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Benchmark Problems (benchmark + problem)

Distribution by Scientific Domains

Engineering	83%
Business, Economics, Finance and Accounting	8%
2 Other Domains	9%

Distribution within Engineering

Numerical Methods & Algorithms	74%
Control Systems Technology	7%
4 Other Subdomains	19%

Selected Abstracts

A simple LMS-based approach to the structural health monitoring benchmark problem

EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 6 2005
J. Geoffrey Chase
Abstract A structure's health or level of damage can be monitored by identifying changes in structural or modal parameters. However, the fundamental modal frequencies can sometimes be less sensitive to (localized) damage in large civil structures, although there are developing algorithms that seek to reduce this difficulty. This research directly identifies changes in structural stiffness due to modeling error or damage using a structural health monitoring method based on adaptive least mean square (LMS) filtering theory. The focus is on computational simplicity to enable real-time implementation. Several adaptive LMS filtering based approaches are used to analyze the data from the IASC,ASCE Structural Health Monitoring Task Group Benchmark problem. Results are compared with those from the task group and other published results. The proposed methods are shown to be very effective, accurately identifying damage to within 1%, with convergence times of 0.4,13.0 s for the twelve different 4 and 12 degree of freedom benchmark problems. The resulting modal parameters match to within 1% those from the benchmark problem definition. Finally, the methods developed require 1.4,14.0 Mcycles of computation and therefore could easily be implemented in real time. Copyright © 2004 John Wiley & Sons, Ltd. [source]

A Comparative Study of Modal Parameter Identification Based on Wavelet and Hilbert,Huang Transforms

COMPUTER-AIDED CIVIL AND INFRASTRUCTURE ENGINEERING, Issue 1 2006
Banfu Yan
Special attention is given to some implementation issues, such as the modal separation and end effect in the WT, the optimal parameter selection of the wavelet function, the new stopping criterion for the empirical mode decomposition (EMD) and the end effect in the HHT. The capabilities of these two techniques are compared and assessed by using three examples, namely a numerical simulation for a damped system with two very close modes, an impact test on an experimental model with three well-separated modes, and an ambient vibration test on the Z24-bridge benchmark problem. The results demonstrate that for the system with well-separated modes both methods are applicable when the time,frequency resolutions are sufficiently taken into account, whereas for the system with very close modes, the WT method seems to be more theoretical and effective than HHT from the viewpoint of parameter design. [source]

A simple LMS-based approach to the structural health monitoring benchmark problem

Modelling the behaviour of an embankment on soft clay with different constitutive models

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 10 2006
M. Karstunen
Abstract The paper investigates the effect of constitutive models on the predicted response of a simplified benchmark problem, an embankment on soft soil. The soft soil is assumed to have the properties of POKO clay from Finland and five different constitutive models are used to model the deposit. Two of the models are isotropic models, i.e. the Modified Cam Clay model and the Soft-Soil model. The other models are recently proposed constitutive models that account for plastic anisotropy. The S-CLAY1 and S-CLAY1S models are embedded in a standard elasto-plastic framework and account for anisotropy via a rotational hardening law. In addition, the S-CLAY1S model accounts for bonding and destructuration. In contrast, the Multilaminate Model for Clay (MMC) accounts for plastic anisotropy by utilizing so-called multilaminate framework. The results of numerical simulations show that accounting for anisotropy results in notable differences in the predicted settlements and horizontal movements compared to the predictions using the isotropic models. There are also significant differences in the K0 predictions by the different constitutive models and this has a significant impact on the results. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Improved implementation and robustness study of the X-FEM for stress analysis around cracks

