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This paper proposes an iteration-based algorithm for the optimum design of a high frequency transformer for solid-state transformer (SST) applications. This algorithm minimizes the total owning cost (TOC) of a distribution type solid-state transformer. The unique features of this algorithm compared with the available algorithms in the literature are as follows: it iterates eight design variables, four constraints are defined for selecting the valid designs, and it works with different core materials and AC test voltages. The algorithm uses various user-defined data inputs to calculate loss capitalization values for TOC calculation. In every iteration, TOC is estimated, and calculated values of design constraints are compared with their threshold limits. A case study is conducted on a high-frequency transformer (HFT) incorporated in 1000-kVA, 11-kV/415-V, Dyn11 three-phase wound core SST. This is to determine the optimum design parameters. In this case study, the algorithm was iterated with 2,100,000 design data inputs, generating 258,272 designs that satisfied all design constraints. The optimum design with minimum TOC is selected from the generated 258,272 designs. The optimum design is validated using finite element analysis in ANSYS software. Comparing the results of both analyses, the deviation is less than 5%. Hence, the algorithm's reliability is proved. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and analyze multilevel inexact Uzawa and Arrow–Hurwicz algorithms for solving saddle point problems. For the definition of the problem and that of the Uzawa and Arrow–Hurwicz algorithms, we adopt the framework introduced in I. Ekeland and R. Temam, convex analysis and variational problems, North-Holland Publishing Company, Amsterdam, Oxford, 1976, where the saddle point is defined by optimizations on convex sets. The results are obtained for Hilbert spaces, and therefore they can be applied to obtain convergence results for the multigrid methods in finite element spaces. We prove the convergence of the two algorithms, the multilevel Uzawa and the multilevel Arrow–Hurwicz algorithms. Also, we give new convergence proofs for the Uzawa and Arrow–Hurwicz algorithms themselves to better characterize their convergence. [ABSTRACT FROM AUTHOR]

In the ever-expanding fields of thickness and topology optimization, there is a research gap for simultaneous and direct optimization of thickness and material for complex shell structures using fully analytical sensitivities, with prevention of coincident material layers. This paper introduces a novel method to fill this gap: concurrent thickness and material optimization (CTMO) based on a gradient-based approach. This proposed formulation determines optimal thickness and material choice for shell elements within a finite element (FE) model design space. The method of moving asymptotes (MMA) is used for optimization, and material interpolation is handled with solid isotropic material with penalization (SIMP). The behavior of this solver is demonstrated with several academic examples, through a series of extensive parameter sweeps of mass fraction, and minimum and maximum designable thickness, for the compliance minimization objective function. The proposed methodology is geared towards practical design of complex structures, allowing for feasible interpretation into actual engineering solutions. As such, optimization of a small aerobatic aircraft wing is conducted with study of several key design factors. The effects of design restriction and filter size are studied to determine best practices for design procedures. To demonstrate the practical utility of this algorithm, a selected wing optimization result is interpreted into a set of complete, industry style designs, verified through finite element analysis (FEA) to determine deviation from the ideal optimum. It is demonstrated that designs can be interpreted faithfully from optimization results with mass and compliance errors of less than 2%, alongside a discussion of pertinent factors. Finally, several areas with potential for future work are explored. [ABSTRACT FROM AUTHOR]

The generalized Schwarz algorithm for a class of elliptic quasi-variational inequalities related to impulse control problems is studied in this paper. The principal result is to prove the error estimate in L ∞ -norm for m subdomains with overlapping nonmatching grids. This approach combines the geometrical convergence and the uniform convergence. [ABSTRACT FROM AUTHOR]

This paper which depended on the foundation of back strip method has established mathematic model to simulate stratum burial history, which considered the computation of stratum skeleton depth based on max depth and the equation-depth point on the procedure to recover stratum by stripping each layer, and put forward the enhanced restoration method taking layers group as studying object. Finally, the method has been applied to build the computer model and program automatic back strip algorithm successfully. Experiments have proved that the method is accurate, applicable, and extensible under the conditions of various complex strata. [ABSTRACT FROM AUTHOR]

Abstract  The models for finite element analysis usually have a number of complex geometric features such as holes, slots, and curved surfaces, etc. The exact description of these features is crucial to the accuracy of finite element analysis. This paper presents an algorithm for the adaptive generation of the initial hexahedral element mesh based on the geometric features of the solid model. This algorithm is a modified grid-based method, in which a new geometry-adaptive hexahedral mesh generation method and a new mesh boundary matching method called threading method are established and employed. Firstly, an initial grid structure, which is uniformly sized or locally refined and encompasses the solid model completely, is generated based on the geometric features of the solid model. Then, an initial indention mesh is generated after removing all the elements in the exterior of the solid model using the even-odd rule. The surface of the indention mesh, which is adaptively generated based on the geometric features, is so complicated and different in size that the match of the edges and surface to the surface of the solid model becomes inconvenient. In this case, the closest position tracing approach used widely is difficult to realize an accurate match. The threading method proposed in this paper can accurately match the boundaries of the indention mesh to the boundaries of the solid model. Especially, it is fit for the generation of the geometry-adaptive mesh and avoids the recurrent search process of characteristic boundary nodes in the closest position tracing method. So the efficiency of the finite element mesh generation is enhanced remarkably. The principles and procedures of the algorithm are illustrated through the geometry-adaptive hexahedral mesh generation of a typical three-dimensional solid model. The effectiveness and robustness of the algorithm are tested by several applications in the complex solid models. [ABSTRACT FROM AUTHOR]

