Search

This paper focuses on numerical algorithms to value American options under regime switching. The prices of such options satisfy a set of complementary parabolic problems on an unbounded domain. Based on our previous experience, the pricing model could be truncated into a linear complementarity problem (LCP) over a bounded domain. In addition, we transform the resulting LCP into an equivalent variational problem (VP), and discretize the VP by an Euler‐finite element method. Since the variational matrix in the discretized system is P‐matrix, a primal‐dual active set (PDAS) algorithm is proposed to evaluate the option prices efficiently. As a specialty of PDAS, the optimal exercise boundaries in all regimes are obtained without further computation cost. Finally, numerical simulations are carried out to test the performance of our proposed algorithm and compare it to existing methods. [ABSTRACT FROM AUTHOR]

In this paper, we propose a fast Alikhanov algorithm with nonuniform time steps for a two dimensional distributed‐order time–space fractional advection–dispersion equation. First, an efficient fast Alikhanov algorithm on the general nonuniform time steps for the evaluation of Caputo fractional derivative is presented to sharply reduce the computational work and storage, and are applied to the distributed‐order time fractional derivative or multi‐term time fractional derivative under the nonsmooth regularity assumptions. And a generalized discrete fractional Grönwall inequality is extended to multi‐term fractional derivative or distributed‐order fractional derivative for analyzing theoretically our algorithm. Then the stability and convergence of time semi‐discrete scheme are investigated. Furthermore, we derive the corresponding fully discrete scheme by finite element method and discuss its convergence. At last, the given numerical examples adequately confirm the correctness of theoretical analysis and compare the computing effectiveness between the fast algorithm and the direct method. [ABSTRACT FROM AUTHOR]

In practice, structural limit state function (LSF) is often combined with finite element (FE) models, and the corresponding time‐dependent reliability assessment (TRA) inevitably involves dealing with computational inefficiency. In this paper, a general moment‐based outcrossing rate (GMO) method is proposed to conduct TRA efficiently, with no limitation in the form of LSF. There are two innovations of GMO method: firstly, an explicit moment‐based outcrossing rate is developed; secondly, a separate algorithm is proposed that facilitates the separation of FE analysis from TRA cycle. The proposed method minimizes the computational cost associated with FE analysis and enables TRA cycle to be conducted more efficiently with the assistance of an explicit moment‐based outcrossing rate and explicit moment‐based outcrossing rate. Three numerical examples are investigated to examine the accuracy and efficiency of GMO method for TRA cycle. GMO method is found from the results that it can efficient and accurate to conduct TRA. Such improvements in computational efficiency are particularly valuable for complex structures where FE analysis is computationally expensive and time‐consuming. [ABSTRACT FROM AUTHOR]

Aiming at the low accuracy or inability to solve the problem when the traditional reliability optimization method deals with the practical engineering reliability analysis problem, this paper proposes a structural reliability analysis method using the improved wolf swarm algorithm (IWSA). Firstly, the reliability optimization mathematical model is established with the minimum reliability index as the objective function and the limit state equation as the equality constraint. Then the augmented multiplier method is used to transform the constrained optimization mathematical model into an unconstrained optimization mathematical model. Finally, IWSA is used to solve the problem. The proposed method is applied to a numerical example and an engineering example. The computation results of the proposed method in solving the numerical example are compared with the Monte Carlo simulation (MCS), which verifies that the proposed method in this paper has good calculation accuracy. The maximum deformation under the working condition is used as the target to establish a limit state function, and the reliability index is obtained by the proposed method combining with the finite element analysis software, which provides a certain theoretical guiding significance for the reliability analysis of engineering structures. [ABSTRACT FROM AUTHOR]

Summary This paper presents an adaptive mesh adjustment algorithm for continuum topology optimization method to describe the structural boundary using nonuniform isoparametric element. A criterion on the basis of the node movement is proposed; herein, the densities and coordinates of the nodes are defined to instruct the deformation of finite elements in subsequent optimization iterations. With such a scheme, the topology optimization can start from a regular mesh discretization then gradually yields an optimal design with clear structural boundaries. The element in the transition along the boundary is refined; on the contrary, the pure solid or void element is coarsen. The contribution of this work is to improve the resolution of the structural boundaries and decrease the percentage of transitional regions with the invariant design variable. Several 2D and 3D numerical examples indicate the effectiveness of our proposed method. Seen from the examples, the structural boundary become smoother and the intermediate densities have been reduced up to 70%. In addition, a design process based on the presented method is proposed to make the optimum solutions be fabricated conveniently and accurately by linking it with the 3D design software, ie, SolidWorks, which is also demonstrated in the numerical examples. [ABSTRACT FROM AUTHOR]

In structural engineering verifications, the plastic capacity of steel members may be utilized for cross sections of class 1 and 2. In literature, algorithms for the primary torsional capacity considering different types of numerical procedures, such as finite element methods, have mainly been addressed. However, there is a lack of explicit illustration of algorithms for cross sections considering combined loading, i.e. procedures for bending and torsional analysis. This paper therefore presents an algorithm for the plastic analysis connected to a cross‐sectional finite element approach. The algorithm considers the description of bilinear material laws, accounting for ideal‐plastic behavior as well as effects of isotropic hardening. Cross sections are discretized by isoparametric two‐dimensional nine‐node elements with curvilinear boundaries, which allow describing any geometry with high accuracy. The study proves that the plastic algorithm combined with the isoparametric elements accurately represents the behavior of cross sections. In addition, precise cross‐sectional capacities of hot‐rolled U‐sections gained by the methodology, i.e. plastic torsional moments and plastic bending moments, are presented. In future research, this methodology will be combined with finite element formulations for beams. [ABSTRACT FROM AUTHOR]