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2005
E. Béchet
Abstract Numerical crack propagation schemes were augmented in an elegant manner by the X-FEM method. The use of special tip enrichment functions, as well as a discontinuous function along the sides of the crack allows one to do a complete crack analysis virtually without modifying the underlying mesh, which is of industrial interest, especially when a numerical model for crack propagation is desired. This paper improves the implementation of the X-FEM method for stress analysis around cracks in three ways. First, the enrichment strategy is revisited. The conventional approach uses a ,topological' enrichment (only the elements touching the front are enriched). We suggest a ,geometrical' enrichment in which a given domain size is enriched. The improvements obtained with this enrichment are discussed. Second, the conditioning of the X-FEM both for topological and geometrical enrichments is studied. A preconditioner is introduced so that ,off the shelf' iterative solver packages can be used and perform as well on X-FEM matrices as on standard FEM matrices. The preconditioner uses a local (nodal) Cholesky based decomposition. Third, the numerical integration scheme to build the X-FEM stiffness matrix is dramatically improved for tip enrichment functions by the use of an ad hoc integration scheme. A 2D benchmark problem is designed to show the improvements and the robustness. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Steady and unsteady incompressible flow in a double driven cavity using the artificial compressibility (AC)-based characteristic-based split (CBS) scheme

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2005
P. Nithiarasu
Abstract In this paper, the explicit characteristic-based split (CBS) scheme has been employed to solve both steady and unsteady flows inside a non-rectangular double driven cavity. This problem is recently suggested as a benchmark problem for incompressible flows. Both unstructured and structured meshes have been employed in the present study to make sure that the predicted results are as close to reality as possible. The results obtained show the existence of steady state at lower Reynolds numbers (,1000) and transient states at higher Reynolds numbers. The flow approaches a turbulent state as the Reynolds number is increased to 10 000. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Parallel multipole implementation of the generalized Helmholtz decomposition for solving viscous flow problems

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2003
Mary J. Brown
Abstract The evaluation of a domain integral is the dominant bottleneck in the numerical solution of viscous flow problems by vorticity methods, which otherwise demonstrate distinct advantages over primitive variable methods. By applying a Barnes,Hut multipole acceleration technique, the operation count for the integration is reduced from O(N2) to O(NlogN), while the memory requirements are reduced from O(N2) to O(N). The algorithmic parameters that are necessary to achieve such scaling are described. The parallelization of the algorithm is crucial if the method is to be applied to realistic problems. A parallelization procedure which achieves almost perfect scaling is shown. Finally, numerical experiments on a driven cavity benchmark problem are performed. The actual increase in performance and reduction in storage requirements match theoretical predictions well, and the scalability of the procedure is very good. Copyright © 2003 John Wiley Sons, Ltd. [source]

Three-dimensional simulation of planar contraction viscoelastic flow by penalty finite element method

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 7 2010
Yue Mu
Abstract The planar contraction flow is a benchmark problem for the numerical investigation of viscoelastic flow. The mathematical model of three-dimensional viscoelastic fluids flow is established and the numerical simulation of its planar contraction flow is conducted by using the penalty finite element method with a differential Phan-Thien,Tanner constitutive model. The discrete elastic viscous split stress formulation in cooperating with the inconsistent streamline upwind scheme is employed to improve the computation stability. The distributions of velocity and stress obtained by simulation are compared with that of Quinzani's experimental results detected by laser,doppler velocimetry and flow-induced birefringence technologies. It shows that the numerical results agree well with the experimental results. The numerical methods proposed in the study can be well used to predict complex flow patterns of viscoelastic fluids. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Discussions on driven cavity flow

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2009
Article first published online: 9 SEP 200, Ercan Erturk
Abstract The widely studied benchmark problem, two-dimensional-driven cavity flow problem is discussed in detail in terms of physical and mathematical and also numerical aspects. A very brief literature survey on studies on the driven cavity flow is given. On the basis of several numerical and experimental studies, the fact of the matter is that physically the flow in a driven cavity is not two-dimensional above moderate Reynolds numbers. However, there exist numerical solutions for two-dimensional-driven cavity flow at high Reynolds numbers. Copyright © 2008 John Wiley & Sons, Ltd. [source]

A semi-Lagrangian level set method for incompressible Navier,Stokes equations with free surface

