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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]

With the aid of the finite element method, a lot of mechanical and thermal phenomena in forming processes can be analysed successfully. However, for industrial purposes the necessary computational time for complex processes is often not acceptable. Many researches have attempted to reduce the computational time which is needed to find a solution. In this paper, new algorithms are described which make use of the existing similarity in some forming processes, especially incremental forming process. Incremental forming processes are characterised by very small deformation zones and approximate self similarity. The described algorithms are based on the transformation and interpolation of already computed solutions. The results from transformation and interpolation are verified by means of some physical constraints. If the results pass the latter check, they will be archived as solution. Consequently, at this time step, no iterative computation will be accomplished by the mechanical solver. Then the calculations by the thermo solver are accomplished conventionally in dependence on the archived mechanical results. With the help of these algorithms, the number of iterations will obviously be reduced and the results will be reasonably acceptable. In this paper, all details are described and two forming processes as validation occur to depict the advantages of this method. [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, 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]

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]

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]

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]

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]

Summary: Analyses of three‐dimensional slope failures can be elaborate because of the complexity owed to the geometry of the failure mechanism that needs to conform to an admissible kinematics of the slope collapse. This admissibility is imposed by the soil limit state condition, the normality plastic flow rule, and the boundary conditions. The kinematic approach of limit analysis is employed, and a rotational 3D slope failure is revisited. The study leads to the conclusion that some geometric constraints used in previous studies limit the range of admissible mechanisms resulting in overestimating stability factors. A set of results is presented that was obtained using an algorithm that allowed eliminating limitations present in previous studies. The largest improvements in the solutions were found for undrained failures of narrow slopes. For a 30° slope limited in width by the width‐to‐height ratio of 0.6, the stability factor calculated in previous studies overestimated the current calculations by nearly 39%. This overestimation is smaller for drained failures, and it drops significantly with an increase in the width of the failure mechanism. [ABSTRACT FROM AUTHOR]

When solving electromagnetic problems by finite element method, the resulting linear systems are ill-conditioned when the PML absorbing layers are adopted. Traditional Krylov iterative algorithms usually converge slowly or may even stagnate. In this paper, the combination of the inner–outer Flexible Generalized Minimum Residual Method (GMRES) and the symmetric successive overrelaxation (SSOR) preconditioning scheme is used to accelerate the iteration for solving a large sparse system of linear equations resulting from the analysis of EM problems by use of edge-based finite element method (FEM). The numerical results show that tens of times convergence improvement can be achieved compared with the conventional GMRES solver. © 2006 Wiley Periodicals, Inc. Microwave Opt Technol Lett 48: 1708–1712, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.21758 [ABSTRACT FROM AUTHOR]

This paper describes a simple and effective adaptive technique for mesh refinement in finite-element method models. The proposed refinement method is based on a modified octree refinement approach, and can be applied to an arbitrary hexahedral unstructured mesh. The implementation, Hex-R, is used in conjunction with the finite-element viewer GPPView, and applied to a complex model. The proposed method is demonstrated to be capable of easily and reliably generating an adaptive mesh. Copyright © 2002 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper proposes an algorithm based on the equivalence principle to calculate, straightforwardly in the time domain, the transient far field response of a two-dimensional structure. The algorithm implementation involves the numerical evaluation of a time integral along the near- to far-field conversion contour of the equivalent currents at the Huygens surface, obtained with the finite-difference time-domain (FDTD) method. © 2000 John Wiley & Sons, Inc. Microwave Opt Technol Lett 27: 427–432, 2000. [ABSTRACT FROM AUTHOR]

