novel two-phase method for two-dimensional (2D) direction-of-arrival (DOA) estimation with L-shaped array based on decoupled atomic norm minimization (DANM) is proposed in this paper. In the first phase, given the sample crosscorrelation matrix, the gridless DANM technique considering the noise and finite snapshots effects is employed to exploit the structure and sparse properties of the crosscorrelation matrix. The resulting DANM-based algorithm not only enables the crosscorrelation matrix reconstruction (CCMR) but also reconstructs the covariance matrix of the L-shaped array. Hence, sequentially, in the second phase, the conventional 2D DOA estimators for the L-shaped array can be adopted for the angle estimation. With appropriate 2D DOA estimators, the resulting proposed algorithms can not only achieve better performance but also detect more source number, compared with conventional crosscorrelation-based DOA estimators. Moreover, the proposed method, termed CCMR-DANM, not only has blind characteristic that it does not require the prior information of source numbers but also is more efficient than the existing CCMR-based counterparts. Numerical simulations demonstrate the effectiveness and outperformance of the proposed method.
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Xi, Rongyan, Dingyou Ma, Xiang Liu, Lei Wang, and Yimin Liu. "Intra-Pulse Frequency Coding Design for a High-Resolution Radar against Smart Noise Jamming." Remote Sensing 14, no. 20 (October 14, 2022): 5149. http://dx.doi.org/10.3390/rs14205149.
Повний текст джерелаАнотація:
Smart noise jamming forms active jamming by intercepting, modulating, and forwarding radar signals into the radar receiver, which seriously affects the radar range recovery performance. In this paper, we propose a novel waveform design approach and an efficient range recovery method for high-resolution radar in the jamming scenario. Firstly, we propose an intra-pulse frequency-coded frequency-modulated continuous waveform (IPFC-FMCW), which contains multiple FMCW chips with different widths and frequencies, to combat the smart noise jamming. After the jamming suppression, the proposed waveform has a low sidelobe level, which is different from traditional FMCW signals for which the observations are periodically missing, resulting in high sidelobe levels. Then, to improve the range recovery performance of the waveform after jamming suppression, we optimize the range profile by designing the transmit waveform and then solve it by a simulated annealing algorithm. Next, based on the designed waveform, we derive the echo model after jamming suppression and propose a gridless compressed sensing (CS) method to recover the range of the targets. Compared with the existing waveforms and methods, the proposed waveform and the processing method achieve better range recovery performance in the jamming scenario. Numerical simulations are utilized to demonstrate the range recovery effectiveness of the proposed waveform and method in smart noise jamming.
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Famoriji, Oluwole John, and Thokozani Shongwe. "Spherical Atomic Norm-Inspired Approach for Direction-of-Arrival Estimation of EM Waves Impinging on Spherical Antenna Array with Undefined Mutual Coupling." Applied Sciences 13, no. 5 (February 27, 2023): 3067. http://dx.doi.org/10.3390/app13053067.
Повний текст джерелаАнотація:
A spherical antenna array (SAA) is an array-designed arrangement capable of scanning in almost all the radiation sphere with constant directivity. It finds recent applications in aerospace, spacecraft, vehicular and satellite communications. Therefore, estimation of the direction-of-arrival (DoA) of electromagnetic (EM) waves that impinge on an SAA with unknown mutual coupling called for research attention. This paper proposed a spherical harmonic atomic norm minimization (SHANM) for DoA estimation using an SAA configuration. The gridless sparse signal recovery problem is considered in the spherical harmonic (SH) domain in conjunction with the atomic norm minimization (ANM). Because of the unavailability of the Vandermonde structure in the SH domain, the theorem of Vandermonde decomposition that is the mathematical basis of the traditional ANM methods finds no application in SH. Addressing this challenge, a low-dimensional semidefinite programming (SDP) approach implementing the SHANM method is developed. This approach is independent of Vandermonde decomposition, and directly recovers the atomic decomposition in SH. The numerical experimental results show the superior performance of the proposed method against the previous methods. In addition, accounting for the impacts of mutual coupling, an experimental measured data, which is the generally accepted ground of testing any method, is employed to illustrate the efficacy and robustness of the proposed methods. Finally, for achieving DoA estimation with sufficient localization accuracy using a SAA, the proposed SHANM-based method is a better option.