Summary: In this paper, we propose a novel unfitted finite element method for the simulation of multiple body contact. The computational mesh is generated independently of the geometry of the interacting solids, which can be arbitrarily complex. The key novelty of the approach is the combination of elements of the CutFEM technology, namely, the enrichment of the solution field via the definition of overlapping fictitious domains with a dedicated penalty‐type regularisation of discrete operators and the LaTIn hybrid‐mixed formulation of complex interface conditions. Furthermore, the novel P1‐P1 discretisation scheme that we propose for the unfitted LaTIn solver is shown to be stable, robust, and optimally convergent with mesh refinement. Finally, the paper introduces a high‐performance 3D level set/CutFEM framework for the versatile and robust solution of contact problems involving multiple bodies of complex geometries, with more than 2 bodies interacting at a single point. [ABSTRACT FROM AUTHOR]

In this paper, we give some new properties of the presented asynchronous algorithms of theta scheme combined with finite elements methods (App. Math. Comp., 217 (2011), 6443-6450) for an evolutionary implicit 2-sided obstacle problem to prove the existence and uniqueness of the discrete solution. Furthermore, an error estimate on the uniform norm is given. [ABSTRACT FROM AUTHOR]

In this paper, we present a numerical scheme which is an improved minimax method proposed by Yao‐Zhou's study along with Newton's method for finding the multiple solutions of p‐area problems. It is combined with Newton's method since the local minimax method stagnates close to a critical point of the functional whereas Newton's method converges rapidly close to a critical point. We discuss the theoretical convergence result of this proposed hybrid scheme and the convergence of the finite element based solutions as well. Further, we carry out instability analysis of the unstable solutions through their local minimax type characterizations, where the instability behavior of a solution can be analyzed before calculating the solution. This analysis also provides ways to numerically compute the Morse index of the solutions. Finally, numerical experiments are performed to demonstrate the algorithm and the theoretical results. [ABSTRACT FROM AUTHOR]

Solutions of boundary value problems in three‐dimensional domains with edges may exhibit singularities which are known to influence both the accuracy of the finite element solutions and the rate of convergence in the error estimates. This paper considers boundary value problems for the Poisson equation on typical domains Ω ⊂ ℝ3 with edge singularities and presents, on the one hand, explicit computational formulas for the flux intensity functions. On the other hand, it proposes and analyzes a nonconforming finite element method on regular meshes for the efficient treatment of the singularities. The novelty of the present method is the use of the explicit formulas for the flux intensity functions in defining a postprocessing procedure in the finite element approximation of the solution. A priori error estimates in H1(Ω) show that the present algorithm exhibits the same rate of convergence as it is known for problems with regular solutions. [ABSTRACT FROM AUTHOR]

In this paper, the forced nonlinear dynamic behavior of functionally graded material (FGM) plate under external dynamic loads is analyzed by means of a high‐order implicit algorithm. The model is developed using the third‐order shear deformation plate kinematics (TSDT). Unlike previous works, in this contribution, the formulation is written without resorting to any homogenization technique neither rule of mixture nor considering FGM as a laminated composite. To handle integrals in the case of inhomogeneous FGMs, the stress vector is split to four parts and it is written in dimensionless form. The resulting equations of motion are established using the Hamilton principle. Finite element discretization is adopted using a four‐node quadrilateral element with seven degrees of freedom per node. The resolution of the nonlinear equations is made by a high‐order implicit algorithm based on the asymptotic numerical method (ANM) techniques. Numerical comparisons of vibration natural frequencies and dynamic response of FGM plates under external loading with literature and laminate composite modeling results are presented to validate the accuracy and the performance of the proposed model. [ABSTRACT FROM AUTHOR]

Brain tissues are known for exhibiting complex nonlinear and time‐dependent properties, which require visco‐hyperelastic constitutive models for proper simulation. In this paper, a Total Lagrangian Explicit Selective Smoothed Finite Element Method (Selective S‐FEM) is formulated to analyze the dynamic behavior of incompressible brain tissues undergoing extremely large deformation. The proposed Selective S‐FEM deals with three‐dimensional problems using four‐node tetrahedron elements that can be automatically generated for geometrically complex soft tissues. It consists of the three key ingredients. (i) A visco‐hyperelastic constitutive model is developed within the framework of S‐FEM in the first time, allowing adequate modeling of the dynamic brain tissue behavior. (ii) Selective S‐FEM strategy is used for overcome the mesh distortion and the volumetric locking that often occurs in soft tissues. (iii) Total Lagrangian formulation is used in an explicit algorithm allowing rigorous simulation of extreme large deformation. (iv) A combined implementation of Selective S‐FEM with the visco‐hyperelastic constitutive model for dynamic simulations. The shear deformation is calculated by Face/Edge‐based S‐FEM, and the volume deformation is calculated by NS‐FEM. Numerical experiments show that Selective S‐FEM is a robust solver with good accuracy, and excellent ability to reduce element distortion effects in simulate time‐dependence behavior of bio‐tissues. [ABSTRACT FROM AUTHOR]