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10 2005
Leo Miguel González Gutiérrez
Abstract In this paper, we formulate a level set method in the framework of finite elements-semi-Lagrangian methods to compute the solution of the incompressible Navier,Stokes equations with free surface. In our formulation, we use a quasi-monotone semi-Lagrangian scheme, which is both unconditionally stable and essentially non oscillatory, to compute the advective terms in the Navier,Stokes equations, the transport equation and the equation of the reinitialization stage for the level set function. The method we propose is quite robust and flexible with regard to the mesh and the geometry of the domain, as well as the magnitude of the Reynolds number. We illustrate the performance of the method in several examples, which range from a benchmark problem to test the volume conservation property of the method to the flow past a NACA0012 foil at high Reynolds number. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Stability and slightly supercritical oscillatory regimes of natural convection in a 8:1 cavity: solution of the benchmark problem by a global Galerkin method

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 2 2004
Alexander Yu.
Abstract The global Galerkin method is applied to the benchmark problem that considers an oscillatory regime of convection of air in a tall two-dimensional rectangular cavity. The three most unstable modes of the linearized system of the Boussinesq equations are studied. The converged values of the critical Rayleigh numbers together with the corresponding oscillation frequencies are calculated for each mode. The oscillatory flow regimes corresponding to each of the three modes are approximated asymptotically. No direct time integration is applied. Good agreement with the previously published results obtained by solution of the time-dependent Boussinesq equations is reported. Copyright © 2004 John Wiley & Sons, Ltd. [source]

Higher order finite element methods and multigrid solvers in a benchmark problem for the 3D Navier,Stokes equations

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 6 2002
Volker John
Abstract This paper presents a numerical study of the 3D flow around a cylinder which was defined as a benchmark problem for the steady state Navier,Stokes equations within the DFG high-priority research program flow simulation with high-performance computers by Schafer and Turek (Vol. 52, Vieweg: Braunschweig, 1996). The first part of the study is a comparison of several finite element discretizations with respect to the accuracy of the computed benchmark parameters. It turns out that boundary fitted higher order finite element methods are in general most accurate. Our numerical study improves the hitherto existing reference values for the benchmark parameters considerably. The second part of the study deals with efficient and robust solvers for the discrete saddle point problems. All considered solvers are based on coupled multigrid methods. The flexible GMRES method with a multiple discretization multigrid method proves to be the best solver. Copyright © 2002 John Wiley & Sons, Ltd. [source]

Higher-order finite element discretizations in a benchmark problem for incompressible flows

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 8 2001
Volker John
Abstract We present a numerical study of several finite element discretizations applied to a benchmark problem for the two-dimensional steady state incompressible Navier,Stokes equations defined in Schäfer and Turek (The benchmark problem ,Flow around a cylinder'. In Flow Simulation with High-Performance Computers II. Notes on Numerical Fluid Mechanics, vol. 52, Hirschel EH (ed.). Vieweg: Wiesbaden, 1996; 547,566). The discretizations are compared with respect to the accuracy of the computed benchmark parameters. Higher-order isoparametric finite element discretizations turned out to be by far the most accurate. The discrete systems obtained with higher-order discretizations are solved with a modified coupled multigrid method whose behaviour within the benchmark problem is also studied numerically. Copyright © 2001 John Wiley & Sons, Ltd. [source]

A hybrid feedback for a benchmark problem of idle speed control

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 5 2010
A. Balluchi
Abstract The ever increasing demands on passengers' comfort, safety, emissions and fuel consumption imposed by car manufacturers and regulations call for advanced techniques and the use of cycle-accurate models in automotive control. In this paper, we focus on such approach to the idle speed control. It is natural to resort to hybrid methodologies, because of the rich combination of time and event-based behaviors exhibited by a controlled engine. A hybrid benchmark problem is considered and addressed first by analyzing the equilibria of the system and then testing a simple hybrid feedback strategy. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Relative Performance Evaluation of Mutual Funds: A Non-Parametric Approach

