A scalable time–space multiscale domain decomposition method: adaptive time scale separation

This paper deals with the scalability of a time–space multiscale domain decomposition method in the framework of time-dependent nonlinear problems. The strategy which is being studied is the multiscale LATIN method, whose scalability was shown in previous works when the distinction between macro and micro parts is made on the spatial level alone. The objective of this work is to propose an explanation of the loss-of-scalability phenomenon, along with a remedy which guarantees full scalability provided a suitable macro time part is chosen. This technique, which is quite general, is based on an adaptive separation of scales which is achieved by adding the most relevant functions to the temporal macrobasis automatically. When this method is used, the numerical scalability of the strategy is confirmed by the examples presented.     

A pioneering video-to-video super-resolution reconstruction algorithm based on segmentation and space–time regularisation

In view of the common existing problems in present video-to-video super-resolution reconstruction, this paper proposes a pioneering video-to-video super-resolution reconstruction algorithm based on segmentation and space–time regularisation to solve these problems. First, a video-to-video super-resolution reconstruction algorithm based on segmentation is proposed to eliminate reconstructed temporal ringing and to improve the times of reconstruction. Second, considering that image mosaic is involved in our proposed reconstruction algorithm, an improved fade-in and fade-out method is proposed to make the mosaic image looks more natural. At last, an improved space–time regularisation algorithm is put forward to remove noise and preserve image edge at the same time. Using several experiments, we prove that the proposed algorithm can achieve state-of-the -art reconstruction effect.     

Models for space–time random functions

Models are developed for random functions $Q(x,t)$ of space $x\in D$ and time $t\in [0,\tau ]$ from samples of these functions and any other information when available. Most of the models in the paper can be viewed as extensions of Karhunen–Loève (KL) representations for random fields. Their samples are linear forms of basis functions with random coefficients which are extracted from samples of $Q(x,t)$ by singular value decomposition. The coefficients of these forms are stochastic processes rather than random variables. The proposed models can be used to generate large sets of samples whose statistics are similar to those of target random functions. Theoretical arguments and numerical examples are presented to establish properties of the proposed models, assess their accuracy, and illustrate their implementation.     

A fast multipole boundary element method based on the improved Burton–Miller formulation for three-dimensional acoustic problems

A fast multipole boundary element method (FMBEM) based on the improved Burton–Miller formulation is presented in this paper for solving large-scale three-dimensional (3D) acoustic problems. Some improvements can be made for the developed FMBEM. In order to overcome the non-unique problems of the conventional BEM, the FMBEM employs the improved Burton–Miller formulation developed by the authors recently to solve the exterior acoustic problems for all wave numbers. The improved Burton–Miller formulation contains only weakly singular integrals, and avoids the numerical difficulties associated to the evaluation of the hypersingular integral, it leads to the numerical implementations more efficient and straightforward. In this study, the fast multipole method (FMM) and the preconditioned generalized minimum residual method (GMRES) iterative solver are applied to solve system matrix equation. The block diagonal preconditioner needs no extra memory and no extra CPU time in each matrix–vector product. Thus, the overall computational efficiency of the developed FMBEM is further improved. Numerical examples clearly demonstrate the accuracy, efficiency and applicability of the FMBEM based on improved Burton–Miller formulation for large-scale acoustic problems.     

Pareto Tracer: a predictor–corrector method for multi-objective optimization problems

This article proposes a novel predictor–corrector (PC) method for the numerical treatment of multi-objective optimization problems (MOPs). The algorithm, Pareto Tracer (PT), is capable of performing a continuation along the set of (local) solutions of a given MOP with k objectives, and can cope with equality and box constraints. Additionally, the first steps towards a method that manages general inequality constraints are also introduced. The properties of PT are first discussed theoretically and later numerically on several examples.     