In this paper, we consider the effect of adding a coarse mesh correction to the two‐grid algorithm for the mixed Navier–Stokes/Darcy model. The method yields both L2 and H1 optimal velocity and piezometric head approximations and an L2 optimal pressure approximation. The method involves solving one small, coupled, nonlinear coarse mesh problem, two independent subproblems (linear Navier–Stokes equation and Darcy equation) on the fine mesh, and a correction problem on the coarse mesh. Theoretical analysis and numerical tests are done to indicate the significance of this method. [ABSTRACT FROM AUTHOR]

This paper studies the behaviour of the error incurred when numerically integrating the elasto-plastic mechanical relationships of a constitutive model for soils using an explicit substepping formulation with automatic error control. The correct update of all the variables involved in the numerical integration of the incremental stress-strain relationships is central to the computational performance of the integration scheme, and, although often missed in the literature, all variables (including specific volume) should be explicitly considered in the algorithmic formulation. This is demonstrated in the paper by studying, in the context of the Cam clay formulations for saturated soils, the influence that the updating of the specific volume has on the accuracy of the numerical solution. The fact that the variation of the local error with the size of the integrated strain depends on the order of local accuracy of the numerical method is also used in the paper to propose a simple and powerful strategy to verify the correctness of the implemented mathematical formulation. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents a modified graded mesh for singularly perturbed two‐parameter problems. The mesh is generated recursively using Newton's algorithm and some implicitly defined function. The problem is solved numerically using the finite element method based on higher order polynomials of degree p≥1. We prove parameter uniform convergence of optimal order in ε‐weighted energy norm. A test example is taken to compare the proposed graded mesh with others found in the literature. [ABSTRACT FROM AUTHOR]

Summary: This paper reports improvements to algorithms for the simulation of 3‐D hydraulic fracturing with the Generalized Finite Element Method (GFEM). Three optimizations are presented and analyzed. First, an improved initial guess based on solving a 3‐D elastic problem with the pressure from the previous step is shown to decrease the number of Newton iterations and increase robustness. Second, an improved methodology to find the time step that leads to fracture propagation is proposed and shown to decrease significantly the number of iterations. Third, reduced computational cost is observed by properly recycling the linear part of the coupled stiffness matrix. Two representative examples are used to analyze these improvements. Additionally, a methodology to include the leak‐off term is presented and verified against asymptotic analytical solutions. Conservation of mass is shown to be well satisfied in all examples. [ABSTRACT FROM AUTHOR]

Preconditioners based on various multilevel extensions of two-level finite element methods (FEM) lead to iterative methods which have an optimal order computational complexity with respect to the size of the system. Such methods were first presented in Axelsson and Padiy (SIAM. J. Sci. Stat. Comp. 1990; 20:1807) and Axelsson and Vassilevski (Numer. Math. 1989; 56:157), and are based on (recursive) two-level splittings of the finite element space. The key role in the derivation of optimal convergence rate estimates is played by the constant γ in the so-called Cauchy–Bunyakowski–Schwarz (CBS) inequality, associated with the angle between the two subspaces of the splitting. It turns out that only existence of uniform estimates for this constant is not enough but accurate quantitative bounds for γ have to be found as well. More precisely, the value of the upper bound for γ∈(0,1) is part of the construction of various multilevel extensions of the related two-level methods. In this paper, an algebraic two-level preconditioning algorithm for second-order elliptic boundary value problems is constructed, where the discretization is done using Crouzeix–Raviart non-conforming linear finite elements on triangles. An important point to make is that in this case the finite element spaces corresponding to two successive levels of mesh refinements are not nested. To handle this, a proper two-level basis is considered, which enables us to fit the general framework for the construction of two-level preconditioners for conforming finite elements and to generalize the method to the multilevel case. The major contribution of this paper is the derived estimates of the related constant γ in the strengthened CBS inequality. These estimates are uniform with respect to both coefficient and mesh anisotropy. To our knowledge, the results presented in the paper are the first such estimates for non-conforming FEM systems. Copyright © 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Bramble et al. (Math. Comput. (2000); 69 (230) : 667–689) discussed the Uzawa type algorithms for iteratively solving nonsymmetric stable saddle point problems. In this paper, we consider the Uzawa type algorithms for iteratively solving generalized saddle point problems. Our main concern is how to accelerate the convergence of the inexact Uzawa type algorithms. The contributions of the paper are that a new non-linear Uzawa type algorithm is presented and its convergence is analysed. Applications to Navier–Stokes equations by mixed finite element discretization with an unstable pair of approximation spaces, i.e. Q1-P0 pair of approximation spaces, are discussed and the results of the numerical experiments of applying our new algorithm are presented. Copyright © 2003 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The first part of the paper presents the implementation and performance of a new absorbing boundary condition (ABC) for truncating finite element meshes. This ABC can be applied conformally to the surface of the structure for scattering and antenna radiation calculations. Consequently, the computational domain is reduced dramatically, thus allowing the simulation of much larger structures, and results are presented for three-dimensional bodies. The latter part of the paper discusses optimization issues relating to the solver's CPU speed on parallel and vector processors. It is shown that a jagged diagonal storage scheme leads to a four-fold increase in the FLOP rate of the code, and a standard matrix profile reduction algorithm substantially reduces the inter-processor communication. [ABSTRACT FROM AUTHOR]

