A Highly Efficient Computer Method for Solving Polynomial Equations Appearing in Engineering Problems

A highly efficient two-step simultaneous iterative computer method is established here for solving polynomial equations. A suitable special type of correction helps us to achieve a very high computational efficiency as compared to the existing methods so far in the literature. Analysis of simultaneous scheme proves that its convergence order is 14. Residual graphs are also provided to demonstrate the efficiency and performance of the newly constructed simultaneous computer method in comparison with the methods given in the literature. In the end, some engineering problems and some higher degree complex polynomials are solved numerically to validate its numerical performance.

A Non-Iterative Problem-Dependent Formula for Stiff Dynamic Problems

A novel one-step formula is proposed for solving initial value problems based on a concept of eigenmode. It is characterized by problem dependency since it has problem-dependent coefficients, which are functions of the product of the step size and the initial physical properties to define the problem under analysis. It can simultaneously combine A-stability, explicit formulation and second order accuracy. A-stability implies no limitation on step size based on stability consideration. An explicit formulation implies no nonlinear iterations for each step. The second order accuracy with an appropriate step size can have a good accuracy in numerical solutions. Thus, it seems promising for solving stiff dynamic problems. Numerical tests affirm that it can have the same performance as that of the trapezoidal rule for solving linear and nonlinear dynamic problems. It is evident that the most important advantage is of high computational efficiency in contrast to the trapezoidal rule due to no nonlinear iterations of each step.

Efficient iterative methods for finding simultaneously all the multiple roots of polynomial equation

Two new iterative methods for the simultaneous determination of all multiple as well as distinct roots of nonlinear polynomial equation are established, using two suitable corrections to achieve a very high computational efficiency as compared to the existing methods in the literature. Convergence analysis shows that the orders of convergence of the newly constructed simultaneous methods are 10 and 12. At the end, numerical test examples are given to check the efficiency and numerical performance of these simultaneous methods.

Weakly Supervised Video Anomaly Detection Based on 3D Convolution and LSTM

Weakly supervised video anomaly detection is a recent focus of computer vision research thanks to the availability of large-scale weakly supervised video datasets. However, most existing research works are limited to the frame-level classification with emphasis on finding the presence of specific objects or activities. In this article, a new neural network architecture is proposed to efficiently extract the prominent features for detecting whether a video contains anomalies. A video is treated as an integral input and the detection follows the procedure of video-label assignment. The extraction of spatial and temporal features is carried out by three-dimensional convolutions, and then their relationship is further modeled using an LSTM network. The concise structure of the proposed method enables high computational efficiency, and extensive experiments demonstrate its effectiveness.

Strip-Map SAR Image Formulation Based on the Modified Alternating Split Bregman Method

Conventional compressive sensing (CS)-based imaging methods allow images to be reconstructed from a small amount of data, while they suffer from high computational burden even for a moderate scene. To address this problem, this paper presents a novel two-dimensional (2D) CS imaging algorithm for strip-map synthetic aperture radars (SARs) with zero squint angle. By introducing a 2D separable formulation to model the physical procedure of the SAR imaging, we separate the large measurement matrix into two small ones, and then the induced algorithm can deal with 2D signal directly instead of converting it into 1D vector. As a result, the computational load can be reduced significantly. Furthermore, thanks to its superior performance in maintaining contour information, the gradient space of the SAR image is exploited and the total variation (TV) constraint is incorporated to improve resolution performance. Due to the non-differentiable property of the TV regularizer, it is difficult to directly solve the induced TV regularization problem. To overcome this problem, an improved split Bregman method is presented by formulating the TV minimization problem into a sequence of unconstrained optimization problem and Bregman updates. It yields an accurate and simple solution. Finally, the synthesis and real experiment results demonstrate that the proposed algorithm remains competitive in terms of high resolution and high computational efficiency.

Study on an Integral Algorithm of Load Identification Based on Displacement Response

Load identification is a very important and challenging indirect load measurement method because load identification is an inverse problem solution with ill-conditioned characteristics. A new method of load identification is proposed here, in which a virtual function was introduced to establish integral structure equations of motion, and partial integration was applied to reduce the response types in the equations. The effects of loading duration, the type of basis function, and the number of basis function expansion items on the calculation efficiency and the accuracy of load identification were comprehensively taken into account. Numerical simulation and experimental results showed that our algorithm could not only effectively identify periodic and random loads, but there was also a trade-off between the calculation efficiency and identification accuracy. Additionally, our algorithm can improve the ill-conditionedness of the solution of load identification equations, has better robustness to noise, and has high computational efficiency.