The lattice structures use has increased in several sectors due to the potential for mass reduction without significant rigidity loss. In this paper, an isogrid tube multi-objective optimization considering six objectives is presented. The finite element method was applied to develop a numerical model for this complex structure, and a new optimization algorithm called the Multi-objective Lichtenberg Algorithm was used to find all the best possible designs. The optimizations were made considering two methodologies: (i) using a surrogate model derived from the design of experiments considering the response surface model and (ii) finite element updating, a direct link between the meta-heuristic and the numerical model. The latter is unprecedented in the literature for isogrid tubes and proved to be the best methodology, besides not even needing explicit equations. It discovered isogrid tube designs using TOPSIS that reduced at least 45.69% of the mass, 18.4% of the instability coefficient, 61.76% of the TW, and increased the natural frequency by at least 52.57%. The results show that optimizations via finite element updating associated with meta-heuristics not only allow the true interpretation of complex problems nature through real Pareto fronts, but can also deliver innovative results. [ABSTRACT FROM AUTHOR]

In order to overcome the problems of large analysis error and low analysis efficiency in the current analysis method of rock and soil slope stability, a new research method based on strength reduction method is proposed in this paper. On the basis of the finite element analysis method, the finite element model is established, including the establishment of geometric model, preparatory work, and the fast triangle algorithm is used to optimize the mesh constructed by the finite element optimization method, and the mesh quality is tested. Secondly, the strength reduction method is used to analyze the advantages of geotechnical slope stability, and the established finite element model is solved by using the strength reduction method to obtain accurate geotechnical slope stability coefficient and complete the accurate analysis of geotechnical slope stability. The experimental results show that compared with the traditional method, the stability coefficient calculated by this method is closer to the actual data, with lower analysis error and higher analysis efficiency, and the maximum analysis time is only 2.5 s. [ABSTRACT FROM AUTHOR]

The direct problem of simple geometrical bodies plays an important role in the gravimetrical processing and modelling tools. We focused on the 3D rectangular prism, which is widely used in such processes. Even though the solution for this body is well known, there are still some issues about it, which are not answered or not answered completely in the available literature, e.g. the presence of the singularities in the source-free points or a continuity of the solutions. We present the singularity-free solution valid for the each position of the calculation point. Next, the analysis of the two basic types of the formulae for the 3D rectangular prism's gravitational effect is held on. We discuss the ways of their derivation, the validity and the problems connected with them. Later, special attention is paid at the problems with the citation of these two formulae types within the gravimetrical literature. [ABSTRACT FROM AUTHOR]

This paper deals with multiobjective optimization programs in which the objective functions are ordered by their degree of priority. A number of approaches have been proposed (and several implemented) for the solution of lexicographic (preemptive priority) multiobjective optimization programs. These approaches may be divided into two classes. The first encompasses the development of algorithms specifically designed to deal directly with the initial model. Considered only for linear multiobjective programs and multiobjective programs with a finite discrete feasible region, the second one attempts to transform, efficiently, the lexicographic multiobjective model into an equvivalent model, i.e. a single objective programming problem. In this paper, we deal with the second approach for lexicographic nonlinear multiobjective programs. [ABSTRACT FROM AUTHOR]

In this paper, we propose and analyze a second-order decoupled algorithm with different subdomain time steps for the non-stationary Stokes/Darcy model. It is based on the second-order spectral deferred correction method in time and the finite element method in space. We provide the stability and convergence results of our decoupled scheme. Last, some numerical experiments are given to illustrate the accuracy and effectiveness of our decoupled scheme. [ABSTRACT FROM AUTHOR]

In this paper, a second-order hyperbolic equation is solved by a two-grid algorithm combined with the expanded mixed finite element method. The error estimate of the expanded mixed finite element method with discrete-time scheme is demonstrated. Moreover, we present a two-grid method and analyze its convergence. It is shown that the algorithm can achieve asymptotically optimal approximation as long as the mesh sizes satisfy H = O (h 1 2) . Finally, some numerical experiments are provided to illustrate the efficiency and accuracy of the proposed method. [ABSTRACT FROM AUTHOR]

Thermal deformation is one of the principal factors that influence the machining accuracy of machine tools, and it can be improved by thermal error compensation. This paper presents a method of thermal error modeling using multisource information fusion, which can further improve the thermal error compensation accuracy. To set up a fusion model with optimal performance, two or more thermal error models should be established, from which a few models should be chosen to complement each other, and then combined into a synthesis model. In this paper, a dynamic thermal error model and a finite element model are combined to build a fusion model for lathe z-direction thermal error according to a fusion algorithm. The inputs for the fusion model are the values detected by the thermal sensors and the infrared imaging. An experiment carried out on a lathe verifies the validity of this modeling method. The results show that the multisource fusion model of thermal error can not only improve the prediction accuracy of thermal error over that of a single model, but also possesses better robustness. [ABSTRACT FROM AUTHOR]