Summary: This paper presents a time‐discontinuous Galerkin space‐time finite element method for the seismic analysis of dam‐reservoir‐soil system. For the reservoir domain an auxiliary variable q, a first‐order time derivative of hydrodynamic pressure is introduced as the primary unknown. Similarly, velocity is taken as the primary unknown in the solid domain. In this approach, secondary unknowns (displacement and pressure) are computed in a postprocessing step by consistent time integration of the primary unknowns. This arrangement leads to a system of linearly coupled algebraic equations, which is solved with a block‐iterative algorithm. In each iteration of the algorithm, two smaller linear systems, ie, one for velocity field and another for the auxiliary field, are solved separately and coupling between these two fields is enforced through iterations. Afterwards, numerical performance of the proposed scheme is demonstrated by solving some benchmark dam‐reservoir interaction problems. It is shown that very few iterations are required for the convergence. Lastly, the method is employed to analyze the effects of dynamic interactions on the response of concrete dam to the earthquake loading. [ABSTRACT FROM AUTHOR]

Summary: We consider obstacle identification using wave propagation. In such problems, one wants to find the location, shape, and size of an unknown obstacle from given measurements. We propose an algorithm for the identification task based on a time‐reversed absorbing condition (TRAC) technique. Here, we apply the TRAC method to time‐dependent linear acoustics, although our methodology can be applied to other wave‐related problems as well, such as elastodynamics. There are two main contributions of our identification algorithm. The first contribution is the development of a robust and effective method for obstacle identification. While the original paper presented criteria for accepting or rejecting regions that enclose the obstacle, we use these criteria to develop an algorithm that automatically identifies the location of the obstacle. The second contribution is the utilization of an improved absorbing boundary condition (ABC) for the identification. We use the second‐order Engquist‐Majda ABC, and we implement it with a finite element scheme. To our knowledge, this is the first time that the second‐order Engquist‐Majda ABC is employed with the finite element method, as this boundary condition does not naturally fit in finite element schemes in its original form. Numerical experiments for the algorithms are presented. [ABSTRACT FROM AUTHOR]

This paper studies the problem of finite-time optimal formation control for second-order multiagent systems in situations where the formation time and/or the cost function need to be considered. The finite-time optimal formation control laws are proposed for the cases with or without a leader, respectively. For the case of control being constrained, the time optimal formation problem is considered and an algorithm is designed to derive a feasible solution for the problem concerned. Although the feasible solution may not be optimal, it can provide a lower bound for time for the formation problem with control constraints. Once the given formation time is lower than this bound, the control constraints cannot be ensured. Finally, some numerical examples are given to illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the full discrete scheme of mixed finite element approximation is introduced for semilinear hyperbolic equations. To solve the nonlinear problem efficiently, two two‐grid algorithms are developed and analyzed. In this approach, the nonlinear system is solved on a coarse mesh with width H, and the linear system is solved on a fine mesh with width h≪H. Error estimates and convergence results of two‐grid method are derived in detail. It is shown that if we choose H = O ( h 1 3 ) in the first algorithm and H = O ( h 1 4 ) in the second algorithm, the two‐grid algorithms can achieve the same accuracy of the mixed finite element solutions. Finally, the numerical examples also show that the two‐grid method is much more efficient than solving the nonlinear mixed finite element system directly. [ABSTRACT FROM AUTHOR]

Saliency and nonlinear magnetization characteristics of switched reluctance motor (SRM) are causes for its poor performance regarding torque ripples. This paper presents an innovative methodology based on a water cycle algorithm (WCA) for SRM speed control with minimum torque ripples and maximum torque per ampere. WCA enhances the dynamic and steady‐state performance of this motor by optimizing a multiobjective function consisting of three parts. The first part is the integral time absolute error (ITAE) of motor speed with respect to a desired reference speed, the second part is an index for a motor torque smoothness factor (TSF), and the third part is the torque per ampere ratio (TAR). The desired output of WCA is the appropriate gains of the PI speed controller and optimum turn on and off angles of the H‐bridge driving circuit. The results obtained from WCA are used to construct an adaptive controller‐based artificial neural network (ANN) to automatically tune the gains of the PI speed controller and the turn on and off angles. The ANN controller ensures superior steady‐state and dynamic motoring operation over a wide range of speed commands and different loads. The results of WCA are verified by other well‐known meta‐heuristic optimized techniques, such as the Genetic algorithm (GA). The suggested method exhibits an excellent speed transient response in addition to minimum torque ripples and maximum TAR. © 2018 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc. [ABSTRACT FROM AUTHOR]

Summary: In this paper, we present a novel scheme to generate trimmed quadrilateral shell meshes using a paving and cutting algorithm. Paving with well‐shaped quadrilateral shell elements is initiated from a seed element placed in the interior of a geometric surface and proceeds around the boundary of the paved mesh in all directions. The paved all‐quadrilateral mesh covering the entire domain is cut by the boundaries of a geometric surface. Pentagonal shell elements are created by cutting the corners of quadrilateral shell elements at the domain boundaries. Pentagonal shape functions are constructed using Wachspress coordinates, and assumed natural strains in the form of the mixed interpolation of tensorial components approach are employed to avoid the transverse shear locking of pentagonal shell elements. Several numerical examples are investigated to show the effectiveness of the present method. [ABSTRACT FROM AUTHOR]

