Well posedness and numerical solution for a non-local pseudohyperbolic initial boundary value problem

ABSTRACT

In this paper, we study a non-local initial boundary value problem for a one-dimensional pseudohyperbolic equation. We first establish the existence and uniqueness of strong solution, then a numerical solutions for the system will be derived by using the finite-difference method.     

COMPUTING ANTICIPATORY PROPERTY IN STOCHASTIC DIFFERENTIAL SYSTEMS

ABSTRACT

This article concerns computing anticipatory property of stochastic systems, which are characterized by forward and/or backward stochastic differential Equations. Since a Pardoux-Peng solution of a Backward Stochastic Differential Equation (BSDE) is required adaptedness to the natural filtration of a standard Brownian motion, it is nonanticipatory in the sense of stochastic calculus. However, the BSDE is solved backwardly with a terminal state and the solution will generally depend on the future state. Hence a system described by Forward and Backward Stochastic Differential Equations (FBSDEs) will be shown to be a strong computing anticipatory system. A stochastic system described by a numerical scheme also has the same property.     

Numerical solution of fuzzy linear system

The aim of this paper is to present a numerical method for solving a general n×n fuzzy system of linear equations of the form Ax=b, where A is a crisp matrix and b an arbitrary fuzzy vector. We obtain the solution of n×n fuzzy linear systems by using Jacobi and Gauss-Seidel iterative methods and also show that the order of system will not be increased and the computing time will be shorter than other numerical methods. Finally, we illustrate this method by offering some numerical examples.     

Achievements and objectives in the 1990s

Abstract

During the 1970s and 1980s polar orbiting and geostationary satellites like NOAA and Meteosat led to new possibilities in weather forecasting. In this presentation we first summarize the use of satellite information in nowcasting, short-range weather forecasting and medium-range weather forecasting in the Netherlands. Then a short review of the research connected with “satellite weather forecasting’ is given. In the 1990s satellites like ERS and a second generation Meteosat will be launched. Applications of the new type of satellite data that will become available in Europe for weather forecasting will be discussed. It is concluded that one of the major objectives for the I990s in weather forecasting will be the development of coupled retrieval methods in which satellite data, classical weather data and guess fields of numerical weather forecast models are used together to obtain an optimum effect.     

Selecting the Numerical Flux in Discontinuous Galerkin Methods for Diffusion Problems

In this paper we present numerical investigations of four different formulations of the discontinuous Galerkin method for diffusion problems. Our focus is to determine, through numerical experimentation, practical guidelines as to which numerical flux choice should be used when applying discontinuous Galerkin methods to such problems. We examine first an inconsistent and weakly unstable scheme analyzed in Zhang and Shu, Math. Models Meth. Appl. Sci. (M ³ AS) 13, 395–413 (2003), and then proceed to examine three consistent and stable schemes: the Bassi–Rebay scheme (J. Comput. Phys. 131, 267 (1997)), the local discontinuous Galerkin scheme (SIAM J. Numer. Anal. 35, 2440–2463 (1998)) and the Baumann–Oden scheme (Comput. Math. Appl. Mech. Eng. 175, 311–341 (1999)). For an one-dimensional model problem, we examine the stencil width, h-convergence properties, p-convergence properties, eigenspectra and system conditioning when different flux choices are applied. We also examine the ramifications of adding stabilization to these schemes. We conclude by providing the pros and cons of the different flux choices based upon our numerical experiments.This revised version was published online in July 2005 with corrected volume and issue numbers.     

Quintic splines method for second-order boundary value problems

Abstract

We develop a numerical method for computing smooth approximations to the solution of a system of second-order boundary value problems associated with obstacle, unilateral and contact problems based on uniform mesh quintic splines. It is shown that this method gives better approximations than those produced by other collocation, finite-difference and spline methods. A numerical example is given to illustrate the applicability of the new method.     

Contaminant transport with adsorption and their inverse problems

In Constales et al. (water Resources Res. 39(30), 1303, 2003) dual-well tests are used to reconstruct the flow and dispersion parameters in contaminant transport. A tracer is introduced by the injection well, which is considered to be in steady-state regime with the extraction well. Then, from measurements of the time evolution of the extracted tracer (breakthrough curve) the required model data has been recovered. In Constales et al. (water Resources Res. 39(30), 1303, 2003), a very precise numerical method has been developed for the solution of the direct problem. In Kačur et al. (Comput. Meth. Appl. Mech. Engo. 194(2–5), 479–489, 2005); Remešiková (J. Comp. Appl. Math. 169(1), 101–116, 2004) an extension has been discussed which adds adsorption terms to the model. The inverse problem of determination of sorption isotherms in nonequilibrium mode was solved by a Levenberg–Marquardt iteration method. In the present paper we develop the adjoint system to evaluate the sensitivity of the solution (via the breakthrough curve) on the sorption parameters in equilibrium and nonequilibrium modes. Possible use of the adjoint system in determining the several parameters occuring in the model is a crucial point for iteration methods. The obtained model parameters then can be used in a 3D flow and transport model with adsorption. The numerical experiments we present, justify the used method.     