In the current study, the problems of elastic and elastoplastic torsion were formulated by finite element method. The finite element code was parallelized on both shared and distributed memory architectures. An assembling method with high parallelism ability and consuming minimum memory was proposed to obtain compressed global stiffness matrix directly. Parallel programming principles were expressed in two shared memory and distributed memory approaches; moreover, parallel well-known mathematical libraries were briefly expressed. In this paper, the main focus was on a lucid explanation of parallelization mechanisms in detail on two memory architectures such as some settings of Linux operating system for large-scale problems. To verify the ability of the proposed method and its parallel performance, several benchmark examples were represented with different mesh sizes and were compared with their respective analytical solutions. Considering the obtained results, the proposed sparse assembling algorithm decreased required memory significantly (about 103.5 to 105.5 times) and the obtained speedup was about 3.4 for the elastoplastic torsion problem in a simple multicore computer. [ABSTRACT FROM AUTHOR]

The element energy projection (EEP) method for computation of superconvergent resulting in a one-dimensional finite element method (FEM) is successfully used to self-adaptive FEM analysis of various linear problems, based on which this paper presents a substantial extension of the whole set of technology to nonlinear problems. The main idea behind the technology transfer from linear analysis to nonlinear analysis is to use Newton's method to linearize nonlinear problems into a series of linear problems so that the EEP formulation and the corresponding adaptive strategy can be directly used without the need for specific super-convergence formulation for nonlinear FEM. As a result, a unified and general self-adaptive algorithm for nonlinear FEM analysis is formed. The proposed algorithm is found to be able to produce satisfactory finite element results with accuracy satisfying the user-preset error tolerances by maximum norm anywhere on the mesh. Taking the nonlinear ordinary differential equation of second-order as the model problem, this paper describes the related fundamental idea, the implementation strategy, and the computational algorithm. Representative numerical examples are given to show the efficiency, stability, versatility, and reliability of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper presents a composite element algorithm of coupled normal stress and fluid flow process for fractured rock mass, developed from the composite element method (CEM). The coupled relation between the fracture flow and normal stress makes use of the 'filled model', which examines the asperities in the fracture as a layer of granular medium having high porosity and being clipped by the two parallel plates. The existence of fractures is not considered in the mesh generation, but it will be considered explicitly in the mapped composite element. The coupled normal stress and fluid flow process has been simulated by applying a cross iterative algorithm between the two fields. The proposed algorithm considers not only the flow through the fractures, but also the flow exchange between fractures and the surrounding rock blocks. In addition, it can be used for both the filled and non-filled fractures. The verification of the proposed algorithm has been conducted through the illustration of three examples by comparison with the conventional finite element method (FEM), from which the advantages and reliability of the proposed algorithm have been shown clearly. [ABSTRACT FROM AUTHOR]

The fractional Fokker–Planck system with multiple internal states is derived in [Xu and Deng, Math. Model. Nat. Phenom., 13 , 10 (2018)], where the space derivative is Laplace operator. If the jump length distribution of the particles is power law instead of Gaussian, the space derivative should be replaced with fractional Laplacian. This paper focuses on solving the two-state Fokker–Planck system with fractional Laplacian. We first provide a priori estimate for this system under different regularity assumptions on the initial data. Then we use L 1 scheme to discretize the time fractional derivatives and finite element method to approximate the fractional Laplacian operators. Furthermore, we give the error estimates for the space semidiscrete and fully discrete schemes without any assumption on regularity of solutions. Finally, the effectiveness of the designed scheme is verified by one- and two-dimensional numerical experiments. [ABSTRACT FROM AUTHOR]

In the present paper, a recent deterministic continuum-strategy two-player discrete-time dynamic leader-follower game with fixed finite time duration and closed-loop information structure is studied. The types of the considered payoff functions can be widely used in different applications (mainly in conflicts of consuming a limited resource, where one player, called the leader, is a superior authority choosing a strategy choice first, and another player, called the follower, chooses after). In case of certain payoff convexity, explicit conditions are given, when it can be known in advance that an equilibrium exists and consists of only two possible choices of both players at each step. The sub-game equilibrium from a given step may depend on the former selections of the players. Thus the continuum-strategy problem has been reduced to a general finite game of two possible choices corresponding to both players. Such type of games could be solved in a standard way with dynamic programming using a computer. Nevertheless, the game can be further simplified, and then an equilibrium can be directly determined, such decreasing the computational demand to a great extent. A solution algorithm and practical examples are also given to support the real-life application of the results. [ABSTRACT FROM AUTHOR]