Summary: In this paper, conserving time‐stepping algorithms for frictionless and full stick friction dynamic contact problems are presented. Time integration algorithms for frictionless and full stick friction dynamic contact problems have been designed to preserve the conservation of key discrete properties satisfied at the continuum level. Energy and energy‐momentum–preserving algorithms for frictionless and full stick friction dynamic contact problems, respectively, have been designed and implemented within the framework of the direct elimination method, avoiding the drawbacks linked to the use of penalty‐based or Lagrange multipliers methods. An assessment of the performance of the resulting formulation is shown in a number of selected and representative numerical examples, under full stick friction and slip frictionless contact conditions. Conservation of key discrete properties exhibited by the time‐stepping algorithm is shown. [ABSTRACT FROM AUTHOR]

This paper presents a Lagrangian formulation of elastoviscoplasticity, on the basis of the particle finite element method, for progressive failure analysis of sensitive clays. The sensitive clay is represented by an elastoviscoplastic model that is a mixture of the Bingham model, for describing rheological behaviour, and the Tresca model with strain softening for capturing the progressive failure behaviour. The finite element formulation for the incremental elastoviscoplastic analysis is reformulated, through the application of the Hellinger-Reissner variational theorem, as an equivalent optimisation program that can be solved efficiently using modern algorithms such as the interior-point method. The recast formulation is then incorporated into the framework of the particle finite element method for investigating progressive failure problems related to sensitive clays, such as the collapse of a sensitive clay column and the retrogressive failure of a slope in sensitive clays, where extremely large deformation occurs. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Higher order finite element discretizations, although providing higher accuracy, are considered to be computationally expensive and of limited use for large-scale problems. In this paper, we have developed an efficient iterative solver for solving large-scale quadratic finite element problems. The proposed approach shares some common features with geometric multigrid methods but does not need structured grids to create the coarse problem. This leads to a robust method applicable to finite element problems discretized by unstructured meshes such as those from adaptive remeshing strategies. The method is based on specific properties of hierarchical quadratic bases. It can be combined with an algebraic multigrid (AMG) preconditioner or with other algebraic multilevel block factorizations. The algorithm can be accelerated by flexible Krylov subspace methods. We present some numerical results on the convection-diffusion and linear elasticity problems to illustrate the efficiency and the robustness of the presented algorithm. In these experiments, the performance of the proposed method is compared with that of an AMG preconditioner and other iterative solvers. Our approach requires less computing time and less memory storage. Copyright © 2010 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we will discuss the geometric-based algebraic multigrid (AMG) method for two-dimensional linear elasticity problems discretized using quadratic and cubic elements. First, a two-level method is proposed by analyzing the relationship between the linear finite element space and higher-order finite element space. And then a geometric-based AMG method is obtained with the existing solver used as a solver on the first coarse level. The resulting AMG method is applied to some typical elasticity problems including the plane strain problem with jumps in Young's modulus. The results of various numerical experiments show that the proposed AMG method is much more robust and efficient than a classical AMG solver that is applied directly to the high-order systems alone. Moreover, we present the corresponding theoretical analysis for the convergence of the proposed AMG algorithms. These theoretical results are also confirmed by some numerical tests. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, a parallel algorithm based on MPI (Message Passing Interface) parallel computing library for the finite element method is presented to analyze three-dimensional electromagnetic devices. The algebraic domain decomposition method is used in the algorithm. The original problem is decomposed into several subproblems according to its features. Each of them is allocated to one process in one computation node and solved independently with a direct method. The data are exchanged by communication between adjacent subdomains with overlapped data based on the MPI network. The example of its application is given. Numerical shows that the proposed algorithm can get excellent performance vs. price ratio and can save much memory and CPU time than sequential computing. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 686–692, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22247 [ABSTRACT FROM AUTHOR]

In this paper, the objective is to derive with guaranteed accuracy all solutions of a finite-dimensional nonlinear equation within a certain range. In order to derive all solutions, it is important to extract efficiently the regions in which no solution exists. A new method is proposed in which nonexistence of solutions in a given region is judged with guaranteed accuracy. By solving specific numerical examples, the effectiveness of the proposed method is verified. © 2003 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 86(5): 45–53, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.10023 [ABSTRACT FROM AUTHOR]

In optimal design of a permanent magnet (PM) motor, many design variables are required to consider some device properties. These variables are, for example, the shape of core and magnet, the tooth length, the number of turns, and the winding radius. Moreover, many restrictions must be considered in practical PM motor design. These restrictions are, for example, the slot space factor and the cogging torque. However, the optimization problem, which has many design variables by the finite element method (FEM), has not been reported. In this paper, the efficiency of PM motor under the considerations given above is optimized by using FEM and optimization algorithm. In this problem, an objective function has many local minima and it is difficult to calculate its gradient. For these reasons, the genetic algorithm (GA) and simulated annealing method (SA), which are stochastic methods, are used for optimization method, because of the possibility of global range search and because gradient calculation is not required. Adding to both optimization methods, in this paper, SA combined with GA is used for one of the optimization methods. It is found that the solutions optimized by these methods are reasonable from an engineering point of view. © 2001 Scripta Technica, Electr Eng Jpn, 138(3): 72–79, 2002 [ABSTRACT FROM AUTHOR]

