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In this paper we describe a hybrid deterministic/Monte Carlo algorithm for neutron transport simulation. The algorithm is based on nonlinear accelerators for source iteration, using Monte Carlo methods for the purely absorbing high-order problem and a Jacobian-free Newton--Krylov iteration for the low-order problem. We couple the Monte Carlo solution with the low-order problem using filtering to smooth the flux and current from the Monte Carlo solver and an analytic Jacobian-vector product to avoid numerical differentiation of the Monte Carlo results. We use a continuous energy deposition tally for the Monte Carlo simulation. We conclude the paper with numerical results which illustrate the effectiveness of the new algorithm. [ABSTRACT FROM AUTHOR]

Abstract: The system of equations arising in finite element simulations of components made of ferroelectroelastic materials is non-linear if the loading is sufficiently high. The Newton–Raphson method represents a widely used iterative technique to solve this system of non-linear equations. However, if the scalar potential formulation is utilised, convergence difficulties may occur. This circumstance can be primarily attributed to the specific form of the non-linear response of typical ferroelectroelastic materials being subjected to electrical loading. The present paper is devoted to modifications of the Newton–Raphson method, which are capable of improving the convergence behaviour experienced in the finite element iteration. We extend an existing modification to the fully coupled, ferroelectroelastic case. Additionally, a new modification of the Newton–Raphson method is proposed. This method applies an iteration algorithm, which is virtually equivalent to the iteration algorithm of the unmodified Newton–Raphson method combined with the vector potential formulation. An important feature of both modifications is that they are applied on the integration point level. Therefore, the global non-linear finite element iteration scheme remains unchanged. Finally, the practicability of the modifications discussed in the paper is shown in a numerical example. [Copyright &y& Elsevier]

Generating synthetic baseline populations is a fundamental step of agent-based modeling and simulation, which is growing fast in a wide range of socio-economic areas including transportation planning research. Traditionally, in many commercial and non-commercial microsimulation systems, the iterative proportional fitting (IPF) procedure has been used for creating the joint distribution of individuals when combining a reference joint distribution with target marginal distributions. Although IPF is simple, computationally efficient, and rigorously founded, it is unclear whether IPF well preserves the dependence structure of the reference joint table sufficiently when fitting it to target margins. In this paper, a novel method is proposed based on the copula concept in order to provide an alternative approach to the problem that IPF resolves. The dependency characteristic measures were computed and the results from the proposed method and IPF were compared. In most test cases, the proposed method outperformed IPF in preserving the dependence structure of the reference joint distribution. [ABSTRACT FROM AUTHOR]

The most useful feature of ultrasound tomography founded on the inverse scattering theory is that it can detect small structures below the wavelength of the pressure wave. A popular method introduced in ultrasound tomography is the Distorted Born Iterative Method (DBIM). Recently, the dual-frequency combination technique has been utilized to improve the reconstruction quality and increase the convergence rate of the DBIM. This method uses two frequencies, f1 (low) and f2 (high), to estimate the sound contrast in N f 1 and N f 2 iterations, respectively. However, the influence of these iteration parameters on the overall performance of the system is not yet known. In this paper, it is shown by using the simulation technique that if we do not pay attention to the choice of these parameters, the reconstruction quality might be worse than that using a single frequency. Furthermore, we focus on the best way to select the parameters in order to improve the reconstruction quality of ultrasound tomography. Given a fixed sum N iter of N f 1 and N f 2 , simulation results show that the best value of N f 1 is N iter /2; this choice of parameters offers a normalized error that reduces by 67.6%, compared to the conventional DBIM using a single frequency. [ABSTRACT FROM AUTHOR]

Abstract: Three-dimensional (3D) cyclic analysis and constitutive material model are needed to better understand the behavior of unreinforced masonry (URM) buildings under earthquake excitations. So far, most of the existing constitutive material models applied to the field of masonry structures have focused on two-dimensional modeling and monotonic loading. In addition, most of the studies have used implicit dynamic procedures in the time domain. Based on the inherent features of implicit formulations for nonlinear problems, a number of iterations are required at each time step to achieve convergence, which leads to intensive computations and lack of convergence in some cases such as cyclic loadings. In this paper, a 3D cyclic constitutive material model implemented within an explicit analysis procedure is proposed, which can be used to model large deformation behavior of masonry walls. A rigorous constitutive material model is proposed and validated with available experimental data from previous researches, and for the attributes for which experimental data is not readily available; a number of new experimental tests has been conducted by the authors. The material model is implemented in a user-defined subroutine and compiled with ABAQUS (VUMAT). The subroutine is then tested by several numerical examples on a single element under cyclic normal and transverse deformations to examine the behavior of the material model. Moreover, several analyses are conducted and the numerical results are compared with experimental data to assess the robustness and predictive capabilities of the proposed material model and the numerical solution algorithms. [Copyright &y& Elsevier]