This paper presents a methodology for an optimal design of interference fit subjected to fatigue loads. Optimization consists in finding a trade-off between mass and competing safety factors at hub and shaft contact zone as well as in shaft fillet. Developing an effective calculation method for fatigue strength of an interference fitted assembly using the finite element method is one of the main steps of the procedure. Meanwhile, coupling the finite elements model of interference fit with an optimization algorithm is not adequate considering the computing time and the significant number of calculations necessary to portrait the assembly behavior. Therefore, a sequential approximate multi-objective optimization algorithm (SAMOO) is presented. The method involves Design Of Experiments (DOE), interpolation with kriging functions, and multi-objective optimization. Preliminary study of parameter variance, and advanced post-processing of multi-objective optimization, provide engineers with valuable information for identifying an optimal design of interference fit assembly using fewer finite element calculations. [ABSTRACT FROM AUTHOR]

Rapid prototyping technology makes the manufacturing of functionally graded material (FGM) objects possible. The FGM production process requires concurrent applications of digital design and manufacturing methods. For this reason, it is imperative to construct and capture information and other critical data regarding the geometry and materials about FGM objects for use in the manufacturing process. This paper proposes a simplex-clear data format for modeling FGM objects. This proposed data format captures both the geometry and material information of an FGM object. It also presents a finite element-based slicing algorithm which slices the FGM object into layers and captures each layer's information for rapid prototyping manufacturing of the object. An example is given at the end of the paper to validate the data format and demonstrate the adaptive slicing algorithm. [ABSTRACT FROM AUTHOR]

The objective of this paper is to introduce an efficient algorithm and implementation for large-scale 3-D topology optimization. The proposed algorithm is an extension of a recently proposed 2-D topological-sensitivity based method that can generate numerous pareto-optimal topologies up to a desired volume fraction, in a single pass. In this paper, we show how the computational challenges in 3-D can be overcome. In particular, we consider an arbitrary 3-D domain-space that is discretized via hexahedral/brick finite elements. Exploiting congruence between elements, we propose a matrix-free implementation of the finite element method. The latter exploits modern multi-core architectures to efficiently solve topology optimization problems involving millions of degrees of freedom. The proposed methodology is illustrated through numerical experiments; comparisons are made against previously published results. [ABSTRACT FROM AUTHOR]

In the majority of the researches presented so far for behavior analysis of complex structures with random loading and material properties, the applications rather than the analysis algorithms have been extended. The present paper is devoted to extending the probabilistic concepts to achieve a stochastic finite element-based consistent reliability algorithm that is more consistent with the design criteria. The proposed procedure is very general and may be employes for vehcle components with complex geometries and load conditions. However, beam-type vehicle components experience simultaneous spatially-random loading conditions and material properties are employed to clarify the proposed algorithm, without loss of the generality. In this regard, important concepts such as the displacement/stress level-crossing concept are incorporated. The stress stochastic formulations are proposed in the present paper, for the first time. [ABSTRACT FROM AUTHOR]

Analysis of transverse vibration of the gear found in a high-speed gearbox considered as an annular plate reflecting gear geometry is the subject of this paper. How gear angular velocity affects the deformation of normal modes of transverse vibration of the system under consideration is analysed. Models considered were discretized by the finite elements method. Numerical computations have been performed in the ANSYS environment. The algorithm to identify the proper distorted mode shapes is presented. The Campbell diagram for the system under consideration is elaborated. The problems discussed here can be useful for engineers dealing with dynamics of rotating machine systems. [ABSTRACT FROM AUTHOR]

It is important to consider the performances of lightweight, stiffness, strength and rollover safety when designing a bus body. In this paper, the finite element (FE) analysis models including strength, stiffness and rollover crashworthiness of a bus body are first built and then validated by physical tests. Based on the FE models, the design of experiment is implemented and multiple surrogate models are created with response surface method and hybrid radial basis function according to the experimental data. After that, a multi-objective optimization problem (MOP) of the bus body is formulated in which the objective is to minimize the weight and maximize the torsional stiffness of the bus body under the constraints of strength and rollover safety. The MOP is solved by employing multi-objective evolutionary algorithms to obtain the Pareto optimal set. Finally, an optimal solution of the set is chosen as the final design and compared with the original design. [ABSTRACT FROM AUTHOR]