Optimization by parameters in the iterative methods for solving non-linear equations

In this paper, we used the necessary optimality condition for parameters in a two-point iterations for solving nonlinear equations. Optimal values of these parameters fully coincide with those obtained in [6] and allow us to increase the convergence order of these iterative methods. Numerical experiments and the comparison of existing robust methods are included to confirm the theoretical results and high computational efficiency. In particular, we considered a variety of real life problems from different disciplines, e.g., Kepler’s equation of motion, Planck’s radiation law problem, in order to check the applicability and effectiveness of our proposed methods.

Multilevel augmented Lagrangian solvers for overconstrained contact formulations

Multigrid methods for two-body contact problems are mostly based on special mortar discretizations, nonlinear Gauss-Seidel solvers, and solution-adapted coarse grid spaces. Their high computational efficiency comes at the cost of a complex implementation and a nonsymmetric master-slave discretization of the nonpenetration condition. Here we investigate an alternative symmetric and overconstrained segment-to-segment contact formulation that allows for a simple implementation based on standard multigrid and a symmetric treatment of contact boundaries, but leads to nonunique multipliers. For the solution of the arising quadratic programs, we propose augmented Lagrangian multigrid with overlapping block Gauss-Seidel smoothers. Approximation and convergence properties are studied numerically at standard test problems.

Ascent Trajectory Optimization for Air-Breathing Hypersonic Vehicles Based on IGS-MPSP

This paper proposes an improved Generalized Quasi-Spectral Model Predictive Static Programming (GS-MPSP) algorithm for the ascent trajectory optimization for hypersonic vehicles in a complex flight environment. The proposed method guarantees the satisfaction of constraints related to the state and control vector while retaining its high computational efficiency. The spectral representation technique is used to describe the control variables, which reduces the number of decision variables and makes the control input smooth enough. Through Taylor expansion, the constraints are transformed into an inequality containing only decision variables, such that it can be added into GS-MPSP framework. By Gauss quadrature collocation method, only a few collocation points are needed to solve the sensitivity matrix, which greatly accelerates the calculation. Subsequently, the analytical expression is obtained by combining the static optimization with the penalty function method. Finally, the simulation results demonstrate that the proposed improved GS-MPSP algorithm can achieve both high computational efficiency and high terminal precision under the constraints.

Ocean Circulation Model Applications for the Estuary-Coastal-Open Sea Continuum

Coastal zones are among the most variable environments. As such, they require adaptive water management to ensure the balance of economic and social interests with environmental concerns. High quality marine data of hydrographic conditions e.g., sea level, temperature, salinity, and currents are needed to provide a sound foundation for the decision making process. Operational models with sufficiently high forecasting quality and resolution can be used for a further extension of the marine service toward the coastal-estuary areas. The Limfjord is a large and shallow water body in Northern Jutland, connecting the North Sea in the West and the Kattegat in the East. It is currently not covered by the CMEMS service, despite its importance for sea shipping, aquaculture and mussel fisheries. In this study, we use the operational HIROMB-BOOS Model (HBM) to resolve the full Baltic-Limfjord-North Sea system with a horizontal resolution of 185.2 m in the Limfjord. The study shows several factors that are essential for successfully modeling the coastal-estuary system: (a) high computational efficiency and flexible grids to allow high resolution in the fjord, (b) an improved short wave radiation scheme to model the thermodynamics and the diurnal variability of the temperature in very shallow waters, (c) high resolution atmospheric forcing, (d) adequate river forcing, and (e) accurate bathymetry in the narrow straits. With properly resolving these issues, the system is able to provide high quality sea level forecast for storm surge warning and hydrography forecasts: temperature, salinity and currents with sufficiently good quality for ecosystem-based management. The model is able to simulate the complex spatial and temporal pattern of sea level, salinity and temperature in the Limfjord and to reproduce their diurnal, seasonal and interannual variability and stratification rather well. Its high computational efficiency makes it possible to model the transition from the basin-scales to coastal- and estuary-scales seamlessly. In total, The HBM model has been successfully extended, to include the complex estuary system of the Limfjord, and shows an adequate model performance with regards to sea level, salinity and temperature predictions, suitable for storm surge warning applications and coastal management applications.