A parallel run‐time iterative load balancing algorithm for solution‐adaptive finite element meshes on hypercubes

Abstract

To efficiently execute a finite element program on a hypercube, we need to map nodes of the corresponding finite element graph to processors of a hypercube such that each processor has approximately the same amount of computational load and the communication among processors is minimized. If the number of nodes of a finite element graph will not be increased during the execution of a program, the mapping only needs to be performed once. However, if a finite element graph is solution‐adaptive, that is, the number of nodes will be increased discretely due to the refinement of some finite elements during the execution of a program, a run‐time load balancing algorithm has to be performed many times in order to balance the computational load of processors while keeping the communication cost as low as possible. In this paper, we propose a parallel iterative load balancing algorithm (ILB) to deal with the load imbalancing problem of a solution‐adaptive finite element program. The proposed algorithm has three properties. First, the algorithm is simple and easy to be implemented. Second, the execution of the algorithm is fast. Third, it guarantees that the computational load will be balanced after the execution of the algorithm. We have implemented the proposed algorithm along with two parallel mapping algorithms, parallel orthogonal recursive bisection (ORB) [19] and parallel recursive mincut bipartitioning (MC) [8], on a 16‐node NCUBE‐2. Three criteria, the execution time of load balancing algorithms, the computation time of an application program under different load balancing algorithms, and the total execution time of an application program (under several refinement phases) are used for performance evaluation. Experimental results show that (1) the execution time of ILB is very short compared to those of MC and ORB; (2) the mappings produced by ILB are better than those of ORB and MC; and (3) the speedups produced by ILB are better than those of ORB and MC.     

A 3D time domain numerical model based on half-space Green’s function for soil–structure interaction analysis

This paper presents a numerical method based on a three dimensional boundary element–finite element (BEM–FEM) coupled formulation in the time domain. The proposed model allows studying soil–structure interaction problems. The soil is modelled with the BEM, where the radiation condition is implicitly satisfied in the fundamental solution. Half-space Green’s function including internal soil damping is considered as the fundamental solution. An effective treatment based on the integration into a complex Jordan path is proposed to avoid the singularities at the arrival time of the Rayleigh waves. The efficiency of the BEM is improved taking into account the spatial symmetry and the invariance of the fundamental solution when it is expressed in a dimensionless form. The FEM is used to represent the structure. The proposed method is validated by comparison with analytical solutions and numerical results presented in the literature. Finally, a soil–structure interaction problem concerning with a building subjected to different incident wave fields is studied.     

Detailed analysis of particle–substrate interaction based on a centrifugal method

The interaction between particles and inclined substrates in a centrifuge was investigated theoretically and experimentally. First, the balance of the force acting on a particle adhering to the substrate, with an inclination angle from 0 to 90° to the horizontal, was formulated separately in the normal and tangential directions. The adhesion force was then derived based on the point-mass model as a function of the angular velocity. Next, the balance of the moments of the forces acting on a particle adhering to the substrate was formulated; theoretical equations for the adhesion force and the effective contact radius were then derived from the angular velocities, obtained at any two inclination angles, based on the rigid-body model. Finally, the removal fraction curves of spherical/nonspherical particles with median diameters of less than 10 µm were experimentally obtained by increasing the angular velocity at each inclination angle. The experimentally obtained angular velocities were substituted into the theoretical equations to compare the point-mass and rigid-body models. The effects of the particle shape on the adhesion force and effective contact radius and that of the inclination angle on the removal fraction curves based on the theoretical equation were also investigated.     

A hybrid Jaya algorithm for reliability–redundancy allocation problems

This article proposes an efficient improved hybrid Jaya algorithm based on time-varying acceleration coefficients (TVACs) and the learning phase introduced in teaching–learning-based optimization (TLBO), named the LJaya-TVAC algorithm, for solving various types of nonlinear mixed-integer reliability–redundancy allocation problems (RRAPs) and standard real-parameter test functions. RRAPs include series, series–parallel, complex (bridge) and overspeed protection systems. The search power of the proposed LJaya-TVAC algorithm for finding the optimal solutions is first tested on the standard real-parameter unimodal and multi-modal functions with dimensions of 30–100, and then tested on various types of nonlinear mixed-integer RRAPs. The results are compared with the original Jaya algorithm and the best results reported in the recent literature. The optimal results obtained with the proposed LJaya-TVAC algorithm provide evidence for its better and acceptable optimization performance compared to the original Jaya algorithm and other reported optimal results.     