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Lao, Bing-Xin, and Aaron Smith. "Resonant-line radiative transfer within power-law density profiles." Monthly Notices of the Royal Astronomical Society 497, no. 3 (August 17, 2020): 3925–42. http://dx.doi.org/10.1093/mnras/staa2198.
Повний текст джерелаАнотація:
ABSTRACT Star-forming regions in galaxies are surrounded by vast reservoirs of gas capable of both emitting and absorbing Lyman α (Lyα) radiation. Observations of Lyα emitters and spatially extended Lyα haloes indeed provide insights into the formation and evolution of galaxies. However, due to the complexity of resonant scattering, only a few analytic solutions are known in the literature. We discuss several idealized but physically motivated scenarios to extend the existing formalism to new analytic solutions, enabling quantitative predictions about the transport and diffusion of Lyα photons. This includes a closed form solution for the radiation field and derived quantities including the emergent flux, peak locations, energy density, average internal spectrum, number of scatters, outward force multiplier, trapping time, and characteristic radius. To verify our predictions, we employ a robust gridless Monte Carlo radiative transfer (GMCRT) method, which is straightforward to incorporate into existing ray tracing codes but requires modifications to opacity-based calculations, including dynamical core-skipping acceleration schemes. We primarily focus on power-law density and emissivity profiles, however both the analytic and numerical methods can be generalized to other cases. Such studies provide additional intuition and understanding regarding the connection between the physical environments and observational signatures of galaxies throughout the Universe.
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Sizykh, Grigory. "New Lagrangian view of vorticity evolution in two-dimensional flows of liquid and gas." Izvestiya VUZ. Applied Nonlinear Dynamics 30, no. 1 (January 31, 2022): 30–36. http://dx.doi.org/10.18500/0869-6632-2022-30-1-30-36.
Повний текст джерелаАнотація:
Purpose of the study is to obtain formulas for such a speed of imaginary particles that the circulation of the speed of a (real) fluid along any circuit consisting of these imaginary particles changes (in the process of motion of imaginary particles) according to a given time law. (Until now, only those speeds of imaginary particles were known, at which the mentioned circulation during the motion remained unchanged). Method. Without implementation of asymptotic, numerical and other approximate methods, a rigorous analysis of the dynamic equation of motion (flow) of any continuous fluid medium, from an ideal liquid to a viscous gas, is carried out. Plane-parallel and nonswirling axisymmetric flows are considered. The concept of motion of imaginary particles is used, based on the K. Zoravsky criterion (which is also called A. A. Fridman’s theorem). Results. Formulas for the speed of imaginary particles are proposed. These formulas include the parameters of the (real) flow, their spatial derivatives and the function of time, which determines the law of the change in time of the (real fluid) velocity circulation along the contours moving together with the imaginary particles. In addition, it turned out that for a given function of time (and, as a consequence, for a given law of change in circulation with respect to time), the speed of imaginary particles is determined ambiguously. As a result, a method is proposed to change the speed and direction of motion of imaginary particles in a certain range (while maintaining the selected law of changes in circulation in time). For a viscous incompressible fluid, formulas are proposed that do not include pressure and its derivatives. Conclusion. A new Lagrangian point of view on the vorticity evolution in two-dimensional flows of fluids of all types is proposed. Formulas are obtained for the velocity of such movement of contours, at which the real fluid velocity circulation along any contour changes according to a given time law. This theoretical result can be used in computational fluid dynamics to limit the number of domains when using a gridless method for calculating flows of a viscous incompressible fluid (the method of viscous vortex domains).