This paper aims to provide a smart design to improve the efficiency of surface permanent magnet synchronous motor. An efficient design strategy involving penalty approaches are considered for extracting all the possible parameter combinations and the solutions in the infeasible region. We compare the performance of tree heuristic optimization algorithms and six penalty methods. The heuristic optimization algorithms are: particle swarm optimization, differential search algorithm, and tree seed algorithm. The penalty methods are: three of which are static penalty approaches, two of dynamic penalty approaches, and Deb's rule. Besides, the optimized motor design is tested with finite element analysis. Two conclusions were drawn from the experiments. First, heuristic algorithms using penalty approaches had significantly better performance compared to standard and popular heuristic algorithms. This emphasizes the importance of using heuristic algorithms with penalty approaches in SPMSM design optimization. Second, the compatibility of design optimization and numerical analysis results are acceptable and highly satisfactory for surface permanent magnet synchronous motor design. According to the analytical design, a 4% improvement in efficiency was achieved with the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the numerical solutions of the coupled fractional Klein-Gordon-Schrödinger equation. The numerical schemes are constructed by combining the Crank-Nicolson/leap-frog difference methods for the temporal discretization and the Galerkin finite element methods for the spatial discretization. We give a detailed analysis of the conservation properties in the senses of discrete mass and energy. Then the numerical solutions are shown to be unconditionally bounded in L2 −norm, H α 2 − semi-norm and L ∞ − norm, respectively. Based on the well-known Brouwer fixed-point theorem and the mathematical induction, the unique solvability of the discrete solutions is proved. Moreover, the schemes are proved to be unconditionally convergent with the optimal order O τ 2 + h r + 1 , where τ is the temporal step, h is the spatial grid size, and r is the order of the selected finite element space. Furthermore, by using the proposed decoupling and iterative algorithms, several numerical examples are included to support theoretical results and show the effectiveness of the schemes. Finally, the fast Krylov subspace solver with suitable circulant preconditioner is designed to effectively solve the Toeplitz-like linear systems. In each iterative step, this method can effectively reduce the memory requirement of above each finite element scheme from O M 2 to O(M), and the computational complexity from O M 3 to O (M log M) , where M is the number of grid nodes. Numerical tests are carried out to show that this fast algorithm is more practical than the traditional backslash and LU factorization/Cholesky decomposition methods, in terms of memory requirement and computational cost. [ABSTRACT FROM AUTHOR]

An optimal pumping policy ensures the sustainability of groundwater resources when groundwater is extracted. In this paper, several simulation models (genetic algorithms, particle swarm optimization and firefly algorithm) are used to evaluate optimal pumping policy in an hypothetical aquifer. In this study, the level of groundwater in an unconfined hypothetical aquifer with a surface area of 1.5 km2 and three different hydraulic conductivities with a thickness of 100 m, as well as four pumping wells were investigated. The finite element method was employed to estimate the groundwater level of the aquifer and the mentioned algorithms were used to optimize the position of the pumping wells. The position of the pumping wells with a specific discharge is optimized to minimize groundwater drawdown in the aquifer. The results indicated that with increasing number of iterations, there was little improvement in the results of the FA, and after five iterations, the algorithm entrapped in local optima. By investigating the values of the objective function of two other algorithms (PSO and GA), the results indicated that the GA has a better performance than the PSO in optimizing groundwater pumping well locations. As a result, the GA reduces the value of objective function by 31% compared to the PSO algorithm. With this value of objective function, the maximum drawdown groundwater was about 2.5 m in the southwest of aquifer. The results indicated that the optimum location of wells is on the western side of the aquifer where the aquifer boundary has a constant head on this side. [ABSTRACT FROM AUTHOR]

Abstract  This paper presents a new mesh optimization approach aiming to improve the mesh quality on the boundary. The existing mesh untangling and smoothing algorithms (Vachal et al. in J Comput Phys 196: 627–644, 2004; Knupp in J Numer Methods Eng 48: 1165–1185, 2002), which have been proved to work well to interior mesh optimization, are enhanced by adding constrains of surface and curve shape functions that approximate the boundary geometry from the finite element mesh. The enhanced constrained optimization guarantees that the boundary nodes to be optimized always move on the approximated boundary. A dual-grid hexahedral meshing method is used to generate sample meshes for testing the proposed mesh optimization approach. As complementary treatments to the mesh optimization, appropriate mesh topology modifications, including buffering element insertion and local mesh refinement, are performed in order to eliminate concave and distorted elements on the boundary. Finally, the optimization results of some examples are given to demonstrate the effectivity of the proposed approach. [ABSTRACT FROM AUTHOR]

Abstract  The existence of holes in meshes makes it difficult for mesh operations, especially when comes to model rebuilding, rapid prototyping and finite element analysis. Existing hole-filling algorithms are capable of filling holes on small and smooth regions of a model. For large holes with complex boundaries or in curved region, they may not result in satisfactory results. This paper proposes an algorithm which first split the holes into flatter ones and then split the complex holes based the concept of edge expansion. It incrementally splits a complex hole into simple ones by respecting the 3D shape of its boundary and the neighboring meshes, and then fills each resulting simple hole with planar triangulation. The proposed algorithm works well for a variety of complex holes and can better preserve the detailed features of the original mesh. [ABSTRACT FROM AUTHOR]

Abstract  Based on two-grid discretizations, some local and parallel finite element algorithms for the Stokes problem are proposed and analyzed in this paper. These algorithms are motivated by the observation that for a solution to the Stokes problem, low frequency components can be approximated well by a relatively coarse grid and high frequency components can be computed on a fine grid by some local and parallel procedure. One technical tool for the analysis is some local a priori estimates that are also obtained in this paper for the finite element solutions on general shape-regular grids. [ABSTRACT FROM AUTHOR]

