Hybrid Strategy of Partitioned and Monolithic Methods for Solving Strongly Coupled Analysis of Inverse and Direct Piezoelectric and Circuit Coupling

The inverse and direct piezoelectric and circuit coupling are widely observed in advanced electro-mechanical systems such as piezoelectric energy harvesters.Existing strongly coupled analysis methods based on direct numerical modeling for this phenomenon can be classified into partitioned or monolithic formulations.Each formulation has its advantages and disadvantages,and the choice depends on the characteristics of each coupled problem.This study proposes a new option:a coupled analysis strategy that combines the best features of the existing formulations,namely,the hybrid partitioned-monolithic method.The analysis of inverse piezoelectricity and the monolithic analysis of direct piezoelectric and circuit interaction are strongly coupled using a partitioned iterative hierarchical algorithm.In a typical benchmark problem of a piezoelectric energy harvester,this research compares the results from the proposed method to those from the conventional strongly coupled partitioned iterative method,discussing the accuracy,stability,and computational cost.The proposed hybrid concept is effective for coupled multi-physics problems,including various coupling conditions.

Partition method for impact dynamics of flexible multibody systems based on contact constraint

The impact dynamics of a flexible multibody system is investigated. By using a partition method, the system is divided into two parts, the local impact region and the region away from the impact. The two parts are connected by specific boundary conditions, and the system after partition is equivalent to the original system. According to the rigid-flexible coupling dynamic theory of multibody system, system＇s rigid-flexible coupling dynamic equations without impact are derived. A local impulse method for establishing the initial impact conditions is proposed. It satisfies the compatibility con- ditions for contact constraints and the actual physical situation of the impact process of flexible bodies. Based on the contact constraint method, system＇s impact dynamic equa- tions are derived in a differential-algebraic form. The contact/separation criterion and the algorithm are given. An impact dynamic simulation is given. The results show that system＇s dynamic behaviors including the energy, the deformations, the displacements, and the impact force during the impact process change dramatically. The impact makes great effects on the global dynamics of the system during and after impact.

Partition method and experimental validation for impact dynamics of flexible multibody system

The impact problem of a flexible multibody system is a non-smooth, high-transient, and strong-nonlinear dynamic process with variable boundary. How to model the contact/impact process accurately and efficiently is one of the main difficulties in many engineering applications. The numerical approaches being used widely in impact analysis are mainly from two fields： multibody system dynamics （MBS） and computational solid mechanics （CSM）. Approaches based on MBS provide a more efficient yet less accurate analysis of the contact/impact problems, while approaches based on CSM are well suited for particularly high accuracy needs, yet require very high computational effort. To bridge the gap between accuracy and efficiency in the dynamic simulation of a flexible multibody system with contacts/impacts, a partition method is presented considering that the contact body is divided into two parts, an impact region and a non-impact region. The impact region is modeled using the finite element method to guarantee the local accuracy, while the non-impact region is modeled using the modal reduction approach to raise the global efficiency. A three-dimensional rod-plate impact experiment is designed and performed to validate the numerical results. The principle for how to partition the contact bodies is proposed： the maximum radius of the impact region can be estimated by an analytical method, and the modal truncation orders of the non-impact region can be estimated by the highest frequency of the signal measured. The simulation results using the presented method are in good agreement with the experimental results. It shows that this method is an effec-rive formulation considering both accuracy and efficiency. Moreover, a more complicated multibody impact problem of a crank slider mechanism is investigated to strengthen this conclusion.

PARTITION OF UNITY FINITE ELEMENT METHOD FOR SHORT WAVE PROPAGATION IN SOLIDS

A partition of unity finite element method for numerical simulation of short wave propagation in solids is presented. The finite element spaces were constructed by multiplying the standard isoparametric finite element shape functions, which form a partition of unity, with the local subspaces defined on the corresponding shape functions, which include a priori knowledge about the wave motion equation in trial spaces and approximately reproduce the highly oscillatory properties within a single element. Numerical examples demonstrate the performance of the proposed partition of unity finite element in both computational accuracy and efficiency.