Abstract: This paper attempts to model complex destination-chain, departure time and route choices based on activity plan implementation and proposes an arc-based cross entropy method for solving approximately the dynamic user equilibrium in multiagent-based multiclass network context. A multiagent-based dynamic activity chain model is developed, combining travelers’ day-to-day learning process in the presence of both traffic flow and activity supply dynamics. The learning process towards user equilibrium in multiagent systems is based on the framework of Bellman’s principle of optimality, and iteratively solved by the cross entropy method. A numerical example is implemented to illustrate the performance of the proposed method on a multiclass queuing network. [Copyright &y& Elsevier]

Abstract: Finite Element Tearing and Interconnecting (FETI) methods are a powerful approach to designing solvers for large-scale problems in computational mechanics. The numerical simulation problem is subdivided into a number of independent sub-problems, which are then coupled in appropriate ways. NURBS- (Non-Uniform Rational B-spline) based isogeometric analysis (IGA) applied to complex geometries requires to represent the computational domain as a collection of several NURBS geometries. Since there is a natural decomposition of the computational domain into several subdomains, NURBS-based IGA is particularly well suited for using FETI methods. This paper proposes the new IsogEometric Tearing and Interconnecting (IETI) method, which combines the advanced solver design of FETI with the exact geometry representation of IGA. We describe the IETI framework for two classes of simple model problems (Poisson and linearized elasticity) and discuss the coupling of the subdomains along interfaces (both for matching interfaces and for interfaces with T-joints, i.e. hanging nodes). Special attention is paid to the construction of a suitable preconditioner for the iterative linear solver used for the interface problem. We report several computational experiments to demonstrate the performance of the proposed IETI method. [Copyright &y& Elsevier]

This paper discusses the weak coupling of nonlinear magnetoquasistatic field models (e.g., of induction motors) to an external electric network model (e.g., of frequency converters). A piece-wise linear inductance (as lumped field model) is not sufficiently accurate if the magnetic field exhibits strong eddy current effects. Here, we propose to represent the field model in the circuit equations by a more complex surrogate model. It is fitted by dynamic iteration (‘waveform relaxation’) during the cosimulation procedure. We demonstrate the link between dynamic iterations and the achievable convergence order of the time integrator numerically. [ABSTRACT FROM PUBLISHER]

Abstract: The bidomain model is widely used in electro-cardiology to simulate spreading of excitation in the myocardium and electrocardiograms. It consists of a system of two parabolic reaction diffusion equations coupled with an ODE system. Its discretisation displays an ill-conditioned system matrix to be inverted at each time step: simulations based on the bidomain model therefore are associated with high computational costs. In this paper we propose a preconditioning for the bidomain model either for an isolated heart or in an extended framework including a coupling with the surrounding tissues (the torso). The preconditioning is based on a formulation of the discrete problem that is shown to be symmetric positive semi-definite. A block LU decomposition of the system together with a heuristic approximation (referred to as the monodomain approximation) are the key ingredients for the preconditioning definition. Numerical results are provided for two test cases: a 2D test case on a realistic slice of the thorax based on a segmented heart medical image geometry, a 3D test case involving a small cubic slab of tissue with orthotropic anisotropy. The analysis of the resulting computational cost (both in terms of CPU time and of iteration number) shows an almost linear complexity with the problem size, i.e. of type nlog α (n) (for some constant α) which is optimal complexity for such problems. [Copyright &y& Elsevier]

Abstract: Some widely used methodologies for simulation of non-Gaussian processes rely on translation process theory which imposes certain compatibility conditions between the non-Gaussian power spectral density function (PSDF) and the non-Gaussian probability density function (PDF) of the process. In many practical applications, the non-Gaussian PSDF and PDF are assigned arbitrarily; therefore, in general they can be incompatible. Several techniques to approximate such incompatible non-Gaussian PSDF/PDF pairs with a compatible pair have been proposed that involve either some iterative scheme on simulated sample functions or some general optimization approach. Although some of these techniques produce satisfactory results, they can be time consuming because of their nature. In this paper, a new iterative methodology is developed that estimates a non-Gaussian PSDF that: (a) is compatible with the prescribed non-Gaussian PDF, and (b) closely approximates the prescribed incompatible non-Gaussian PSDF. The corresponding underlying Gaussian PSDF is also determined. The basic idea is to iteratively upgrade the underlying Gaussian PSDF using the directly computed (through translation process theory) non-Gaussian PSDF at each iteration, rather than through expensive ensemble averaging of PSDFs computed from generated non-Gaussian sample functions. The proposed iterative scheme possesses two major advantages: it is conceptually very simple and it converges extremely fast with minimal computational effort. Once the underlying Gaussian PSDF is determined, generation of non-Gaussian sample functions is straightforward without any need for iterations. Numerical examples are provided demonstrating the capabilities of the methodology. [Copyright &y& Elsevier]