This paper formulates, analyses and discusses 2D and 3D static and dynamic model problems in the orthopaedic practice. Finite element approximations, algorithms and iterative methods for constrained optimization are discussed. Since the conjugate gradient method is one of the most effective methods for both unconstrained and constrained optimization, it can be applied without or with preconditioning for solving the basic step of the discretized problem. A comparison of several preconditioned conjugate gradient methods is discussed. The problems discussed are applied to analyses of real patients. Finally, the the numerical results are discussed. Copyright © 1999 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Summary: We present an original mathematical formulation for optimizing structural topology while simultaneously identifying an optimal set of design materials that are selected from a larger set of candidate materials. This design task is analogous to that, which is commonly encountered in additive manufacturing applications in which the 3D printer can print parts containing up to 3 distinct materials that can be selected from a larger suite of usable materials. The material distribution is parameterized via the shape functions with penalization formulation in which a set of activation functions, which are derived from a partition of the unit hypercube, is used to determine the effective local elasticity modulus within a single finite element. Additionally, we introduce an inverse p‐norm function, which is used to ensure that the optimized material properties converge to a set of discrete values corresponding to the available candidate materials. The algorithm has been implemented on a set of 2D benchmark problems. Numerical results show that the formulation combining the inverse p‐norm function with the activation functions successfully produces optimized multimaterial solutions containing no more than the prescribed number of distinct materials. [ABSTRACT FROM AUTHOR]

In a recent paper we presented a data structure to be used with multigrid techniques on non- homogeneously refined FEM meshes. This paper focuses on the adaptive refinement techniques used there. The error estimate is obtained from standard Taylor series. For each element we compute its efficiency in terms of the size, the norm of the second derivatives of the unknown and the parameter p, where Lp is the chosen norm. The way the norm influences the optimal mesh is studied. The number of elements to be refined at each step is such to produce a fast convergence to the optimal mesh, followed by successive homogeneous refinements. We hope that the analysis of these two subjects could be of value for people working with other (perhaps very dissimilar) adaptive refinement techniques (error estimate and data structure, for instance). [ABSTRACT FROM AUTHOR]

The finite element method (FEM) with local absorbing boundary conditions has been recently applied to compute electromagnetic scattering from large 3-D geometries. In this paper, we present details pertaining to code implementation and optimization. Various types of sparse matrix storage schemes are discussed and their performance is examined in terms of vectorization and net storage requirements. The system of linear equations is solved using a preconditioned biconjugate gradient (BCG) algorithm and a fairly detailed study of existing point and block preconditioners (diagonal and incomplete LU) is carried out. A modified ILU preconditioning scheme is also introduced which works better than the traditional version for our matrix systems. The parallelization of the iterative sparse solver and the matrix generation/assembly as implemented on the KSR1 multiprocessor is described and the interprocessor communication patterns are analysed in detail. Near-linear speed-up is obtained for both the iterative solver and the matrix generation/assembly phases. Results are presented for a problem having 224,476 unknowns and validated by comparison with measured data. [ABSTRACT FROM AUTHOR]

This paper presents a general method to associate the operator splitting for the Peaceman-Rachford procedure with a decomposition of the domain in problems arising from finite element discretization of partial differential equations. The algorithm is provably convergent without any symmetry requirement. Moreover, this method possesses the significant advantage of making the linear systems of the Peaceman-Rachford iteration block diagonal and therefore perfectly appropriate for parallel processing. Not only is sparsity not affected but a reduction of the bandwidth occurs. In fact, for appropriate choices of nonconforming finite element spaces, this method makes directly possible elementwise processing. This option remains available in general for higher-dimensional problems by applying the splitting algorithm recursively. Practical implementation requires nothing more than the standard finite element assembly procedure and some bookkeeping to relate a few different orderings of the nodes. In addition to all these attractive features, the method is rapidly convergent and remains highly competitive even when used on a serial machine. [ABSTRACT FROM AUTHOR]

We consider a paper by Stelzer and Welzel (1987) about a new contour lines algorithm. Because of its exactness and its convincing straightforwardness we have tested it and incorporated it into our post- processing software. This paper describes some aspects we experienced during the numerical experimentation which may be helpful for people considering using the method. Although the cited paper deals with both linearly interpolated isoparametric elements and quadratic ones we have restricted ourselves to the linear type to keep the relationships as simple as possible. [ABSTRACT FROM AUTHOR]