In this paper an efficient algorithm is presented for the development of compact and passive macro-models of electromagnetic devices through the systematic reduction of the order of discrete models for these devices obtained through the use of finite elements. The proposed methodology is founded on a new finite element formulation that casts Maxwell's curl equations in a state-space form. Such state-space representations are very compatible with a class of robust model order reduction techniques based on Krylov subspaces. However, the advantage of this compatibility appears to be hindered by the fact that the state matrix of the discretized Maxwellian system is of dimension almost twice that obtained from the finite element approximation of the electromagnetic vector wave equation. It is shown in this paper that the apparent penalty in both memory and computation efficiency can be avoided by a proper selection of the finite element expansion functions used for the discretization of the electromagnetic fields. More specifically, it is shown that the proper selection of expansion functions renders the state-space form of the Maxwellian system equivalent to the discrete problem obtained from the approximation of the vector wave equation using tangentially continuous vector finite elements. This equivalence is then used to effect Krylov-based model order reduction directly from the finite element approximation of the vector wave equation. In particular, a passive model order reduction algorithm is used for this purpose. The proposed reduced order macro-modelling algorithm is demonstrated through its application to a variety of microwave passive components. Copyright © 2002 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents an efficient solution for solving the generalized eigenvalue equation arising in the finite-element (FE) formulation of propagation characterization of planar transmission-line structures. A two-dimensional (2-D) finite-element method (FEM) is used for analyzing the uniform planar transmission lines. The Arnoldi algorithm is used in conjunction with the multifrontal decomposition of the system matrix for solving the eigensystem. Convergence is typically obtained within a few iterations of the Arnoldi process, and the formulation has proven to be robust, even when dealing with a significantly large number of unknowns. Numerical results are presented for the case of a uniform microstrip line, which clearly show the computational savings resulting from the use of the present approach. © 2001 John Wiley & Sons, Inc. Microwave Opt Technol Lett 31: 194–197, 2001. [ABSTRACT FROM AUTHOR]

In this paper, a new discrete elements generation method based on geometry is proposed to fill geometric domains with particles (disks or spheres). By generating particles each one with a random radius or with a radius calculated from the iteration to ensure no overlaps exist between particles and identifying unstable particles and changing them to stable ones, a dense and stable packing can be created. A partitioning particle radius interval method and a particle stability inspection and improvement method are introduced to guarantee the algorithm's success and the stability of the particles. Some packings were created to evaluate the performances of the new method. The results showed that the algorithm was very efficient and was able to create isotropic packings of low porosities and large coordinate numbers. The partitioning particle radius interval method improved the generation efficiency significantly and increased the packing densities. Through the comparisons with several existing methods proposed recently, the method proposed in this work is found to be more efficient and can fill geometric domains with the lowest porosities. In addition, the stability of the particles is guaranteed and no complex triangular or tetrahedral mesh is required in particle generation, thereby making the new method simpler. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A key advantage of working with structured grids (e.g., images) is the ability to directly tap into the powerful machinery of linear algebra. This is not much so for unstructured grids where intermediate bookkeeping data structures stand in the way. On modern high performance computing hardware, the conventional wisdom behind these intermediate structures is further challenged by costly memory access, and more importantly by prohibitive memory resources on environments such as graphics hardware. In this paper, we bypass this problem by introducing a sparse matrix representation for unstructured grids which not only reduces the memory storage requirements but also cuts down on the bulk of data movement from global storage to the compute units. In order to take full advantage of the proposed representation, we augment ordinary matrix multiplication by means of action maps, local maps which encode the desired interaction between grid vertices. In this way, geometric computations and topological modifications translate into concise linear algebra operations. In our algorithmic formulation, we capitalize on the nature of sparse matrix-vector multiplication which allows avoiding explicit transpose computation and storage. Furthermore, we develop an efficient vectorization to the demanding assembly process of standard graph and finite element matrices. [ABSTRACT FROM AUTHOR]

The paper proposes a stress-driven integration strategy for Perzyna-type viscoplastic constitutive models, which leads also to a convenient algorithm for viscoplastic relaxation schemes. A generalized trapezoidal rule for the strain increment, combined with a linearized form of the yield function and flow rules, leads to a plasticity-like compliance operator that can be explicitly inverted to give an algorithmic tangent stiffness tensor also denoted as the m-AGC tangent operator. This operator is combined with the stress-prescribed integration scheme, to obtain a natural error indicator that can be used as a convergence criterion of the intra-step iterations (in physical viscoplasticity), or to a variable time-step size in viscoplastic relaxation schemes based on a single linear calculation per time step. The proposed schemes have been implemented for an existing zero-thickness interface constitutive model. Some numerical application examples are presented to illustrate the advantages of the new schemes proposed. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we study an a posteriori error indicator introduced in E. Dari, R.G. Durán, and C. Padra, Appl. Numer. Math., 2012, for the approximation of the Laplace eigenvalue problem with Crouzeix-Raviart nonconforming finite elements. In particular, we show that the estimator is robust also in presence of eigenvalues of multiplicity greater than one. Some numerical examples confirm the theory and illustrate the convergence of an adaptive algorithm when dealing with multiple eigenvalues. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The constant γ in the strengthened Cauchy-Buniakowski-Schwarc (CBS) inequality plays a key role in the convergence analysis of the multilevel iterative methods. We consider in this paper the approximation of the two-dimensional elasticity problem by bilinear rectangle finite elements. Two semi-coarsening refinement procedures are studied. We prove for both cases new estimates of the constant γ, uniformly on the Poisson ratio. As a result of the presented analysis we obtain an optimal order algebraic multiLevel iteration (AMLI) method for the case of balanced semi-coarsening mesh refinement. The total computational complexity of the algorithm is proportional to the size of the discrete problem with a proportionality constant independent of the Poisson ratio, that is, the algorithm is of optimal order for almost incompressible elasticity problems. Copyright © 1999 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper proposes an algorithm with a guaranteed accuracy for the finite-dimensional nonlinear equation. First, an algorithm is shown which can determine the interval containing the true solution, based on the given approximate solution. This method is based on the interval analysis and considers the representation error of the equation. Then the interval iteration method is shown which can arbitrarily reduce the interval. The rational number arithmetic is used and the rounding of the rational number us utilized effectively. Finally, an experimental implementation of the algorithm on a computer is presented, together with some numerical examples. [ABSTRACT FROM AUTHOR]