JOURNAL OF BUSINESS FINANCE & ACCOUNTING, Issue 7-8 2001
Yoon K. Choi
We propose an alternative mutual fund performance index which addresses the benchmark problem and controls for economies of scale in managing mutual funds. We advance a new concept of ,return-cost' efficiency as another important element in evaluating portfolio management, in addition to the mean-variance efficiency concept. Our index based on a non-parametric estimation is shown to be similar to the Sharpe index with multiple slopes (or factors). We have shown that all fund categories, except income funds, have similar average efficiency scores after controlling for economies of scale. Most funds operate in increasing returns to scale and seem to be successful in holding mean-variance efficient portfolios, but unsuccessful in allocating transaction costs efficiently, evidenced by excessive turnovers and loads. [source]

Fountain flow revisited: The effect of various fluid mechanics parameters

AICHE JOURNAL, Issue 5 2010
Evan Mitsoulis
Abstract Numerical simulations have been undertaken for the benchmark problem of fountain flow present in injection-mold filling. The finite element method (FEM) is used to provide numerical results for both cases of planar and axisymmetric domains under laminar, isothermal, steady-state conditions for Newtonian fluids. The effects of inertia, gravity, surface tension, compressibility, slip at the wall, and pressure dependence of the viscosity are all considered individually in parametric studies covering a wide range of the relevant parameters. These results extend previous ones regarding the shape of the front, and in particular the centerline front position, as a function of the dimensionless parameters. The pressures from the simulations have been used to compute the excess pressure losses in the system (front pressure correction or exit correction). Inertia leads to highly extended front positions relative to the inertialess Newtonian values, which are 0.895 for the planar case and 0.835 for the axisymmetric one. Gravity acting in the direction of flow shows the same effect, while gravity opposing the flow gives a reduced bulge of the fountain. Surface tension, slip at the wall, and compressibility, all decrease the shape of the front. Pressure-dependence of the viscosity leads to increased front position as a corresponding dimensionless parameter goes from zero (no effect) to higher values of the pressure-shift factor. The exit correction increases monotonically with inertia, compressibility, and gravity, while it decreases monotonically with slip and pressure-dependence of the viscosity. Contour plots of the primary variables (velocity-pressure) show interesting trends compared with the base case (zero values of the dimensionless parameters and of surface tension). © 2009 American Institute of Chemical Engineers AIChE J, 2010 [source]

Reduced-order suboptimal control design for a class of nonlinear distributed parameter systems using POD and ,,D techniques

OPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 3 2008
Radhakant Padhi
Abstract A new computational tool is presented in this paper for suboptimal control design of a class of nonlinear distributed parameter systems (DPSs). In this systematic methodology, first proper orthogonal decomposition-based problem-oriented basis functions are designed, which are then used in a Galerkin projection to come up with a low-order lumped parameter approximation. This technique has evolved as a powerful model reduction technique for DPSs. Next, a suboptimal controller is designed using the emerging ,,D technique for lumped parameter systems. This time domain control solution is then mapped back to the distributed domain using the same basis functions, which essentially leads to a closed form solution for the controller in a state-feedback form. We present this technique for the class of nonlinear DPSs that are affine in control. Numerical results for a benchmark problem as well as for a more challenging representative real-life nonlinear temperature control problem indicate that the proposed method holds promise as a good optimal control design technique for the class of DPSs under consideration. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Online identification of nonlinear multivariable processes using self-generating RBF neural networks