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Laville, Bastien, Laure Blanc-Féraud, and Gilles Aubert. "Off-The-Grid Variational Sparse Spike Recovery: Methods and Algorithms." Journal of Imaging 7, no. 12 (December 6, 2021): 266. http://dx.doi.org/10.3390/jimaging7120266.
Повний текст джерелаАнотація:
Gridless sparse spike reconstruction is a rather new research field with significant results for the super-resolution problem, where we want to retrieve fine-scale details from a noisy and filtered acquisition. To tackle this problem, we are interested in optimisation under some prior, typically the sparsity i.e., the source is composed of spikes. Following the seminal work on the generalised LASSO for measures called the Beurling-Lasso (BLASSO), we will give a review on the chief theoretical and numerical breakthrough of the off-the-grid inverse problem, as we illustrate its usefulness to the super-resolution problem in Single Molecule Localisation Microscopy (SMLM) through new reconstruction metrics and tests on synthetic and real SMLM data we performed for this review.
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Wang, Bin, Yin Feng, Juan Du, Yihui Wang, Sijie Wang, and Ruiyue Yang. "An Embedded Grid-Free Approach for Near-Wellbore Streamline Simulation." SPE Journal 23, no. 02 (December 4, 2017): 567–88. http://dx.doi.org/10.2118/182614-pa.
Повний текст джерелаАнотація:
Summary Reactive-transport phenomena, such as carbon dioxide sequestration and microbial enhanced oil recovery (EOR), have been of interest in streamline-based simulation (SLS). Tracing streamlines launched from a wellbore is important, especially for time-sensitive transport behaviors. However, discretized gridblocks are usually too large compared with the wellbore radius. Field-scale simulations with local-grid-refinement (LGR) models often consume huge computational time. An embedded grid-free approach to integrate near-wellbore transport behaviors into streamline simulations is developed, comprising two stages of development: tracing streamlines in a wellblock (a gridblock containing wells) and coupling streamlines with neighboring grids. The velocity field in a wellblock is produced using a gridless virtual-boundary-element method (VBEM), where streamlines are numerically traced with the fourth-order Runge-Kutta (RK4) method (Butcher 2008). The local streamline system is then connected with the global streamline system, which is produced with the Pollock (1988) algorithm. Finally, the reactive-transport equation will be solved along these streamlines. The algorithm presented for solving near-wellbore streamlines is verified by both a commercial finite-element simulator and a Pollock-algorithm-based 3D streamline simulator. A series of computational cases of reactive-transport simulation is studied to demonstrate the applicability, accuracy, and efficiency of the proposed method. Velocity field, time-of-flight (TOF), streamline pattern, and concentration distribution produced by different approaches are analyzed. Results show that the presented method can accurately perform near-wellbore streamline simulations in a time-effective manner. The algorithm can be directly applied to one grid containing multiple wells or to off-center wells. Furthermore, assuming streamlines are evenly launched from the gridblock boundary or ignoring transport in the wellblock is not always reasonable, and may lead to a significant error. This study provides a simple and grid-free solution, but is capable of capturing the flow field near the wellbore with significant accuracy and computational efficiency. The method is promising for reservoir SLS with time-sensitive transport, and other simulations requiring an accurate assessment of interactions between wells in one particular gridblock.
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Cao, Cheng, Hongquan Chen, and Jiale Zhang. "Preconditioned gridless methods for solving three-dimensional Euler equations at low Mach numbers." International Journal of Modeling, Simulation, and Scientific Computing, October 19, 2020, 2050055. http://dx.doi.org/10.1142/s1793962320500555.