We present physically based algorithms for interactive deformable shape and motion modelling. We coarsely sample the objects with simulation nodes, and apply a meshless finite element method to obtain realistic deformations at interactive frame rates. This shape deformation algorithm is then used to specify keyframe poses and a smooth interpolating motion is obtained by solving for an energy-minimizing trajectory. We show how to handle collisions between different deformable objects as well as with static or moving scene objects. Secondary motion is added as a post-process by running a meshless elastic solid simulation. We enforce precomputed trajectories using control forces computed using shape matching. Key to the efficiency of our method is a sparse deformation representation and an adaptive optimization algorithm that automatically introduces new degrees of freedom in problematic regions. An accurate temporal interpolation scheme that exactly recovers rigid motions keeps the number of unknowns low and achieves realistic deformations with very few keyframes. We also show how the algorithm allows combining purely physical simulation with keyframe-based scripted animation. The presented results illustrate that our framework can handle complex shapes at interactive rates, making it a valuable tool for animators to realistically model deformable 3D shapes and their motion. [ABSTRACT FROM AUTHOR]

An algorithm for analysis of periodic oscillations of forced elastic systems with geometric nonlinearity is presented in this paper. Modal decomposition of the solution, computation of periodic oscillations for every eigenmode and estimation of geometric nonlinearities using the method of initial deformations enable to construct a computational technique that can be very effective in computation of steady-state periodic motions of slightly damped structures under periodic forcing. It is shown that the developed algorithm can be successfully exploited for the calculation of structural response of a micromechanical cantilever. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

An algorithm combining the numerical execution in time of implicit and explicit methods of solution is presented in this paper. The algorithm swaps between both methods as required for the analysis. The whole mesh is solved for an unique method at once, i.e. there are no partitions of the mesh for separate implicit or explicit treatment of the solution. The combination is in-time, in such a manner that if the implicit method starts diverging the explicit one is initiated by appropriate conditions of transition. The formulation is presented first and its implementation is validated by the analysis of a key numerical example. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper describes a finite element solution algorithm for the numerical solution of large size three-dimensional flow problems on a personal computer. To demonstrate the algorithm, the Stokes equations in velocity–vorticity form are solved for a lid-driven cubical cavity problem. The Galerkin's weighted residual form of the governing equations is evaluated for all the elements of the computational domain and kept as element-matrices and element-vectors. This results in a set of simultaneous equations corresponding to the global nodes of each element. Those elements that contain the boundary nodes are modified to incorporate the Dirichlet boundary conditions. A conjugate gradient iterative scheme is employed to solve the simultaneous equations in element form to get the solution at the global nodes. The matrix–vector products used in the conjugate gradient iterative solver are performed in element level, assembling only the element-level vectors to form the global vectors. Since the element-level computation has eluded the formation of global matrices, the numerical solution of three-dimensional Stokes equations using a mesh of size as high as 513 could be achieved on a personal computer. The algorithm is validated by comparing the results for a three-dimensional transient diffusion problem and Stokes flow in a lid-driven cubical cavity. Copyright © 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents a new scheme of time stepping for solving non-linear dynamic problems. By expanding variables in a discretized time interval, FEM-based recurrent formulae are derived leading to a self-adaptive algorithm for different sizes of time steps. There will be no requirement of iteration for the non-linear solutions. Numerical validation shows satisfactory results. Copyright © 2001 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we attempt to give analysis of the covolume method for solving general self-adjoint elliptic problems. We first present some useful superconvergence results for the deviation between the solution of the covolume method and the solution of the induced finite element method, in the energy norm and maximum norm, respectively. With these results, we then reproduce the maximum norm estimates obtained by Chou and Li for the covolume method easily. Furthermore, based on the covolume method, we propose a high-accuracy algorithm for solving general self-adjoint elliptic problems. Compared with the original covolume method, the computation work of the new algorithm is increased slightly, but the approximate error is improved remarkably. Copyright © 2001 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