Fluid-Structure Interaction Analysis of Flexible Plate with Partitioned Coupling Method

The development and rapid usage of numerical codes for fluid-structure interaction(FSI) problems are of great relevance to researchers in many engineering fields such as civil engineering and ocean engineering. This multidisciplinary field known as FSI has been expanded to engineering fields such as offshore structures, tall slender structures and other flexible structures applications. The motivation of this paper is to investigate the numerical model of two-way coupling FSI partitioned flexible plate structure under fluid flow. The adopted partitioned method and approach utilized the advantage of the existing numerical algorithms in solving the two-way coupling fluid and structural interactions. The flexible plate was subjected to a fluid flow which causes large deformation on the fluid domain from the oscillation of the flexible plate. Both fluid and flexible plate are subjected to the interaction of load transfer within two physics by using the strong and weak coupling methods of MFS and Load Transfer Physics Environment, respectively. The oscillation and deformation results have been validated which demonstrate the reliability of both strong and weak method in resolving the two-way coupling problem in contribution of knowledge to the feasibility field study of ocean engineering and civil engineering.

Numerical Dispersion Relation of Multi-symplectic Runge-Kutta Methods for Hamiltonian PDEs

Numerical dispersion relation of the multi-symplectic Runge-Kutta （MSRK） method for linear Hamiltonian PDEs is derived in the present paper, which is shown to be a discrete counterpart to that possessed by the differential equation. This provides further understanding of MSRK methods. However, much still remains to be investigated further.

MSPRK Methods for the Korteweg-de Vries Equation

We consider the Korteweg-de Vries （KdV） equation in the form ut＋uux＋uxxx=0,（1） which is a nonlinear hyperbolic equation and has smooth solutions for all the time. There are a vast of results can be found in the literature for this equation, both theoretical and numerical. However, several good reasons account for needs of another numerical study of this equation are listed in [1].

A nested partitioning-based solution method for seru scheduling problem with resource allocation

This paper investigates the production scheduling problems of allocating resources and sequencing jobs in the seru production system(SPS).As a new-type manufacturing mode arising from Japanese production practices,seru production can achieve efficiency,flexibility,and responsiveness simultaneously.The production environment in which a set of jobs must be scheduled over a set of serus according to due date and different execution modes is considered,and a combination optimization model is provided.Motivated by the problem complexity and the characteristics of the proposed seru scheduling model,a nested partitioning method(NPM)is designed as the solution approach.Finally,computational studies are conducted,and the practicability of the proposed seru scheduling model is proven.Moreover,the efficiency of the nested partitioning solution method is demonstrated by the computational results obtained from different scenarios,and the good scalability of the proposed approach is proven via comparative analysis.

A method of solving the stiffness problem in Biot＇s poroelastic equations using a staggered high-order finite-difference

In modelling elastic wave propagation in a porous medium, when the ratio between the fluid viscosity and the medium permeability is comparatively large, the stiffness problem of Blot＇s poroelastic equations will be encountered. In the paper, a partition method is developed to solve the stiffness problem with a staggered high-order finite-difference. The method splits the Biot equations into two systems. One is stiff, and solved analytically, the other is nonstiff, and solved numerically by using a high-order staggered-grid finite-difference scheme. The time step is determined by the staggered finite-difference algorithm in solving the nonstiff equations, thus a coarse time step may be employed. Therefore, the computation efficiency and computational stability are improved greatly. Also a perfect by matched layer technology is used in the split method as absorbing boundary conditions. The numerical results are compared with the analytical results and those obtained from the conventional staggered-grid finite-difference method in a homogeneous model, respectively. They are in good agreement with each other. Finally, a slightly more complex model is investigated and compared with related equivalent model to illustrate the good performance of the staggered-grid finite-difference scheme in the partition method.

Fast image super-resolution algorithm based on multi-resolution dictionary learning and sparse representation

Sparse representation has attracted extensive attention and performed well on image super-resolution（SR） in the last decade. However, many current image SR methods face the contradiction of detail recovery and artifact suppression. We propose a multi-resolution dictionary learning（MRDL） model to solve this contradiction, and give a fast single image SR method based on the MRDL model. To obtain the MRDL model, we first extract multi-scale patches by using our proposed adaptive patch partition method（APPM）. The APPM divides images into patches of different sizes according to their detail richness. Then, the multiresolution dictionary pairs, which contain structural primitives of various resolutions, can be trained from these multi-scale patches.Owing to the MRDL strategy, our SR algorithm not only recovers details well, with less jag and noise, but also significantly improves the computational efficiency. Experimental results validate that our algorithm performs better than other SR methods in evaluation metrics and visual perception.

