Добірка наукової літератури з теми "Gridless numerical method"

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

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.

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.

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.

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.

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.

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.

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.

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.

O método numérico para fluidos incompressíveis desenvolvido no presente estudo é o Moving Particle Semi-Implicit Method (MPS) que enxerga o domínio discretizado em partículas, é baseado em representação lagrangeana e não tem a necessidade de utilização de malhas. O método MPS tem como equações governantes uma forma particular da equação de Navier-Stokes e a equação da continuidade para fluidos incompressíveis e não viscosos. Os métodos de simulação de fluidos mais comumente utilizados são baseados em representação euleriana e utilizam malhas para descrever a geometria do domínio a ser simulado. Devido a essas diferenças, uma das grandes virtudes do método de partículas é a facilidade de investigação de fenômenos altamente não-lineares como o de superfície livre com quebra de ondas, de líquidos no interior de uma embarcação em movimento, de ondas batendo na parte externa do casco de um navio, etc. Em artigos já publicados, resultados de experimentos físicos mostraram boa aderência aos resultados numéricos de simulações realizadas com o método MPS. No presente trabalho, resultados das forças de excitação das simulações com ondas regulares foram comparados com os resultados do programa Wave Analysis MIT (WAMIT) que é um programa consagrado no meio científico. Houve uma boa concordância de resultados entre os dois programas. A otimização do cálculo de vizinhança forneceu uma grande economia de tempo computacional. A maior contribuição deste estudo foi a otimização da função que resolve o sistema linear implementando no código desenvolvido um código paralelizado de uso público existente chamado Portable, Extensible Toolkit for Scientific Computation (PETSc) que proporcionou um bom ganho de desempenho.
A numerical method called Moving Particle Semi-implicit (MPS) method was developed in this study to analyze incompressible fluids. It is a particle method using a lagrangean representation without any grid. The governing equations are the Navier-Stokes equation and continuity equation for incompressible and non-viscous flow. Most of the computational fluid dynamics (CFD) methods are based on eulerian representation and use grids to describe the geometry of the simulated domain. These differences make the MPS method easier to analyze highly nonlinear phenomena as free surface with wave breaking, sloshing, slamming, etc. In previously published articles, results of physical experiments had shown good agreement with the numerical results obtained with MPS method. In the present work, results of exciting forces were compared with the results obtained with a validated program called Wave Analysis MIT (WAMIT). It had a good agreement of results between these two programs. The optimization of the neighborhood calculation function got a good economy of computational time. The greatest contribution of this study was the optimization of the linear system solver. It was made implementing in the developed code a parallelized public code called Portable, Extensible Toolkit for Scientific Computation (PETSc) that provided a good performance profit.

Abstract Coalbed methane (CBM) has emerged as one of the clean unconventional resources to supplement the rising demand of conventional hydrocarbons. Analyzing and predicting CBM production performance is 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 Multi-Layer Perceptron (MLP) combined neural network (GRU-MLP model). The model architecture is optimized by the multiobjective algorithm: nondominated sorting genetic algorithm Ⅱ (NSGA Ⅱ). The proposed framework was used to predict synthetic cases with various fracture-network-complexities and two multistage-fractured wells in field sites located at Qinshui basin and Ordos basin, China. The results indicated that the proposed GRU-MLP combined neural network was able to accurately and stably predict the production performance of multi-fractured horizontal CBM wells in a fast manner. Compared with Simple Recurrent Neural Network (RNN), Gated Recurrent Unit (GRU) and Long Short-Term Memory (LSTM), the proposed GRU-MLP had the highest accuracy and stability especially for gas production in late-time. Consequently, a physics-constrained data-driven approach performed better than a pure data-driven method. Moreover, the optimum GRU-MLP model architecture was a group of optimized solutions, rather than a single solution. Engineers can evaluate the tradeoffs within this set according to the field-site requirements. This study provides a novel machine learning approach based on a GRU-MLP combined neural network model to estimate production performances in CBM wells. The method is simple and gridless, 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.