ASIAN JOURNAL OF CONTROL, Issue 5 2010
Karim Salahshoor
Abstract This paper addresses the problem of online model identification for multivariable processes with nonlinear and time-varying dynamic characteristics. For this purpose, two online multivariable identification approaches with self-organizing neural network model structures will be presented. The two adaptive radial basis function (RBF) neural networks are called as the growing and pruning radial basis function (GAP-RBF) and minimal resource allocation network (MRAN). The resulting identification algorithms start without a predefined model structure and the dynamic model is generated autonomously using the sequential input-output data pairs in real-time applications. The extended Kalman filter (EKF) learning algorithm has been extended for both of the adaptive RBF-based neural network approaches to estimate the free parameters of the identified multivariable model. The unscented Kalman filter (UKF) has been proposed as an alternative learning algorithm to enhance the accuracy and robustness of nonlinear multivariable processes in both the GAP-RBF and MRAN based approaches. In addition, this paper intends to study comparatively the general applicability of the particle filter (PF)-based approaches for the case of non-Gaussian noisy environments. For this purpose, the Unscented Particle Filter (UPF) is employed to be used as alternative to the EKF and UKF for online parameter estimation of self-generating RBF neural networks. The performance of the proposed online identification approaches is evaluated on a highly nonlinear time-varying multivariable non-isothermal continuous stirred tank reactor (CSTR) benchmark problem. Simulation results demonstrate the good performances of all identification approaches, especially the GAP-RBF approach incorporated with the UKF and UPF learning algorithms. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source]

Robust Resource Allocation Decisions in Resource-Constrained Projects,

DECISION SCIENCES, Issue 1 2007
Filip Deblaere
ABSTRACT The well-known deterministic resource-constrained project scheduling problem involves the determination of a predictive schedule (baseline schedule or pre-schedule) of the project activities that satisfies the finish,start precedence relations and the renewable resource constraints under the objective of minimizing the project duration. This baseline schedule serves as a baseline for the execution of the project. During execution, however, the project can be subject to several types of disruptions that may disturb the baseline schedule. Management must then rely on a reactive scheduling procedure for revising or reoptimizing the baseline schedule. The objective of our research is to develop procedures for allocating resources to the activities of a given baseline schedule in order to maximize its stability in the presence of activity duration variability. We propose three integer programming,based heuristics and one constructive procedure for resource allocation. We derive lower bounds for schedule stability and report on computational results obtained on a set of benchmark problems. [source]

A simple LMS-based approach to the structural health monitoring benchmark problem

Integrated Optimization by Multi-Objective Particle Swarm Optimization

IEEJ TRANSACTIONS ON ELECTRICAL AND ELECTRONIC ENGINEERING, Issue 1 2010
Masaru Kawarabayashi Student Member
Abstract In this letter, integrated optimization system, a new framework of practical optimization, is expanded to multi-objective optimization problem. This system is used in order to reduce the number of accesses to a simulator. On the basis of simulation results using some typical benchmark problems, it is shown that the proposed integrated optimization system enables to obtain relatively good Pareto solutions with drastic reduction in the number of function calls for evaluating the performance index values of systems. Copyright © 2010 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc. [source]

Particle Swarm Optimization with Diverse Parameters

IEEJ TRANSACTIONS ON ELECTRICAL AND ELECTRONIC ENGINEERING, Issue 4 2008
Mari Takei Student Member
Abstract This paper proposes a particle swarm optimization (PSO) with diverse parameters that achieve an appropriate balance between diversification and intensification during the search based on numerical stability analysis. Numerical experiments using seven typical benchmark problems with 100, 500, and 1000 dimensions validate the robustness and search capabilities of the proposed PSO. © 2008 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc. [source]

Computational methods for optical molecular imaging

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 12 2009
Duan Chen
Abstract A new computational technique, the matched interface and boundary (MIB) method, is presented to model the photon propagation in biological tissue for the optical molecular imaging. Optical properties have significant differences in different organs of small animals, resulting in discontinuous coefficients in the diffusion equation model. Complex organ shape of small animal induces singularities of the geometric model as well. The MIB method is designed as a dimension splitting approach to decompose a multidimensional interface problem into one-dimensional ones. The methodology simplifies the topological relation near an interface and is able to handle discontinuous coefficients and complex interfaces with geometric singularities. In the present MIB method, both the interface jump condition and the photon flux jump conditions are rigorously enforced at the interface location by using only the lowest-order jump conditions. This solution near the interface is smoothly extended across the interface so that central finite difference schemes can be employed without the loss of accuracy. A wide range of numerical experiments are carried out to validate the proposed MIB method. The second-order convergence is maintained in all benchmark problems. The fourth-order convergence is also demonstrated for some three-dimensional problems. The robustness of the proposed method over the variable strength of the linear term of the diffusion equation is also examined. The performance of the present approach is compared with that of the standard finite element method. The numerical study indicates that the proposed method is a potentially efficient and robust approach for the optical molecular imaging. Copyright © 2008 John Wiley & Sons, Ltd. [source]