Повний текст джерелаАнотація:
In this paper, preconditioned gridless methods are developed for solving the three-dimensional (3D) Euler equations at low Mach numbers. The preconditioned system is obtained by multiplying a preconditioning matrix of the type of Weiss and Smith to the time derivative of the 3D Euler equations, which are discretized under the clouds of points distributed in the computational domain by using a gridless technique. The implementations of the preconditioned gridless methods are mainly based on the frame of the traditional gridless method without preconditioning, which may fail to have convergence for flow simulations at low Mach numbers, therefore the modifications corresponding to the affected terms of preconditioning are mainly addressed in the paper. An explicit four-stage Runge–Kutta scheme is first applied for time integration, and the lower-upper symmetric Gauss-Seidel (LU-SGS) algorithm is then introduced to form the implicit counterpart to have the further speed up of the convergence. Both the resulting explicit and implicit preconditioned gridless methods are validated by simulating flows over two academic bodies like sphere or hemispherical headform, and transonic and nearly incompressible flows over one aerodynamic ONERA M6 wing. The gridless clouds of both regular and irregular points are used in the simulations, which demonstrates the ability of the method presented for coping with flows over complicated aerodynamic geometries. Numerical results of surface pressure distributions agree well with available experimental data or simulated solutions in the literature. The numerical results also show that the preconditioned gridless methods presented still functions for compressible transonic flow simulations and additionally, for nearly incompressible flow simulations at low Mach numbers as well. The convergence of the implicit preconditioned gridless method, as expected, is much faster than its explicit counterpart.
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Ding, Yarong, Shiwei Ren, Weijiang Wang, and Chengbo Xue. "DOA estimation based on sum–difference coarray with virtual array interpolation concept." EURASIP Journal on Advances in Signal Processing 2021, no. 1 (August 12, 2021). http://dx.doi.org/10.1186/s13634-021-00782-y.
Повний текст джерелаАнотація:
AbstractThe sum–difference coarray is the union of difference coarray and the sum coarray, which is capable to obtain a higher number of degrees of freedom (DOF) than the difference coarray. However, this method fails to use all information provided by the coprime array because of the existence of holes. In this paper, we introduce the virtual array interpolation into the sum–difference coarray domain. After interpolating the virtual array, we estimate the DOA by reconstructing the covariance matrix to resolve an atomic norm minimization problem in a gridless way. The proposed method is gridless and can effectively utilize the DOF of a larger virtual array. Numerical simulation results verify the effectiveness and the superior performance of the proposed algorithm.
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Liu, Hui-Hai, Jilin Zhang, Feng Liang, Cenk Temizel, Mustafa A. Basri, and Rabah Mesdour. "Incorporation of Physics into Machine Learning for Production Prediction from Unconventional Reservoirs: A Brief Review of the Gray-Box Approach." SPE Reservoir Evaluation & Engineering, June 1, 2021, 1–12. http://dx.doi.org/10.2118/205520-pa.
Повний текст джерелаАнотація:
Summary Prediction of well production from unconventional reservoirs is often a complex problem with an incomplete understanding of physics and a considerable amount of data. The most effective way for dealing with it is to use the gray-box approach that combines the strengths of physics-based models and machine learning (ML) used for dealing with certain components of the prediction where physical understanding is poor or difficult. However, the development of methodologies for the incorporation of physics into ML is still in its infancy, not only in the oil and gas industry, but also in other scientific and engineering communities, including the physics community. To set the stage for further advancing the use of combining physics-based models with ML for predicting well production, in this paper we present a brief review of the current developments in this area in the industry, including ML representation of numerical simulation results, determination of parameters for decline curve analysis (DCA) models with ML, physics-informed ML (PIML) that provides an efficient and gridless method for solving differential equations and for discovering governing equations from observations, and physics-constrained ML (PCML) that directly embeds a physics-based model into a neural network. The advantages and potential limitations of the methods are discussed. The future research directions in this area include, but are not limited to, further developing and refining methodologies, including algorithm development, to directly embed physics-based models into ML; exploring the usefulness of PIML for reservoir simulations; and adapting the new developments of how the physics and ML are incorporated in other communities to the well-production prediction. Finally, the methodologies we discuss in the paper can be generally applied to conventional reservoirs as well, although the focus here is on unconventional reservoirs.
