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We develop new high‐order positive, monotone and convex interpolations, which are to be used in the multigrid context. This means that the value of the interpolant is calculated only at the midpoints lying between the locations of the given values. As a consequence, these interpolants can be calculated very efficiently. They are then tested in a time‐dependent very large scale integration process simulation application.

The purpose of this paper is to simplify the Explicit Nonlinear Model Predictive Controller (ENMPC) by linearizing the trajectory with Quantum-behaved Pigeon-Inspired Optimization (QPIO).

The paper deduces the nonlinear model of the quadrotor and uses the ENMPC to track the trajectory. Since the ENMPC has high demand for the state equation, the trajectory needed to be differentiated many times. When the trajectory is complicate or discontinuous, QPIO is proposed to linearize the trajectory. Then the linearized trajectory will be used in the ENMPC.

Applying the QPIO algorithm allows the unequal distance sample points to be acquired to linearize the trajectory. Comparing with the equidistant linear interpolation, the linear interpolation error will be smaller.

Small-sized quadrotors were adopted in this research to simplify the model. The model is supposed to be accurate and differentiable to meet the requirements of ENMPC.

Traditionally, the quadrotor model was usually linearized in the research. In this paper, the quadrotor model was kept nonlinear and the trajectory will be linearized instead. Unequal distance sample points were utilized to linearize the trajectory. In this way, the authors can get a smaller interpolation error. This method can also be applied to discrete systems to construct the interpolation for trajectory tracking.

The purpose of this study is to compare interpolation algorithms and deep neural networks for inverse transfer problems with linear and nonlinear behaviour.

A series of runs were conducted for a canonical test problem. These were used as databases or “learning sets” for both interpolation algorithms and deep neural networks. A second set of runs was conducted to test the prediction accuracy of both approaches.

The results indicate that interpolation algorithms outperform deep neural networks in accuracy for linear heat conduction, while the reverse is true for nonlinear heat conduction problems. For heat convection problems, both methods offer similar levels of accuracy.

This is the first time such a comparison has been made.

The numerical solution of the diffusion equation in VLSI process simulation leads to large systems of nonlinear equations which have to be solved at every time step. For this purpose, a multigrid (MG) algorithm with locally refined grids is constructed. It is demonstrated that the method used here yields typical MG algorithm convergence rates, and reduces the amount of work considerably. The local refinements are controlled by an estimation of the discretization error which is calculated within the nonlinear MG method (FAS) and requires no extra computational work.

A boundary element method has been developed to calculate the added mass matrix of fluid coupled structures in the case when the fluid is assumed to be compressible and inviscid. The potential flow is represented by a double layer density with linear interpolation functions. A linear set of equations for the fluid motion is obtained by Galerkin's procedure. The added mass matrix is not symmetric but a symmetrization procedure is established. The method has been implemented into a computer code for two‐dimensional geometries, whose results are presented here. A comparison with the analytical results already shows excellent agreement for coarse discretizations.

To propose a novel method for defect reconstruction in electromagnetic non‐destructive testing (NDT).

The inversion method is based on an optimized database that contains the measured signals for some predefined defect prototypes. The database is supported by an anisotropic simplex mesh, which has been generated adaptively in the abstract n‐dimensional space, spanned by the model parameters of the defect type. The actual reconstruction reduces to a mesh search and interpolation. The described theory is demonstrated in the paper by a solved NDT test problem.

We have realized that in addition to sole defect reconstruction, the database provides meta‐information about the quality of the inversion, the suitability of the chosen defect model parameters, as well as the capabilities of the testing experiment.

Defect models having several parameters require a sophisticated mesh generation algorithm, which works in higher dimensions.

In the authors' opinion the mesh database approach offers a totally new point of view of a given inverse problem, and may help in the better understanding of its nature.

The purpose of the paper is to propose some modifications to the SIMPLE (semi-implicit method for pressure-linked equations) algorithm. These modifications can ensure the numerical robustness and optimize computational efficiency. They remarkably promote the ability of the SIMPLE algorithm for incompressible DNS (direct numerical simulation) of multiscale problems, such as transitional flows and turbulent flows, by improving the properties of dispersion and dissipation.

The MDCD (minimized dispersion and controllable dissipation) scheme and MMIM (modified momentum interpolation method) are introduced. Six typical test cases are used to validate the modified algorithm, including the linear convective flow, lid-driven cavity flow, laminar boundary layer, Taylor vortex and DHIT (decaying homogenous isotropic turbulence). Particularly, a highly unsteady DNS of separated-flow transition in turbomachinery is precisely predicted by the modified algorithm.

The numerical examples show the distinct superiority of the modified algorithm in both internal flows and external flows. The advantages of the MDCD scheme and MMIM make the SIMPLE algorithm a promising method for DNS.

Some effective modifications to the SIMPLE algorithm are addressed. It is the first attempt to introduce the MDCD approach into the SIMPLE-type algorithms. The new algorithm is especially suitable for the incompressible DNS of convection-dominated flows.

Nonlinear systems identification from experimental data without any prior knowledge of the system parameters is a challenge in control and process diagnostic. It determines mathematical model parameters that are able to reproduce the dynamic behavior of a system. This paper aims to combine two fundamental research areas: MIMO state space system identification and nonlinear control system. This combination produces a technique that leads to robust stabilization of a nonlinear Takagi–Sugeno fuzzy system (T-S).

The first part of this paper describes the identification based on the Numerical algorithm for Subspace State Space System IDentification (N4SID). The second part, from the identified models of first part, explains how we use the interpolation of linear time invariants models to build a nonlinear multiple model system, T-S model. For demonstration purposes, conditions on stability and stabilization of discrete time, T-S model were discussed.

Stability analysis based on the quadratic Lyapunov function to simplify implementation was explained in this paper. The linear matrix inequalities technique obtained from the linearization of the bilinear matrix inequalities was computed. The suggested N4SID2 algorithm had the smallest error value compared to other algorithms for all estimated system matrices.

The stabilization of the closed-loop discrete time T-S system, using the improved parallel distributed compensation control law, was discussed to reconstruct the state from nonlinear Luenberger observers.

We use Cross-National Equivalent File (CNEF) data from the United States and Great Britain to investigate the association between adults’ health and the income inequality they experienced as children up to 80 years earlier. Our inequality data track shares of national income held by top income percentiles from the early 20th century. We average those data over the same early-life years and merge them to CNEF data from both countries that measure self-reported health of individuals between 1991 and 2007. Observationally, adult men and women in the United States and Great Britain less often report being in better health if inequality was higher in their first five years of life. Although the trend in inequality is similar in both countries over the past century, the empirical association between health and inequality in the United States differs substantially from the estimated relationship in Great Britain. When we control for demographic characteristics, measures of permanent income, and early-life socio-economic status, the health–inequality association remains robust only in the U.S. sample. For the British sample, the added controls drive the coefficient on inequality toward zero and statistical insignificance.