An algorithm for the generation of general shape functions is presented here. The algorithm is coded using the Macsyma program which has symbolic/algebraic manipulation capabilities. The current technique is based on the direct approach of calculating shape functions which is seldom used due to manual algebraic tediousness. Listing of the code is included in this paper as well as examples showing how it correctly generates some of the common shape functions with ease. Two examples of new shape functions were created for C2 elements. Hence, the more useful purpose of this algorithm is that it can be used to investigate the existence of new types of shape functions by making use of the power of symbolic computational software. Copyright © 2000 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Finding a good graph coloring quickly is often a crucial phase in the development of efficient, parallel algorithms for many scientific and engineering applications. In this paper we consider the problem of solving the graph coloring problem itself in parallel. We present a simple and fast parallel graph coloring heuristic that is well suited for shared memory programming and yields an almost linear speedup on the PRAM model. We also present a second heuristic that improves on the number of colors used. The heuristics have been implemented using OpenMP. Experiments conducted on an SGI Cray Origin 2000 supercomputer using very large graphs from finite element methods and eigenvalue computations validate the theoretical run-time analysis. Copyright © 2000 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper describes an analytical model for a beam system, based on a modified Timoshenko theory, where the beam is pinned to a hub driven by an actuator at one end and is subject to a heavy load at the other end. A new efficient computational algorithm is then proposed for solving the higher-order non-canonical partial differential equation model, which is developed based on the generalized difference method. This allows a suitable selection of different trial and test spaces, so as to improve the computational efficiency while preserving the high convergence rate of the standard finite element method. With the trial space of cubic Hermite finite elements and the test space of piecewise linear functions, the computational scheme reduces to a semi-discretized or even fully discretized computational algorithm. A numerical simulation result is included to visualize the theoretical modelling and computational results. Copyright © 1999 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In the paper the author presents a novel point of view for the refinement and derefinement algorithms of triangular nested meshes using fractal concepts and iterated function systems (IFS). The fractal behaviour can be understood in the sense that these meshes feature a remarkable amplifying invariance under changes of magnification. Here we compare the meshes obtained by the combination of these algorithms with those presented by Bova and Carey (1992). Although both of the meshes are very similar, the current algorithms automatically build and manage sequences of nested irregular discretizations of the domain. The author illustrates here how the application of IFS families is equivalent to the use of an adaptive strategy that combines the refinement procedure with the derefinement one. [ABSTRACT FROM AUTHOR]

The paper is devoted to the analysis of two- or three-dimensional contact problems with Coulomb friction and large deformation. The classical approach is based on two minimum principles or two variational inequalities: the first for unilateral contact and the second for friction. A coupled approach using only one principle or one inequality is presented. This new approach allows us to extend the notion of normality law to dissipative behaviors with a non-associated flow rule, such as surface friction. Non-differentiable contact potentials are regularized by means of the augmented Lagrangian method. Using the C++ language, an object-oriented finite element database is created, which allows us to implement the contact and friction in an existing code in a very simple and neat way. Numerical examples are carried out in many difficult cases such as shock absorber and three-dimensional contact. The numerical results prove that this approach is robust and efficient concerning numerical stability. [ABSTRACT FROM AUTHOR]

Explicit finite-element programs, such as DYNA3D, are frequently used to solve large structural problems, such as automobile impacts, that involve tens of thousands of shell elements. Since the explicit finite-element programs do not use a stiffness matrix, the major cost of the calculation is the evaluation of the force vector. A significant part of that cost is the evaluation of the constitutive models. The standard algorithm for integrating J2 plasticity at the stress points is the radial return method. An iterative variation of radial return is commonly used to impose the zero normal stress condition within the shell elements. In this paper we explore several different non-iterative methods that impose the zero normal stress condition in an approximate manner. We show that the cost of the constitutive evaluation can be reduced by 25 per cent without introducing significant errors. [ABSTRACT FROM AUTHOR]