A method for merging flow-dependent forecast error statistics from an ensemble with static statistics for use in high resolution variational data assimilation

The background error covariance matrix, B, is often used in variational data assimilation for numerical weather prediction as a static and hence poor approximation to the fully dynamic forecast error covariance matrix, P^f. In this paper the concept of an Ensemble Reduced Rank Kalman Filter (EnRRKF) is outlined. In the EnRRKF the forecast error statistics in a subspace defined by an ensemble of states forecast by the dynamic model are found. These statistics are merged in a formal way with the static statistics, which apply in the remainder of the space. The combined statistics may then be used in a variational data assimilation setting. It is hoped that the nonlinear error growth of small-scale weather systems will be accurately captured by the EnRRKF, to produce accurate analyses and ultimately improved forecasts of extreme events.     

ON SYSTEMS' RELIABILITY AND REDUNDANCY

Abstract

A prime requirement of a system is that it be reliable and that the system designer has been able to estimate the reliability in numerical terms. Should it turn out that certain sections of the system arc too prone to fait the designer may consider duplicating such sections in some manner, i.e. the designer tries to enhance the overall reliability through use of redundancy. But how much—if anything—will be gained reliability wise by such a design change? A possible gain is hard to assess due to interaction between former and new components; however, it is frequently possible, by fairly simple means, to find upper and lower bounds for such gain in reliability

The purpose of this paper is twofold: first to introduce the readers to some fundamental concepts in the theory of system reliability, and second to present two new results valid for redundant system configurations (we ask the question: what arc the upper and lower bounds for the expected life or a parallel configuration, when the expected life for each of the blocks is parallel is known). (An expanded version of the paper is available from the authors upon request.)     

Numerical studies on the microclimate around a sleeping person and the related thermal neutrality issues

This article reports on two numerical studies on the microclimate around, and the thermal neutrality of, a sleeping person in a space installed with a displacement ventilation system. The development of a sleeping computational thermal manikin (SCTM) placed in a space air-conditioned by a displacement ventilation system is first described. This is followed by reporting the results of the first numerical study on the microclimate around the SCTM, including air temperature and velocity distributions and the heat transfer characteristics. Then the outcomes of the other numerical study on the thermal neutrality of a sleeping person are presented, including the thermal neutrality for a naked sleeping person and the effects of the total insulation value of a bedding system on the thermal neutrality of a sleeping person.

Statement of relevance: The thermal environment would greatly affect the sleep quality of human beings. Through developing a SCTM, the microclimate around a sleeping person has been numerically studied. The thermal neutral environment may then be predicted and contributions to improved sleep quality may be made.     

Integration of Dynamic Equation of Spring-Mass-Damper Systems via Chebyshev Polynomials

A numerical scheme based on Chebyshev polynomials for the determination of the response of spring-mass-damper systems is presented. The state vector of the differential equation of the spring-mass-damper system is expanded in terms of Chebyshev polynomials. This expansion reduces the original differential equations to a set of linear algebraic equations where the unknowns are the coefficient of Chebyshev polynomials. A formal procedure to generate the coefficient matrix and the right-hand side vector of this system of algebraic equations is discussed. The numerical efficiency of the proposed method is compared with that of Runge-Kutta method. It is shown that this scheme is accurate and is computationally efficient.     

大规模流体场景的真实感与实时模拟

目的 基于物理的流体动画模拟是计算机图形学领域中的研究热点,针对实际应用中仍难以实现大规模流体场景的真实感与实时模拟,提出了基于shallow water方程的物理模拟方法。方法 首先,给出shallow water方程的稳定欧拉数值求解方法,解决模拟过程中存在的毛刺、陡坡水滴斑点等数值求解的不稳定性问题;其次,提出刚体和粒子系统与流体高度场的稳定耦合模型,实现双向固流耦合和流体表面细节的真实感模拟;最后,设计高度场的多精度网格算法以及粒子的隔点采样方法,加速大规模流体的物理模拟计算。结果 实验结果表明,本文方法解决了传统欧拉方法求解shallow water方程的流体模拟过程中存在的不稳定和计算复杂等问题,在300×300网格分辨率和2.2×10⁴粒子数的规模下,达到了20帧/s的实时模拟速度。结论 本文算法具有良好的高效性和稳定性,适用于电子游戏和视景仿真等实时应用领域中的大规模流体场景的真实感模拟。     

Stochastic grid bundling method for backward stochastic differential equations

ABSTRACT

In this work, we apply the Stochastic Grid Bundling Method (SGBM) to numerically solve backward stochastic differential equations (BSDEs). The SGBM algorithm is based on conditional expectations approximation by means of bundling of Monte Carlo sample paths and a local regress-later regression within each bundle. The basic algorithm for solving the backward stochastic differential equations will be introduced and an upper error bound is established for the local regression. A full error analysis is also conducted for the explicit version of our algorithm and numerical experiments are performed to demonstrate various properties of our algorithm.     