Abstract: Fluid–structure interaction problems arise in many fields of application such as flows around elastic structures and blood flow in arteries. The method presented in this paper for solving such a problem is based on a reduction to an equation at the interface, involving the so-called Steklov–Poincaré operators. This interface equation is solved by a Newton iteration, for which directional derivatives involving shape derivatives with respect to the interface perturbation have to be evaluated appropriately. One step of the Newton iteration requires the solution of several decoupled linear sub-problems in the structure and the fluid domains. These sub-problems are spatially discretized by a finite element method on hybrid meshes. For the time discretization, implicit first-order methods are used for both sub-problems. The discretized equations are solved by algebraic multigrid methods. [Copyright &y& Elsevier]

Abstract: The design of the extreme-scale platforms that are expected to become available in the forthcoming decade will represent a convergence of technological trends and the boundary conditions imposed by over half a century of algorithm and application software development. These platforms will be hierarchical because they provide coarse grain parallelism between nodes and fine grain parallelism within each node. They are also expected to be very heterogeneous since multi-core chips and accelerators have completely different architectures and potentials. It is clear that such a degree of complexity will embody radical changes that will render obsolete the current software infrastructure for large-scale scientific applications. In this paper, we illustrate a hierarchical algorithmic approach for the implementation of an efficient parallel sparse linear solver that combines direct and iterative methods. Such a hybrid approach exploits the advantages of both numerical techniques and enables the use of several levels and grains of parallelism. This combination express different levels of parallelism and permits an optimal trade-off between numerical and parallel efficiency. Consequently, such a numerical technique appears as a promising candidate for intensive simulations on future many-core parallel platforms. [Copyright &y& Elsevier]

Abstract: Many existing algorithms taking the seminorm in for regularization have achieved great success in image processing. However, this paper considers the total bounded variation regularization based approach to perform image deblurring. Based on this novel model, we introduce an extended split Bregman iteration to obtain the optimum solution quickly. We also provide the rigorous convergence analysis of the iterative algorithm here. Compared with the results of the ROF method, numerical simulations illustrate the more excellent reconstruction performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Abstract: This paper is concerned with a system modeling a competitor–competitor–mutualist three-species Lotka–Volterra model. By Schauder fixed point theory, the existence of positive solutions to a strongly coupled elliptic system is given. Applying the method of upper and lower solutions and its associated monotone iterations, the true solutions are constructed and a numerical simulation is also presented. Our results show that this system possesses at least one coexistence state if cross-diffusions and cross-reactions are weak. [Copyright &y& Elsevier]

Abstract: This paper carries out the integration of a few nonlinear wave equations to obtain topological as well as non-topological soliton solutions. The mathematical techniques used to obtain the soliton solutions are He’s variational iteration method, the tanh method and the ansatz method. The nonlinear wave equations that are studied are coupled mKdV equations, Drinfeld–Sokolov equation and its generalized version. Finally, some numerical simulations are given to support the analytical solutions. [Copyright &y& Elsevier]

Abstract: If the energy bands of a phononic crystal are calculated by the finite difference time domain (FDTD) method combined with the fast Fourier transform (FFT), good estimation of the eigenfrequencies can only be ensured by the postprocessing of sufficiently long time series generated by a large number of FDTD iterations. In this paper, a postprocessing method based on the high-resolution spectral estimation via the Yule–Walker method is proposed to overcome this difficulty. Numerical simulation results for three-dimensional acoustic and two-dimensional elastic systems show that, compared with the classic FFT-based postprocessing method, the proposed method can give much better estimation of the eigenfrequencies when the FDTD is run with relatively few iterations. [Copyright &y& Elsevier]

Abstract: In this paper, we model the metal–oxide–semiconductor field effect transistor (MOSFET) radio frequency (RF) circuit as a system of nonlinear ordinary differential equations. Then we solve them with the waveform relaxation method, the monotone iterative method, and Runge–Kutta method directly in time domain. With the monotone iterative method, we prove that each decoupled and transformed circuit equation converges monotonically. In comparison with the HSPICE outputs, results calculated with our method are stable and robust in both the time and frequency domains. Convergence properties for the monotone iterative and outer iterative loops are also presented and discussed. This method provides an alternative in the time domain numerical solution of MOSFET RF circuit equations. [Copyright &y& Elsevier]