A numerical algorithm useful for simulation of the wave propagation in an optical waveguide is proposed. An actual formulation is carried out for a two-dimensional planar structure. In this method, the one- dimensional finite-element method is used in the cross-sectional direction (along the y-axis) and the finite-difference method (the direct integration method) is used in the direction of the wave propagation (along the z-axis). Hence, once an arbitrary incident condition is given, the subsequent variation and evolution of the excited wave can be derived successively. Thus, in this method, there is no restriction on the medium parameters under the situation in which the reflected wave is negligible. For this reason, it is possible to describe quantitatively the behavior of the light wave along the propagation direction in an arbitrarily shaped wave- guide and a nonlinear waveguide including the branches, tapers and bends. Also, a unified formulation is possible for both TE and TM waves. Due to the fore- going advantages, the proposed method is expected to be a practical scheme for simulating the behavior of the light wave propagating in an arbitrarily shaped planar wave- guide including a nonlinear waveguide. Specifically, the problem of propagation in a nonlinear three-layer slab waveguide made of an intensity-dependent dielectric medium is analyzed. Through a number of numerical results, the validity and usefulness of the present algorithm are verified. [ABSTRACT FROM AUTHOR]

The calculation of the pressure cycle is of crucial importance for the successful development of a thin sheet superplastic forming process. The pressure cycle must be such that the forming time is minimized while maintaining a strain rate that maximizes the strain-rate sensitivity parameter, in order to reduce the propensity of the material to undergo localized necking. One way of dealing with this problem is to control the pressure by constraining the maximum equivalent strain rate. This paper presents a general numerical algorithm for achieving such control, in conjunction with a finite element analysis of the forming process. Three examples are given of strain-rate controlled pressure cycles for the forming of a plane-strain strip. [ABSTRACT FROM AUTHOR]

This paper describes a numerical procedure for the solution of stiff dynamic system equations which are written in implicit form f(x,x,t)=0. This study, based on the Broyden's updating method gives a more efficient way to solve the differential/algebraic equations simultaneously. Using a rank-one inverse Jacobian updating formula, the inverse Jacobian matrix is corrected directly at each iteration. The algorithm is investigated for several dynamic systems. [ABSTRACT FROM AUTHOR]

This paper presents the development of several analytical relationships for use in the gradient calculations common to sensitivity analysis and configuration optimization. The methods discussed are oriented toward two- and three- dimensional continua modeled with isoparametric finite elements, and design parameters which control the geometric layout of the structure. The notable feature of these formulae is their simplicity, which leads to quick and systematic computational algorithms for most standard elements. [ABSTRACT FROM AUTHOR]

Summary: The subloading surface model released from a purely elastic domain is capable of describing not only monotonic but also cyclic loading behaviors accurately. It is expected that elastoplastic deformation analyses can be performed with high accuracy and efficiency by the complete implicit stress integration algorithm with a return‐mapping projection. Various implicit stress integration algorithms for the subloading surface model have been proposed. However, they are applicable only to the monotonic loading behavior since they adopt the incorrect loading criterion presuming that the subloading surface expands in the plastic loading process. In fact, however, the plastic strain rate is induced even when the subloading surface contracts in the elastic trial step. Therefore, erroneous results in the descriptions of unloading‐reloading and cyclic loading behaviors are caused in the calculations with the existing algorithms. The complete implicit stress integration method is formulated adopting the rigorous loading criterion and implemented in Abaqus in this study. Numerical analyses for the elastoplastic deformation behaviors in the single‐element are performed by the present and the existing algorithms. In addition, the deformation analysis of the R‐notched cylinder is performed by the present algorithm. High performability of the present algorithm is confirmed by these numerical calculation results. [ABSTRACT FROM AUTHOR]