A sub-cycling integration algorithm (or named multi-time-steps integration algorithm), which has been successfully applied to FEM dynamical analysis, was firstly presented by Belytschko et al. (Comput Methods Appl Mech Eng 17/18:259–275, 1979). However, the problem of how to apply this type of algorithm to flexible multi-body dynamics (FMD) problems still lacks investigation up to now. Similar to the region-partitioning method used in FEM, this paper presents a central-difference-based sub-cycling integral method by decomposing the variables of an FMD equation into several groups and adopting different integral step sizes to each group of the variables. Based on the condensed form of an FMD equation, a group of common update formulae and a sub-step update formula, which constitute the sub-cycling together, are established in the paper. Furthermore, an implementation flowchart of the sub-cycling is presented. Stability of the sub-cycling will be analyzed and numerical examples will be performed to verify availability and precision of the sub-cycling in part II of the paper. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with a new algorithm for multichain finite state Markov decision processes which finds an average optimal policy through the decomposition of the state space into some communicating classes and a transient class. For each communicating class, a relatively optimal policy is found, which is used to find an optimal policy by applying the value iteration algorithm. Using a pattern matrix determining the behaviour pattern of the decision process, the decomposition of the state space is effectively done, so that the proposed algorithm simplifies the structured one given by the excellent Leizarowitz’s paper (Math Oper Res 28:553–586, 2003). Also, a numerical example is given to comprehend the algorithm. [ABSTRACT FROM AUTHOR]

This paper focuses on the generation of a three-dimensional (3D) mesh sizing function for geometry-adaptive finite element (FE) meshing. The mesh size at a point in the domain of a solid depends on the geometric complexity of the solid. This paper proposes a set of tools that are sufficient to measure the geometric complexity of a solid. Discrete skeletons of the input solid and its surfaces are generated, which are used as tools to measure the proximity between geometric entities and feature size. The discrete skeleton and other tools, which are used to measure the geometric complexity, generate source points that determine the size and local sizing function at certain points in the domain of the solid. An octree lattice is used to store the sizing function as it reduces the meshing time. The size at every lattice-node is calculated by interpolating the size of the source points. The algorithm has been tested on many industrial models, and it can be extended to consider other non-geometric factors that influence the mesh size, such as physics, boundary conditions, etc. [ABSTRACT FROM AUTHOR]

In order to generate efficient tool path with given precision requirements, scallop height should be kept under a given limit, while the tool path should be as short as possible to reduce machining time. Traditional methods generate CC curves one by one, which makes the final tool path far from being globally optimal. This paper presents an optimal tool path generation model for a ball-end tool which strives to globally optimize a tool path with various objectives and constraints. Two scalar functions are constructed over the part surface to represent the path intervals and the feedrate (with directions). Using the finite element method (FEM), the tool path length minimization model and the machining time minimization model are solved numerically. The proposed method is also suitable for tool path generation on mesh surfaces. Simulation results show that the generated tool path can be direction parallel or contour parallel with different boundary conditions. Compared to most of the conventional tool path generation methods, the proposed method is able to generate more effective tool paths due to the global optimization strategy. [ABSTRACT FROM AUTHOR]

In this paper, the investigation of groups with additional finiteness conditions is continued. Criteria of residual finiteness and of almost local solvability of a periodic F* -group are obtained. [ABSTRACT FROM AUTHOR]

This paper presents a method to find all intersections between curved lines such as structural line elements and finite element meshes with intentions to generate smaller, non-compatible, line cells (e.g. bar elements) between crossings. The intersection finding algorithm works for two and three-dimensional meshes constituted by linear, quadratic or higher order elements. Using the proposed algorithm, meshes can then be automatically prepared for finite element analyses with techniques for embedding elements within others or analyses that require lines within solids. The application of the method is demonstrated by a number of numerical examples illustrating its capabilities in handling complex geometries, relative speed and convenience. [ABSTRACT FROM AUTHOR]

This paper presents a new isogeometric mortar contact formulation based on an extended finite element interpolation to capture physical pressure discontinuities at the contact boundary. The so called two-half-pass algorithm is employed, which leads to an unbiased formulation and, when applied to the mortar setting, has the additional advantage that the mortar coupling term is no longer present in the contact forces. As a result, the computationally expensive segmentation at overlapping master-slave element boundaries, usually required in mortar methods (although often simplified with loss of accuracy), is not needed from the outset. For the numerical integration of general contact problems, the so-called refined boundary quadrature is employed, which is based on adaptive partitioning of contact elements along the contact boundary. The contact patch test shows that the proposed formulation passes the test without using either segmentation or refined boundary quadrature. Several numerical examples are presented to demonstrate the robustness and accuracy of the proposed formulation. [ABSTRACT FROM AUTHOR]

The analysis of adaptive finite element methods in practice immediately leads to eigenvalue clusters which requires the simultaneous marking in adaptive finite element methods. A first analysis for multiple eigenvalues of the recent work Dai et al. (arXiv Preprint 1210.1846v2, ) introduces an adaptive method whose marking strategy is based on the element-wise sum of local error estimator contributions for multiple eigenvalues. This paper proves the optimality of a practical adaptive algorithm based on a lowest-order conforming finite element method for eigenvalue clusters for the eigenvalues of the Laplace operator in terms of nonlinear approximation classes. All estimates are explicit in the initial mesh-size, the eigenvalues and the cluster width to clarify the dependence of the involved constants. [ABSTRACT FROM AUTHOR]