Abstract: The Schwinger method for solving inverse transport problems is applied to the problems of interface location identification, shield material identification, source isotope weight fraction identification, and material mass density identification (separately) in multilayered two-dimensional cylindrical gamma radiation source/shield systems. The method is iterative and estimates unknown interface locations, source isotope weight fractions, and material densities directly, while the unknown shield material is identified by estimating its total macroscopic gamma-ray cross sections. The energies of discrete gamma-ray lines emitted by the source are assumed to be known, while the unscattered flux of the lines is assumed to be measured at points external to the system. In numerical test cases, the Schwinger method correctly identifies the unknowns when the same deterministic ray-tracing code is used for both the parameter estimation process and simulation of the measured data. With realistic simulation of the measured data using a Monte Carlo code, the method produces more ambiguous results for interface location, shield material identification, and material density identification. The method works well for source weight fraction identification with measured data simulated by Monte Carlo. In addition to the application to more realistic (two-dimensional) problems, this paper extends previous work on the Schwinger inverse method by using surface formulas for unknown interface locations, automatic correction attempts for violated constraints, and ray-tracing instead of discrete-ordinates for transport calculations. [Copyright &y& Elsevier]

One of the key steps in compressed sensing is to solve the basis pursuit problem $min _{uin mathbb {R}^n}{|u|_1:Au=f}$. Bregman iteration was very successfully used to solve this problem in [40]. Also, a simple and fast iterative algorithm based on linearized Bregman iteration was proposed in [40], which is described in detail with numerical simulations in [35]. A convergence analysis of the smoothed version of this algorithm was given in [11]. The purpose of this paper is to prove that the linearized Bregman iteration proposed in [40] for the basis pursuit problem indeed converges. [ABSTRACT FROM AUTHOR]

Kolodko and Schoenmakers (2006) and Bender and Schoenmakers (2006) introduced a policy iteration that allows the achievement of a tight lower approximations of the price for early exercise options via a nested Monte Carlo simulation in a Markovian setting. In this paper we enhance the algorithm by a scenario selection method. It is demonstrated by numerical examples that the scenario selection can significantly reduce the number of inner simulations actually performed, and thus can greatly speed up the method (by up to a factor of 15 in some examples). Moreover, it is shown that the modified algorithm retains the desirable properties of the original, such as the monotone improvement property, termination after a finite number of iteration steps, and numerical stability. [ABSTRACT FROM AUTHOR]

Abstract: The aim of this paper is to present a limited memory iterative method, called the Broyden Rank Reduction method, to simulate periodically forced processes in plug-flow reactors with radial gradients taken into account. The simulation of periodically forced processes in plug-flow reactors leads to the development of partial differential equations that are normally solved in time using dynamical simulation. Depending on the convergence properties of the system at hand, the number of cycles that needs to be computed up to a cyclic steady state is reached can be large. Therefore direct iterative methods are essential in order to capture the long time dynamics of such systems. In order to overcome severe memory constraints many authors have reverted to pseudo-homogeneous 1D models and to coarse grid discretization, which renders such models inadequate or inaccurate. The results that we present show that the long time dynamics actually depends on the radius of the reactor and, hence, the full 2D model is essential in order to simulate periodically forced processes in plug-flow reactors accurately. [Copyright &y& Elsevier]

It is well known that at low-bit-rate block discrete cosine transform compressed image exhibits visually annoying blocking and ringing artifacts. In this paper, we propose a noniterative, wavelet-based deblocking algorithm to reduce both types of artifacts. The algorithm exploits the fact that block discontinuities are constrained by the dc quantization interval of the quantization table, as well as the behavior of wavelet modulus maxima evolution across wavelet scales to derive appropriate threshold maps at different wavelet scales. Since ringing artifacts occur near strong edges, which can be located either along block boundaries or within blocks, suppression of block discontinuities does not always reduce ringing artifacts. By exploiting the behavior of ringing artifacts in the wavelet domain, we propose a simple yet effective method for the suppression of such artifacts. The proposed algorithm can suppress both block discontinuities and ringing artifacts effectively while preserving true edges and textural information. Simulation results and extensive comparative study with both iterative and noniterative methods reported in the literature have shown the effectiveness of our algorithm. [ABSTRACT FROM AUTHOR]

This paper shows the ability of a domain decomposition method with a Neumann-Neumann preconditioner to solve industrial and biomechanical problems. For a mid-size biomedical simulation involving soft tissues the results obtained by using this algorithm are comapred to those obtained by more classical methods. The present algorithm thus appears to be more reliable than standard iterative methods and more efficient than a direct method. Copyright © 1999 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In the numerical formulation of electromagnetic field problems, the presence of field-dependent material properties causes the solution matrices to be non-linear. Iterative procedures have been developed for solving such nonlinear problems. The paper presents a brief survey of simple iteration schemes from an error, or energy, point of view, which is found to open up interesting possibilities.