COLLABORATIVE DESIGN OF MULTIPHYSICS PROBLEMS

Collaborative design is recommended to solve multiphysics problems （MPPS）. Firstly, mathematical model of MPPS is constructed and solved by a proposed partitioned method, analysis of which suggests that collaborative design be feasible to solve MPPS. As the key technology of col-laborative design of MPPS, a task collaboration algorithm is then proposed. To develop the applica-tion framework of collaborative design, applied unified process（AUP） is proposed based on rational unified process（RUP）. Then AUP is used to develop the collaborative design platform, whose function framework is constructed according to the process of project management. Finally three MPPS are solved on this platform and the results suggest that the proposed model, algorithm and framework be feasible.

ENERGY AND QUADRATIC INVARIANTS PRESERVING METHODS FOR HAMILTONIAN SYSTEMS WITH HOLONOMIC CONSTRAINTS

We introduce a new class of parametrized structure–preserving partitioned RungeKutta(α-PRK)methods for Hamiltonian systems with holonomic constraints.The methods are symplectic for any fixed scalar parameterα,and are reduced to the usual symplectic PRK methods like Shake-Rattle method or PRK schemes based on Lobatto IIIA-IIIB pairs whenα=0.We provide a new variational formulation for symplectic PRK schemes and use it to prove that theα-PRK methods can preserve the quadratic invariants for Hamiltonian systems subject to holonomic constraints.Meanwhile,for any given consistent initial values(p0,q0)and small step size h>0,it is proved that there existsα∗=α(h,p0,q0)such that the Hamiltonian energy can also be exactly preserved at each step.Based on this,we propose some energy and quadratic invariants preservingα-PRK methods.Theseα-PRK methods are shown to have the same convergence rate as the usual PRK methods and perform very well in various numerical experiments.

CONVERGENCE ANALYSIS OF SOME FINITE ELEMENT PARALLEL ALGORITHMS FOR THE STATIONARY INCOMPRESSIBLE MHD EQUATIONS

By combination of iteration methods with the partition of unity method(PUM),some finite element parallel algorithms for the stationary incompressible magnetohydrodynamics(MHD)with different physical parameters are presented and analyzed.These algorithms are highly efficient.At first,a global solution is obtained on a coarse grid for all approaches by one of the iteration methods.By parallelized residual schemes,local corrected solutions are calculated on finer meshes with overlapping sub-domains.The subdomains can be achieved flexibly by a class of PUM.The proposed algorithm is proved to be uniformly stable and convergent.Finally,one numerical example is presented to confirm the theoretical findings.

A SIMPLE WAY CONSTRUCTING SYMPLECTICRUNGE-KUTTA METHODS

Presents a study which derived a way of constructing symplectic methods with the help of symplecticity conditions of partitioned Runge-Kutta methods. Classes of symplectic Runge-Kutta methods; Relationship between Runge-Kutta methods.

OPTIMAL ERROR ESTIMATES OF THE PARTITION OF UNITY METHOD WITH LOCAL POLYNOMIAL APPROXIMATION SPACES

In this paper, we provide a theoretical method（PUFEM）, which belongs to the analysis of the partition of unity finite element family of meshfree methods. The usual error analysis only shows the order of error estimate to the same as the local approximations[12]. Using standard linear finite element base functions as partition of unity and polynomials as local approximation space, in l-d case, we derive optimal order error estimates for PUFEM interpolants. Our analysis show that the error estimate is of one order higher than the local approximations. The interpolation error estimates yield optimal error estimates for PUFEM solutions of elliptic boundary value problems.

Partition of unity interpolation on multivariate convex domains

In this paper,we present an algorithm for multivariate interpolation of scattered data sets lying in convex domainsΩ⊆R^(N),for any N≥2.To organize the points in a multidimensional space,we build a kd-tree space-partitioning data structure,which is used to efficiently apply a partition of unity interpolant.This global scheme is combined with local radial basis function(RBF)approximants and compactly supported weight functions.A detailed description of the algorithm for convex domains and a complexity analysis of the computational procedures are also considered.Several numerical experiments show the performances of the interpolation algorithm on various sets of Halton data points contained inΩ,whereΩcan be any convex domain,like a 2D polygon or a 3D polyhedron.Finally,an application to topographical data contained in a pentagonal domain is presented.