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Yang, Ruiyue, Xiaozhou Qin, Wei Liu, Zhongwei Huang, Yu Shi, Zhaoyu Pang, Yiqun Zhang, Jingbin Li, and Tianyu Wang. "A Physics-Constrained Data-Driven Workflow for Predicting Coalbed Methane Well Production Using Artificial Neural Network." SPE Journal, February 1, 2022, 1–22. http://dx.doi.org/10.2118/205903-pa.
Повний текст джерелаАнотація:
Summary Coalbed methane (CBM) has emerged as one of the clean unconventional resources to supplement the rising demand of oil and gas. Analyzing and predicting CBM production performance are critical in choosing the optimal completion methods and parameters. However, the conventional numerical simulation has challenges of complicated gridding issues and expensive computational costs. The huge amount of available production data that has been collected in the field site opens up a new opportunity to develop data-driven approaches in predicting the production rate. Here, we proposed a novel physics-constrained data-driven workflow to effectively forecast the CBM productivity based on a gated recurrent unit (GRU) and multilayer perceptron (MLP) combined neural network (GRU-MLP model). The model architecture is optimized automatically by the multiobjective algorithm: nondominated sorting genetic algorithm Ⅱ (NSGA Ⅱ). The proposed framework was used to predict gas and water production in synthetic cases with various fracture-network-complexity/connectivity and two multistage fractured horizontal wells in field sites located at Ordos Basin and Qinshui Basin, China. The results indicated that the proposed GRU-MLP combined neural network was able to accurately and stably predict the production performance of CBM fractured wells in a fast manner. Compared with recurrent neural network (RNN), GRU, and long short-term memory (LSTM), the proposed GRU-MLP had the highest accuracy, stability, and generalization, especially in the peak or trough and late-time production periods, because it could capture the production-variation trends precisely under the static and dynamic physical constraints. Consequently, a physics-constrained data-driven approach performed better than a pure data-driven method. Moreover, the contributions of constraints affecting the model prediction performance were clarified, which could provide insights for the practicing engineers to choose which categorical constraints are needed to focus on and preferentially treated if there are uncertainties and unknowns in a realistic reservoir. In addition, the optimum GRU-MLP model architecture was a group of optimized solutions, rather than a single solution. Engineers can evaluate the tradeoffs within this optimal set according to the field-site requirements. This study provides a novel machine learning approach based on a GRU-MLP combined neural network to estimate production performances in naturally fractured reservoir. The method is gridless and simple, but is capable of predicting the productivity in a computational cost-effective way. The key findings of this work are expected to provide a theoretical guidance for the intelligent development in oil and gas industry.
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Chen, Tao, Lin Shi, and Yongzhi Yu. "Gridless DOA estimation with finite rate of innovation reconstruction based on symmetric Toeplitz covariance matrix." EURASIP Journal on Advances in Signal Processing 2020, no. 1 (October 28, 2020). http://dx.doi.org/10.1186/s13634-020-00701-7.
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Abstract Due to the rapid development and wide application of compressed sensing and sparse reconstruction theory, there exists a series of sparsity-based methods for the antenna sensor array direction of arrival (DOA) estimation with excellent performance. However, it is known that this kind of algorithms always suffers from the problem of grid mismatch. To overcome this shortcoming, a gridless DOA estimation algorithm with finite rate of innovation (FRI) based on a symmetric Toeplitz covariance matrix is proposed for uniform linear array (ULA) in this paper. In particular, a multiple measurement vector (MMV) FRI reconstruction model is built by exploiting the covariance data denoised according to covariance fitting criteria rather than the direct data or the original covariance data, which is commonly used in other representative gridless DOA estimation methods. Next, DOA can be retrieved from the recovered covariance matrix by utilizing an annihilating filter because each covariance data is a linear combination of complex exponentials. It guarantees to produce an exact spatial sparse estimate without discretization required by existing sparsity-based DOA estimation methods. Finally, the effectiveness and superiority of the proposed algorithm are demonstrated by numerical simulations.