3D non-linear time domain FEM–BEM approach to soil–structure interaction problems

Dynamic soil–structure interaction is concerned with the study of structures supported on flexible soils and subjected to dynamic actions. Methods combining the finite element method (FEM) and the boundary element method (BEM) are well suited to address dynamic soil–structure interaction problems. Hence, FEM–BEM models have been widely used. However, non-linear contact conditions and non-linear behavior of the structures have not usually been considered in the analyses. This paper presents a 3D non-linear time domain FEM–BEM numerical model designed to address soil–structure interaction problems. The BEM formulation, based on element subdivision and the constant velocity approach, was improved by using interpolation matrices. The FEM approach was based on implicit Green's functions and non-linear contact was considered at the FEM–BEM interface. Two engineering problems were studied with the proposed methodology: the propagation of waves in an elastic foundation and the dynamic response of a structure to an incident wave field.     

Accurate phase extraction algorithm based on Gram–Schmidt orthonormalization and least square ellipse fitting method

An accurate algorithm by combing Gram–Schmidt orthonormalization and least square ellipse fitting technology is proposed, which could be used for phase extraction from two or three interferograms. The DC term of background intensity is suppressed by subtraction operation on three interferograms or by high-pass filter on two interferograms. Performing Gram–Schmidt orthonormalization on pre-processing interferograms, the phase shift error is corrected and a general ellipse form is derived. Then the background intensity error and the corrected error could be compensated by least square ellipse fitting method. Finally, the phase could be extracted rapidly. The algorithm could cope with the two or three interferograms with environmental disturbance, low fringe number or small phase shifts. The accuracy and effectiveness of the proposed algorithm are verified by both of the numerical simulations and experiments.     

A novel Temperature–Humidity–Time defrosting control method based on a frosting map for air-source heat pumps

To improve the defrosting accuracy and the energy efficiency of the air-source heat pump (ASHP) under frosting and defrosting conditions, a novel Temperature–Humidity–Time (T–H–T) defrosting control method, based on a frosting map for the ASHP unit, is proposed in this paper. A field test was conducted for two heating seasons, to verify the feasibility and applicability of the T–H–T method. The advantages of the T–H–T method, compared to the conventional Temperature–Time (T–T) defrosting control method, are presented. In total, eight cases are shown in this paper. Cases 1 to 4 were chosen to reveal the T–H–T performance under different frosting conditions. It was found that no matter what kind of frosting conditions, defrosting was always initiated in a similar situation: ∼90% of the outdoor coil surface was covered by frost; the temperature difference between the compressor suction and discharge increased by ∼20%; and the heating capacity decreased by ∼30%. These results indicate that the T–H–T method can make an accurate decision under different frosting conditions. Cases 5a, 5b and Cases 6a, 6b were two groups of cases to compare the advantages of the T–H–T method against the conventional T–T method. Cases 5a and 5b were chosen for the non-frosting condition. It was found that the T–T method initiated the defrosting operation 31 times within 24 h. However, none of the defrosting operations was conducted for the T–H–T method. Cases 6a and 6b were chosen to compare these two methods under consecutive and variable frosting conditions. For the T–T method, 63% of the defrosting processes were found to be executed under conditions where defrosting was not necessary. However, for the T–H–T method, all the defrosting controls were found to be accurate and reasonable. These results indicated that the novel T–H–T method is suitable for the defrosting control of the ASHP, and has a more competitive performance than the conventional T–T method.     

Optical activities as computing resources for space–time symmetries

It is known that optical activities can perform rotations. It is shown that the rotation, if modulated by attenuations, can perform symmetry operations of Wigner's little group which dictates the internal space–time symmetries of elementary particles.     

Teaching–learning-based optimization algorithm for unconstrained and constrained real-parameter optimization problems

An efficient optimization algorithm called teaching–learning-based optimization (TLBO) is proposed in this article to solve continuous unconstrained and constrained optimization problems. The proposed method is based on the effect of the influence of a teacher on the output of learners in a class. The basic philosophy of the method is explained in detail. The algorithm is tested on 25 different unconstrained benchmark functions and 35 constrained benchmark functions with different characteristics. For the constrained benchmark functions, TLBO is tested with different constraint handling techniques such as superiority of feasible solutions, self-adaptive penalty, ?-constraint, stochastic ranking and ensemble of constraints. The performance of the TLBO algorithm is compared with that of other optimization algorithms and the results show the better performance of the proposed algorithm.     