Remote geovisualization has gained momentum to support large‐scale geospatial data analysis and complex decision‐making over the last few years. Cloud computing, due to its capabilities to deliver on‐demand computing resources, has been embraced to develop and deploy interactive and scalable remote geovisualization applications. However, current cloud computing frameworks do not offer a versatile resource management scheme that is readily applicable for online remote visualization services, which usually require maintaining a satisfactory service level over time under dynamic workloads. To address this gap, we propose an automatic cloud resource management approach based on a bi‐level scheduling and horizontal scaling scheme to exploit cloud resources efficiently. At the lower level, a dynamic task‐scheduling scheme using collaborative filtering techniques is proposed to allocate virtual cloud resources to execute sub‐tasks. The scheduling scheme considers spatio‐temporal patterns presented in visualization views. At the upper level, reinforcement learning is adopted to perform resource auto‐scaling based on a reward function that integrates three different facets, namely: time cost, resource cost, and service stability. The original reinforcement learning algorithm is improved in two main aspects: (1) considering the delay of resource provisioning that is common in cloud environments; and (2) using online Gaussian estimation to estimate Q values. Task scheduling and auto‐scaling interact with each other and are integrated to deliver a comprehensive and responsive resource management solution. Experimental results demonstrate that our approach outperforms several existing cloud resource management methods. The proposed approach is also applicable for other interactive visualization applications, which have similar workload characteristics and performance requirements as interactive remote geovisualization. [ABSTRACT FROM AUTHOR]

SUMMARY This work discusses the performance impact from the tetrahedralization of non-conforming meshes generated by a parallel octree method capable of handling arbitrary immersed geometries. First, we review conforming techniques for meshes created from octrees. Then we implement a tetrahedralization scheme based on templates in a parallel meshing algorithm that uses a linear octree with 2:1 balancing constraint. Besides, we also propose a change on the partitioning strategy for the same meshing algorithm to improve the octree refinement load balancing. Scalability analyses show that the chosen tetrahedralization technique preserves algorithm performance. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The concept of representative directions is intended to generalize one-dimensional material models for uniaxial tension to complete three-dimensional constitutive models for the finite element method. The concept is applicable to any model which is able to describe uniaxial loadings, even to those for inelastic material behavior without knowing the free energy. The typical characteristics of the respected material class are generalized in a remarkable similarity to the input model. The algorithm has already been implemented into the finite element systems ABAQUS and MSC.MARC considering several methods to increase the numerical efficiency. The implementation enables finite element simulations of inhomogeneous stress conditions within technical components, though the input model predicts uniaxial material behavior only. [ABSTRACT FROM AUTHOR]

Generating realistic geometric models from 3D segmented images is an important task in many biomedical applications. Segmented 3D images impose particular challenges for meshing algorithms because they contain multi-material junctions forming features such as surface patches, edges and corners. The resulting meshes should preserve these features to ensure the visual quality and the mechanical soundness of the models. We present a feature preserving Delaunay refinement algorithm which can be used to generate high-quality tetrahedral meshes from segmented images. The idea is to explicitly sample corners and edges from the input image and to constrain the Delaunay refinement algorithm to preserve these features in addition to the surface patches. Our experimental results on segmented medical images have shown that, within a few seconds, the algorithm outputs a tetrahedral mesh in which each material is represented as a consistent submesh without gaps and overlaps. The optimization property of the Delaunay triangulation makes these meshes suitable for the purpose of realistic visualization or finite element simulations. [ABSTRACT FROM AUTHOR]

The article presents a study on a combination of an artificial neural network (ANN) with a differential evolution algorithm, which is suggested to replace the finite-element numerical model in water resources management problems. It states that the employment of methodologies such as ANNs, which estimate the complicated behaviors and response of physical systems, allows the optimization of a huge number of case scenarios with different set of constraints within a short period of time, whereas the corresponding simulation time using a numerical method would be prohibitive.