The paper complements and extends the previous works on partitioned explicit wave propagation analysis methods, which were presented for discontinuous wave propagation problems in solids. An efficient implementation of the partitioned explicit wave propagation analysis methods is introduced. The present implementation achieves about 25% overall computational effort compared with the previous implementation with the same accuracy. The present algorithm tracks, with different integration time step sizes in accordance with their different wave speeds, the propagation fronts of longitudinal and shear waves. This is accomplished by integrating separately the element-by-element partitioned longitud inal and shear equations of motion. The state vectors (displacements, velocity and accelerations) of the longitudinal and shear components are reconciled at the end of each time step. The reconciliation procedure does not require any system parameters such as material properties, density, unlike conventional artificial viscosity methods. Numerical examples are presented as applied to linear and non-linear wave propagation problems, which demonstrate high-fidelity wavefront tracking ability of the present method, and compared with existing conventional wave propagation analysis methods. [ABSTRACT FROM AUTHOR]

In this paper, we propose an algorithm that optimizes the ventricular fiber structure of the human heart. A number of histological studies and diffusion tensor magnetic resonance imaging analyses have revealed that the myocardial fiber forms a right-handed helix at the endocardium. However, the fiber formation changes its orientation as a function of transmural depth, becoming a left-handed helix at the epicardium. To determine how nature can construct such a structure, which obtains surprising pumping performance, we introduce macroscopic modeling of the branching structure of cardiac myocytes in our finite element ventricular model and utilize this in an optimization process. We put a set of multidirectional fibers around a central fiber orientation at each point of the ventricle walls and simulate heartbeats by generating contraction forces along each of these directions. We examine two optimization processes using the workloads or impulses measured in these directions to update the central fiber orientation. Both processes improve the pumping performance towards an optimal value within several tens of heartbeats, starting from an almost-flat fiber orientation. However, compared with the workload optimization, the impulse optimization produces better agreement with experimental studies on transmural changes of fiber helix angle, streamline patterns of characteristic helical structures, and temporal changes in strain. Furthermore, the impulse optimization is robust under geometrical changes of the heart and tends to homogenize various mechanical factors such as the stretch and stretch rate along the fiber orientation, the contraction force, and energy consumption. [ABSTRACT FROM AUTHOR]

In this paper, details of an implementation of a numerical code for computing the Kohn-Sham equations are presented and discussed. A fully self-consistent method of solving the quantum many-body problem within the context of density functional theory using a real-space method based on finite element discretisation of realspace is considered. Various numerical issues are explored such as (i) initial mesh motion aimed at co-aligning ions and vertices; (ii) a priori and a posteriori optimization of the mesh based on Kelly's error estimate; (iii) the influence of the quadrature rule and variation of the polynomial degree of interpolation in the finite element discretisation on the resulting total energy. Additionally, (iv) explicit, implicit and Gaussian approaches to treat the ionic potential are compared. A quadrupole expansion is employed to provide boundary conditions for the Poisson problem. To exemplify the soundness of our method, accurate computations are performed for hydrogen, helium, lithium, carbon, oxygen, neon, the hydrogen molecule ion and the carbon-monoxide molecule. Our methods, algorithms and implementation are shown to be stable with respect to convergence of the total energy in a parallel computational environment. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The advent of pixelated detectors for time-of-flight neutron transmission experiments has raised significant interest in terms of the potential for tomographic reconstructions of triaxial strain distributions. A recent publication by Lionheart and Withers [WRB Lionheart and PJ Withers, 'Diffraction tomography of strain', Inverse Problems, v31:045005, 2015] has demonstrated that reconstruction is not possible in the general sense; however, various special cases may exist. In this paper, we outline a process by which it is possible to tomographically reconstruct average triaxial elastic strains within individual particles in a granular assembly from a series of Bragg edge strain measurements. This algorithm is tested on simulated data in two and three dimensions and is shown to be capable of rejecting Gaussian measurement noise. Sources of systematic error that may present problems in an experimental implementation are briefly discussed. [ABSTRACT FROM AUTHOR]