This paper introduces a methodology for creating geometrically consistent subsurface simulation models, and subsequently tetrahedral finite element (FE) meshes, from geometric entities generated in gOcad software. Subsurface simulation models have an intrinsic heterogeneous characteristic due to the different geomechanics properties of each geological layer. This type of modeling should represent geometry of natural objects, such as geological horizons and faults, which have faceted representations. In addition, in subsurface simulation modeling, lower-dimension degenerated parts, such as dangling surfaces, should be represented. These requirements pose complex modeling problems, which, in general, are not treated by a generic geometric modeler. Therefore, this paper describes four important modeling capabilities that are implemented in a subsurface simulation modeler: surface re-triangulation, surface intersection, automatic volume recognition, and tetrahedral mesh generation. Surface re-triangulation is used for regenerating the underlying geometric support of surfaces imported from gOcad and of surface patches resulting from intersection. The same re-triangulation algorithm is used for generating FE surface meshes. The proposed modeling methodology combines, with some adaptation, meshing algorithms previously published by the authors. Two novel techniques are presented, the first for surface intersection and the second for automatic volume recognition. The main contribution of the present work is the integration of such techniques through a methodology for the solution of mesh generation problems in subsurface simulation modeling. An example illustrates the capabilities of the proposed methodology. Shape quality of generated triangular surface and tetrahedral meshes, as well as the efficiency of the 3D mesh generator, is demonstrated by means of this example. [ABSTRACT FROM AUTHOR]

This paper considers generalized neural elements and identifies the conditions for implementation of functions of algebra of logic from these elements. We introduce the concept of a modified core of Boolean functions with respect to the system of characters of a group on which functions of algebra of logic are given. The criteria of belonging these functions to the class of generalized neurofunctions are provided. The algebraic structure of cores of Boolean neurofunctions is studied. On the basis of properties of tolerance matrices, a number of necessary conditions for implementation of Boolean functions by one generalized neural element are obtained. The obtained results allow to develop efficient methods of synthesis of integer-valued generalized neural elements with a large number of inputs that can be successfully applied in solving information compression and transmission problems, as well as discrete signal recognition problems. [ABSTRACT FROM AUTHOR]

In this paper, a piecewise constant time-stepping discontinuous Galerkin method combined with a piecewise linear finite element method is applied to solve control constrained optimal control problem governed by time fractional diffusion equation. The control variable is approximated by variational discretization approach. The discrete first-order optimality condition is derived based on the first discretize then optimize approach. We demonstrate the commutativity of discretization and optimization for the time-stepping discontinuous Galerkin discretization. Since the state variable and the adjoint state variable in general have weak singularity near t = 0and t = T, a time adaptive algorithm is developed based on step doubling technique, which can be used to guide the time mesh refinement. Numerical examples are given to illustrate the theoretical findings. [ABSTRACT FROM AUTHOR]

Compressed sensing ensures the accurate reconstruction of sparse signals from far fewer samples than required in the classical Shannon-Nyquist theorem. In this paper, a generalized hard thresholding pursuit (GHTP) algorithm is presented that can recover unknown vectors without the sparsity level information. We also analyze the convergence of the proposed algorithm. Numerical experiments are given for synthetic and real-world data to illustrate the validity and the good performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper investigates the use of inverse finite-element modeling (IFEM)-based methods for tissue parameter identification using a rolling indentation probe for surgical palpation. An IFEM-based algorithm is proposed for tissue parameter identification through uniaxial indentation. IFEM-based algorithms are also created for locating and identifying the properties of an embedded tumor through rolling indentation of the soft tissue. Two types of parameter identification for the tissue tumor are investigated (1) identifying the stiffness (μ) of a tumor at a known depth and (2) estimating the depth of the tumor (D) with known mechanical properties. The efficiency of proposed methods has been evaluated through silicone and porcine kidney experiments for both uniaxial indentation and rolling indentation. The results show that both of the proposed IFEM methods for uniaxial indentation and rolling indentation have good robustness and can rapidly converge to the correct results. The tissue properties estimated using the developed method are generic and in good agreement with results obtained from standard material tests. The estimation error of μ through uniaxial indentation is below 3 % for both silicone and kidney; the estimation error of μ for the tumor through rolling indentation is 7-9 %. The estimation error of D through rolling indentation is 1-2 mm. [ABSTRACT FROM AUTHOR]

A review of the recent development of the machining fixture configuration/layout is presented in this paper. The literature review is mainly focused on the recently developed optimal fixture configuration under the dynamic conditions of the workpiece. In this review paper, the fixture design, fixture analysis, fixture synthesis, fixture layout design, optimization of fixture layout design, various optimization algorithms, and case studies of two- and three-dimensional workpiece geometries under dynamic conditions have been emphasized specially. The further scopes of the research are finally summarized. [ABSTRACT FROM AUTHOR]