A gradient recovery–based adaptive finite element method for convection-diffusion-reaction equations on surfaces

In this paper, we present an adaptive mesh refinement method for solving convection-diffusion-reaction equations on surfaces, which is a fundamental subproblem in many models for simulating the transport of substances on biological films and solid surfaces. The method considered is a combination of well-known techniques: the surface finite element method, streamline diffusion stabilization, and the gradient recovery–based Zienkiewicz-Zhu error estimator. The streamline diffusion method overcomes the instability issue of the finite element method for the dominance of the convection. The gradient recovery–based adaptive mesh refinement strategy enables the method to provide high-resolution numerical solutions by relatively fewer degrees of freedom. Moreover, the implementation detail of a surface mesh refinement technique is presented. Various numerical examples, including the convection-dominated diffusion problems with large variations of solutions, nearly singular solutions, discontinuous sources, and internal layers on surfaces, are presented to demonstrate the efficacy and accuracy of the proposed method.     

A new harmony search algorithm for solving mixed–discrete engineering optimization problems

In general design optimization problems, it is usually assumed that the design variables are continuous. However, many practical problems in engineering design require considering the design variables as integer or discrete values. The presence of discrete and integer variables along with continuous variables adds to the complexity of the optimization problem. Very few of the existing methods can yield a globally optimal solution when the objective functions are non-convex and non-differentiable. This article presents a mixed–discrete harmony search approach for solving these nonlinear optimization problems which contain integer, discrete and continuous variables. Some engineering design examples are also presented to demonstrate the effectiveness of the proposed method.     

Adaptive meshless local maximum-entropy finite element method for convection–diffusion problems

In this paper, a meshless local maximum-entropy finite element method (LME-FEM) is proposed to solve 1D Poisson equation and steady state convection–diffusion problems at various Peclet numbers in both 1D and 2D. By using local maximum-entropy (LME) approximation scheme to construct the element shape functions in the formulation of finite element method (FEM), additional nodes can be introduced within element without any mesh refinement to increase the accuracy of numerical approximation of unknown function, which procedure is similar to conventional p-refinement but without increasing the element connectivity to avoid the high conditioning matrix. The resulted LME-FEM preserves several significant characteristics of conventional FEM such as Kronecker-delta property on element vertices, partition of unity of shape function and exact reproduction of constant and linear functions. Furthermore, according to the essential properties of LME approximation scheme, nodes can be introduced in an arbitrary way and the $C^0$ continuity of the shape function along element edge is kept at the same time. No transition element is needed to connect elements of different orders. The property of arbitrary local refinement makes LME-FEM be a numerical method that can adaptively solve the numerical solutions of various problems where troublesome local mesh refinement is in general necessary to obtain reasonable solutions. Several numerical examples with dramatically varying solutions are presented to test the capability of the current method. The numerical results show that LME-FEM can obtain much better and stable solutions than conventional FEM with linear element.     

Adaptive radial basis function–generated finite differences method for contact problems

This paper proposes an original adaptive refinement framework using radial basis function–generated finite differences method. Node distributions are generated with a Poisson disc sampling–based algorithm from a given continuous density function, which is altered during the refinement process based on the error indicator. All elements of the proposed adaptive strategy rely only on meshless concepts, which leads to great flexibility and generality of the solution procedure. The proposed framework is tested on four gradually more complex contact problems. First, a disc under pressure is considered and the computed stress field is compared to the closed-form solution of the problem to assess the behaviour of the algorithm and the influence of free parameters. Second, a Hertzian contact problem is studied to analyse the proposed algorithm with an ad hoc error indicator and to test both refinement and derefinement. A contact problem, typical for fretting fatigue, with no known closed-form solution is considered and solved next. It is demonstrated that the proposed methodology produces results comparable with finite element method without the need for manual refinement or any human intervention. In the last case, generality of the proposed approach is demonstrated by solving a three-dimensional Boussinesq's problem.     

The combined finite–discrete element method for structural failure and collapse

A combined finite–discrete element model for failure and collapse of structural systems comprising of reinforced concrete beam or column type structural members has been developed and implemented into a combined finite–discrete element code. The results obtained using the proposed model compare well with analytical and experimental results. In addition the rotational capacities obtained are in good agreement with published experimental results.