A 2D electrical impedance tomography (EIT) system has been developed at Duke University as an experimental system to test the forward and inverse algorithms for EIT application. The forward model is based on the 2nd-order finite element method (FEM), while the image reconstruction is based on the distorted Born iterative method (DBIM). The major contributions of this work are the application of the higher-order FEM as a forward solver, and the DBIM as an inverse solver to the integrated EIT system. The forward model has been validated with the measured data to within 0.5% accuracy. Excellent images have been reconstructed with these collected EIT data sets. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 2989–2998, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22938 [ABSTRACT FROM AUTHOR]

A combined algorithm of the edge-based finite-element method (FEM) and the short-open calibration (SOC) technique is presented in order to analyze periodic structures. The computational domain is reduced to a unit cell through the use of waveguide simulators. To accurately predict the characteristics of periodic structures, the SOC technique is directly accommodated into the FEM formulation and removes unwanted parasitic errors brought about by the approximation of exciting sources. The developed FEM algorithm improves the accuracy of the solution and causes the rapid convergence of iterative solvers, when compared to the FEM combined with perfectly matching layers (PMLs) or absorbed boundary conditions (ABCs). The results for some periodic structures are given to show the accuracy and rapidity of the algorithm. © 2005 Wiley Periodicals, Inc. Microwave Opt Technol Lett 45: 427–430, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20844 [ABSTRACT FROM AUTHOR]

The FETI method with the natural coarse grid is combined with the penalty method to develop an efficient solver for elliptic variational inequalities. A proof is given that a prescribed bound on the norm of feasibility of solution may be achieved with a value of the penalty parameter that does not depend on the discretization parameter and that an approximate solution with the prescribed bound on violation of the Karush–Kuhn–Tucker conditions may be found in a number of steps that does not depend on the discretization parameter. Results of numerical experiments with parallel solution of a model problem discretized by up to more than eight million of nodal variables are in agreement with the theory and demonstrate numerically both optimality of the penalty and scalability of the algorithm presented. Copyright © 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

We investigate the application of preconditioned generalized minimal residual (GMRES) algorithm to the equations of hydrodynamic model of semiconductor devices. An introduction to such a model is presented. We use finite-element method P1-isoP2 element to discretize the equations. A preconditioning technique is proposed. The CPU times are presented for n+-n-n+ diodes and 0.25 μm gate length Si MESFETs by using the preconditioned GMRES algorithm and the GMRES algorithm. The numerical results show that the preconditioning technique accelerates effectively the velocity of convergence. Copyright © 2003 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In three-dimensional electromagnetic field analysis by the finite element method, the function space of the higher-order vector elements is separated into the gradient field and the rotational field and a new configuration method for the shape function is proposed. For a large-dimensional eigenvalue problem with unique zero eigenvalue in the electromagnetic eigenvalue problem, the subspace method containing an algorithm eliminating the null space is proposed. When these methods are applied to the analysis of a cubic cavity resonator, fast analysis of a large-dimensional eigenvalue problem becomes possible. In addition, it is found that more accurate solutions can be obtained with the higher-order vector elements in the same computation time. © 2002 Wiley Periodicals, Inc. Electron Comm Jpn Pt 2, 85(7): 57–65, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjb.10017 [ABSTRACT FROM AUTHOR]

A fast, higher order three-dimensional finite-element method is presented for the efficient and accurate analysis of microwave waveguide devices. Two solution algorithms are designed. The first one uses mixed-order triangular prism elements in conjunction with a special frontal solver. It has a very low memory requirement, and is extremely fast for waveguide devices with one dimension longer than the other two. However, the solution must be repeated at each frequency. The second solution algorithm employs higher order tetrahedral elements, which are particularly suitable for modeling complex devices, in conjunction with the multifrontal solver. This algorithm has the major advantage that it can be combined with the asymptotic waveform evaluation and complex frequency-hopping techniques to perform fast frequency-sweep calculations to obtain the response of a device over a wide band. Numerical results are presented to demonstrate the performance of both solution algorithms and their higher order convergence. It is shown that, using the first solution algorithm, the solution accuracy increases with the order of elements for a fixed number of unknowns, while the computing time and memory requirements remain basically unchanged. With the second solution algorithm, the solution accuracy improves even faster with the increase in the order of elements for a fixed number of unknowns, and very surprisingly, the computing time and memory requirements actually decrease sometimes. © 2002 John Wiley & Sons, Inc. Microwave Opt Technol Lett 32: 344–352, 2002. [ABSTRACT FROM AUTHOR]