Mesh cleaning is the procedure of removing duplicate nodes, sequencing the indices of remaining nodes, and then updating the mesh connectivity for a topologically invalid Finite Element mesh. To the best of our knowledge, there has been no previously reported work specifically focused on the cleaning of large Finite Element meshes. In this paper we specifically present a generic and straightforward algorithm, MeshCleaner, for cleaning large Finite Element meshes. The presented mesh cleaning algorithm is composed of (1) the stage of compacting and reordering nodes and (2) the stage of updating mesh topology. The basic ideas for performing the above two stages efficiently both in sequential and in parallel are introduced. Furthermore, one serial and two parallel implementations of the algorithm MeshCleaner are developed on multi-core CPU and/or many-core GPU. To evaluate the performance of our algorithm, three groups of experimental tests are conducted. Experimental results indicate that the algorithm MeshCleaner is capable of cleaning large meshes very efficiently, both in sequential and in parallel. The presented mesh cleaning algorithm MeshCleaner is generic, simple, and practical. [ABSTRACT FROM AUTHOR]

BRDF continues to be used as a fundamental tool for representing material appearance in computer graphics. In this paper we present a practical adaptive method for acquisition of anisotropic BRDF, based on sparse adaptive measurement of the complete four-dimensional BRDF space by means of one-dimensional slices, which form a sparse four-dimensional structure in the BRDF space, and can be measured by continuous movements of a light source and sensor. Such a sampling approach is advantageous especially for gonioreflectometer-based measurement devices where the mechanical travel of a light source and a sensor imposes a significant time constraint. In order to evaluate our method, we have performed adaptive measurements of three materials and we simulated adaptive measurements of thirteen others. This method has one quarter the reconstruction error of that resulting from regular non-adaptive BRDF measurements using the same number of measured samples. Our method is almost twice as good as a previous adaptive method, and it requires from two to five times fewer samples to achieve the same results as alternative approaches. [ABSTRACT FROM AUTHOR]

Shot peen forming is often used to form the aerodynamic configurations of aircraft integral wing panels. The component is traditionally regarded as perfectly constrained target in peen forming process. However, weak-stiffness of the component results in concomitant macroscopic bending and stretching deformations, and releasing of peening stresses. Subsequent peening stresses are induced by shot impacts based on the current released stresses. In this paper, a intermittently peening-releasing finite element simulation model is used to study peening stress evolution in lowrigidity plate. An algorithm is proposed to calculate the increment of subsequent peening stress by connecting current stresses to the peening stresses in perfectly constrained target.With the algorithm, the peen forming deformations of freely constrained plates are calculated by equivalently simulating the peen forming process. And strip peen forming deformations are calculated and compared with experimental data. The comparison shows the peening deformation of a low-rigidity component should be treated as an incremental process and the algorithm can be used to predict the deformation with good accuracy. [ABSTRACT FROM AUTHOR]

In this paper, a novel energy-preserving numerical scheme for nonlinear Hamiltonian wave equations with Neumann boundary conditions is proposed and analyzed based on the blend of spatial discretization by finite element method (FEM) and time discretization by Average Vector Field (AVF) approach. We first use the finite element discretization in space, which leads to a system of Hamiltonian ODEs whose Hamiltonian can be thought of as the semi-discrete energy of the original continuous system. The stability of the semi-discrete finite element scheme is analyzed. We then apply the AVF approach to the Hamiltonian ODEs to yield a new and efficient fully discrete scheme, which can preserve exactly (machine precision) the semi-discrete energy. The blend of FEM and AVF approach derives a new and efficient numerical scheme for nonlinear Hamiltonian wave equations. The numerical results on a single-soliton problem and a sine-Gordon equation are presented to demonstrate the remarkable energy-preserving property of the proposed numerical scheme. [ABSTRACT FROM AUTHOR]

This paper presents a reduced-order finite element (ROFE) method with seldom degrees of freedom for the incompressible miscible displacement problem, where the proper orthogonal decomposition (POD) technique is used. The algorithm process for the ROFE method is provided. Some numerical experiments are presented to help us understand this method and verify the accuracy and efficiency of this method. Meanwhile, numerical results reflect the robustness of the ROFE method in the face of anisotropic and heterogeneous oil reservoir problems. [ABSTRACT FROM AUTHOR]

In this paper, heat transfer problems with sharp spatial gradients are analyzed using the Generalized Finite Element Method with global-local enrichment functions ( GFEM). With this approach, scale-bridging enrichment functions are generated on the fly, providing specially-tailored enrichment functions for the problem to be analyzed with no a-priori knowledge of the exact solution. In this work, a decomposition of the linear system of equations is formulated for both steady-state and transient heat transfer problems, allowing for a much more computationally efficient analysis of the problems of interest. With this algorithm, only a small portion of the global system of equations, i.e., the hierarchically added enrichments, need to be re-computed for each loading configuration or time-step. Numerical studies confirm that the condensation scheme does not impact the solution quality, while allowing for more computationally efficient simulations when large problems are considered. We also extend the GFEM to allow for the use of hexahedral elements in the global domain, while still using tetrahedral elements in the local domain, to allow for automatic localized mesh refinement without the use of constrained approximations. Simulations are run with the use of linear and quadratic hexahedral and tetrahedral elements in the global domain. Convergence studies indicate that the use of a different partition of unity (PoU) in the global (hexahedral elements) and local (tetrahedral elements) domains does not adversely impact the solution quality. [ABSTRACT FROM AUTHOR]