In digital image correlation (DIC), a global approach is more and more used aside from the traditional subset method. The biggest advantages of the global approach are the continuity of the displacement field and the clear link to finite element analysis. In this paper, the traditional subset method is compared to several implementations of the global method, to investigate the importance of continuity in DIC. As first, the most known Q4-DIC is implemented, where linear elements describe the deformation. The second implementation is the so-called p-DIC where the element mesh used in the correlation can be updated to higher-order elements to describe more complex deformations. The third implementation is a newly proposed C1-continuous global algorithm. This algorithm is similar to the other global approaches but uses a triangular finite element mesh where the triangular elements within the mesh have a generic pth-order description. Accordingly, elements can vary both in size and element order to describe more complex deformations while preserving C1-continuity. The four implementations are made in the same platform, leading to a more robust comparison. In the comparison, both numerical and experimental tests are conducted, and the relation between resolution and special resolution is investigated for all approaches. It is concluded that continuity itself does not have a major influence on the methods performance. The choice of algorithm will be based on the desired specifications of the measurement. [ABSTRACT FROM AUTHOR]

When applying the combined finite-discrete element method for analysis of dynamic problems, contact is often encountered between the finite elements and discrete elements, and thus an effective contact treatment is essential. In this paper, an accurate and robust contact detection algorithm is proposed to resolve contact problems between spherical particles, which represent rigid discrete elements, and convex quadrilateral mesh facets, which represent finite element boundaries of structural components. Different contact scenarios between particles and mesh facets, or edges, or vertices have been taken into account. For each potential contact pair, the contact search is performed in an hierarchical way starting from mesh facets, possibly going to edges and even further to vertices. The invalid contact pairs can be removed by means of two reasonable priorities defined in terms of geometric primitives and facet identifications. This hierarchical contact searching scheme is effective, and its implementation is straightforward. Numerical examples demonstrated the accuracy and robustness of the proposed algorithm. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Traditional principles of mechanics are primarily conceived for constant mass systems, which are only valid if mass is gained or lost at null velocity with respect to an inertial reference frame for variable mass systems, thus the numerical algorithms for time-varying structures based on these principles are only suitable for this special case. In this paper, Hamilton's law of variable mass system is derived based on Meshchersky's fundamental equation, and two classes of novel time finite element formulations for linear systems with arbitrary continuous time-varying parameters are developed based on the previous law. The formulations are verified extensively through numerical examples in which the convergence and effectiveness of algorithms are evaluated. Numerical examples demonstrate that compared with the algorithms for time-varying structures that developed based on traditional principles of mechanics, the proposed algorithms provide extended capabilities in both time-varying mass problems that mass is gained or lost at any velocity (such as rocket problem) and moving-mass problems (such as vehicle-bridge interaction problem) besides the time-varying stiffness and damping problems, the proposed algorithms have a wider range of application. In particular, Hamilton's law of variable mass system provides a solid theoretical foundation for further research on the algorithm design for time-varying structures. [ABSTRACT FROM AUTHOR]

SUMMARY Finite element method (FEM) with fixed representative volume element (RVE) encounters some difficulties in simulating the periodical postbuckling behaviors of infinite long beam or infinite large film on soft substrate under compression, because the wavelength and pattern of buckling are not known before simulation and will change with the increase of compression strain. In this paper, an adaptive periodical RVE is constructed in a mapping space to avoid remeshing in the real space, and the mapping coefficients, that is, the dimension and shape of RVE in real space, are treated as variables in average energy density minimization to obtain correct postbuckling configurations. The validness and efficiency of the proposed algorithm have been demonstrated by our numerical examples. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY Continuum theories can be equipped with additional inertia terms to make them capable of capturing wave dispersion effects observed in micro-structured materials. Such terms, often called micro-inertia, are convenient and straightforward extensions of classical continuum theories. Furthermore, the critical time step is usually increased via the inclusion of micro-inertia. However, the drawback exists that standard finite element discretisation leads to mass matrices that cannot be lumped without losing the micro-inertia terms. In this paper, we will develop a solution algorithm based on Neumann expansions by which this disadvantage is avoided altogether. The micro-inertia terms are translated into modifications of the residual force vector, so that the system matrix is the usual lumped mass matrix and all advantages of explicit time integration are maintained. The numerical stability of the algorithm and its effect on the dispersive properties of the model are studied in detail. Numerical examples are used to illustrate the various aspects of the algorithm. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY This paper presents an advanced failure surface propagation concept based on the marching cubes algorithm initially proposed in the field of computer graphics and applies it to the embedded finite element method. When modeling three-dimensional (3D) solids at failure, the propagation of the failure surface representing a crack or shear band should not exhibit a strong sensitivity to the details of the finite element discretization. This results in the need for a propagation of the discrete failure zone through the individual finite elements, which is possible for finite elements with embedded strong discontinuities. Whereas for two-dimensional calculations the failure zone propagation location is easily predicted by the maximal principal stress direction, more advanced strategies are needed to achieve a smooth failure surface in 3D simulations. An example for such method is the global tracking algorithm, which predicts the crack path by a scalar level set function computed on the basis of the solution of a simplified heat conduction like problem. Its prediction may though lead to various scenarios on how the failure surface may propagate through the individual finite elements. In particular, for a hexahedral eight-node finite element, 256 such cases exist. To capture all those possibilities, the marching cubes algorithm is combined with the global tracking algorithm and the finite elements with embedded strong discontinuities in this work. In addition, because many of the possible cases result in non-planar failure surfaces within a single finite element and because the local quantities used to describe the kinematics of the embedded strong discontinuities are physically meaningful in a strict sense only for planar failure surfaces, a remedy for such scenarios is proposed. Various 3D failure propagation simulations outline the performance of the proposed concept. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]