Certainty equivalence adaptation combined with super-twisting sliding-mode control

ABSTRACT

In this paper, a Lyapunov-based control concept is presented that combines variable structure and adaptive control. The considered system class consists of nonlinear single input systems which are affected by matched structured and unstructured uncertainties. Resorting to the certainty equivalence principle, the controller exploits advantages of both the sliding-mode and the adaptive control methodology. It is demonstrated that the gains of the discontinuous control action may be reduced remarkably when compared with pure sliding-mode-based approaches. The efficiency of the presented concept is demonstrated in detail, using results of numerical simulations.     

Combinatorial Grouping— A Lattice-Theoretic Method for the Design of Manufacturing Systems

Abstract

This paper presents a combinatorial method of grouping objects into guest families, and of providing accommodation in a system of host cells. The method maximises the amount of hospitality extended by the hosts towards the guests. A guest job requiring few facilities will have a greater chance of finding a host cell than a more demanding guest job, and not all the host cells will be equally busy. As a consequence, there will be greater scheduling flexibility and better cell utilisation.     

PHoM – a Polyhedral Homotopy Continuation Method for Polynomial Systems

PHoM is a software package in C++ for finding all isolated solutions of polynomial systems using a polyhedral homotopy continuation method. Among three modules constituting the package, the first module StartSystem constructs a family of polyhedral-linear homotopy functions, based on the polyhedral homotopy theory, from input data for a given system of polynomial equations f(x)=0. The second module CMPSc traces the solution curves of the homotopy equations to compute all isolated solutions of f(x)=0. The third module Verify checks whether all isolated solutions of f(x)=0 have been approximated correctly. We describe numerical methods used in each module and the usage of the package. Numerical results to demonstrate the performance of PHoM include some large polynomial systems that have not been solved previously.AMS Subject Classification: Primary: 65H10 system of equations, secondary: 65H20 global methods, including homotopy approaches.     

Rough set-based approach to rule generation and rule induction

During the last decade, databases have been growing rapidly in size and number as a result of rapid advances in database capacity and management techniques. This expansive growth in data and databases has caused a pressing need for the development of more powerful techniques to convert the vast pool of data into valuable information. For the purpose of strategic and decision-making, many companies and researchers have recognized mining useful information and knowledge from large databases as a key research topic and as an opportunity for major revenues and improving competitiveness. In this paper, we will explore a new rule generation algorithm (based on rough sets theory) that can generate a minimal set of rule reducts, and a rule generation and rule induction program (RGRIP) which can efficiently induce decision rules from conflicting information systems. All the methods will also be illustrated with numerical examples.     

Controlling co-generation: conservation laws,modelling and Lyapunov synthesis

ABSTRACT

The paper considers a model of co-generation with distributed parameters, described by a non-standard boundary value problem with nonlinear boundary conditions with respect to a system of conservation laws. For the aforementioned model, well posedness in the sense of Hadamard, existence of some invariant sets, equilibria and their stability will be studied. The stabilising feedback laws are synthesised using a suitably constructed Lyapunov functional.     

An adaptive doctor-recommender system

ABSTRACT

Recommender systems use machine-learning techniques to make predictions about resources. The medical field is one where much research is currently being conducted on recommender system utility. In the last few years, the amount of information available online that relates to healthcare has increased tremendously. Patients nowadays are more aware and look for answers to healthcare problems online. This has resulted in a dire need of an effective reliable online system to recommend the physician that is best suited to a particular patient in a limited time. In this article, a hybrid doctor-recommender system is proposed, by combining different recommendation approaches: content base, collaborative and demographic filtering to effectively tackle the issue of doctor recommendation. The proposed system addresses the issue of personalization through analysing patient's interest towards selecting a doctor. It uses a novel adoptive algorithm to construct a doctor's ranking function. Moreover, this ranking function is used to translate patients’ criteria for selecting a doctor into a numerical base rating, which will eventually be used in the recommendation of doctors. The system has been evaluated thoroughly, and result show that recommendations are reasonable and can fulfil patient's demand for reliable doctor's selection effectively.     

A Chebyshev Finite Difference Method For Solving A Class Of Optimal Control Problems

A new Chebyshev finite difference method for solving class of optimal control problem is proposed. The algorithm is based on Chebyshev approximations of the derivatives arising in system dynamics. In the performance index, we use Chebyshev approximations for integration. The numerical examples illustrate the robustness, accuracy and efficiency of the proposed technique.