On a multilevel preconditioning module for unstructured mesh Krylov solvers: two-level Schwarz

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 6 2002
R. S. Tuminaro
Abstract Multilevel methods offer the best promise to attain both fast convergence and parallel efficiency in the numerical solution of parabolic and elliptic partial differential equations. Unfortunately, they have not been widely used in part because of implementation difficulties for unstructured mesh solvers. To facilitate use, a multilevel preconditioner software module, ML, has been constructed. Several methods are provided requiring relatively modest programming effort on the part of the application developer. This report discusses the implementation of one method in the module: a two-level Krylov,Schwarz preconditioner. To illustrate the use of these methods in computational fluid dynamics (CFD) engineering applications, we present results for 2D and 3D CFD benchmark problems. Copyright © 2002 John Wiley & Sons, Ltd. [source]

Optimal transportation meshfree approximation schemes for fluid and plastic flows

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2010
B. Li
Abstract We develop an optimal transportation meshfree (OTM) method for simulating general solid and fluid flows, including fluid,structure interaction. The method combines concepts from optimal transportation theory with material-point sampling and max-ent meshfree interpolation. The proposed OTM method generalizes the Benamou,Brenier differential formulation of optimal mass transportation problems to problems including arbitrary geometries and constitutive behavior. The OTM method enforces mass transport and essential boundary conditions exactly and is free from tension instabilities. The OTM method exactly conserves linear and angular momentum and its convergence characteristics are verified in standard benchmark problems. We illustrate the range and scope of the method by means of two examples of application: the bouncing of a gas-filled balloon off a rigid wall; and the classical Taylor-anvil benchmark test extended to the hypervelocity range. Copyright © 2010 John Wiley & Sons, Ltd. [source]

Modeling three-dimensional crack propagation,A comparison of crack path tracking strategies

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 9 2008
P. Jäger
Abstract The development of a new finite element technique for the simulation of discontinuous failure phenomena in three dimensions is the key objective of this study. In contrast to the widely used extended finite element technique, we apply a purely deformation-based strategy based on an independent interpolation of the deformation field on both sides of the discontinuity. This method has been applied successfully for two-dimensional crack propagation problems in the past. However, when it comes to three-dimensional failure phenomena, it faces the same difficulties as the extended finite element method. Unlike in two dimensions, the characterization for the three-dimensional failure surface is non-unique and the tracking of the discrete crack can be performed in several conceptually different ways. In this work, we review the four most common three-dimensional crack tracking strategies. We perform a systematic comparison in terms of standard algorithmic quality measures such as mesh independency, efficiency, robustness, stability and computational cost. Moreover, we discuss more specific issues such as crack path continuity and integratability in commercial finite element packages. The features of the suggested crack tracking algorithms will be elaborated by means of characteristic benchmark problems in failure analysis. Copyright © 2008 John Wiley & Sons, Ltd. [source]

A two-dimensional stochastic algorithm for the solution of the non-linear Poisson,Boltzmann equation: validation with finite-difference benchmarks,

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2006
Kausik Chatterjee
Abstract This paper presents a two-dimensional floating random walk (FRW) algorithm for the solution of the non-linear Poisson,Boltzmann (NPB) equation. In the past, the FRW method has not been applied to the solution of the NPB equation which can be attributed to the absence of analytical expressions for volumetric Green's functions. Previous studies using the FRW method have examined only the linearized Poisson,Boltzmann equation. No such linearization is needed for the present approach. Approximate volumetric Green's functions have been derived with the help of perturbation theory, and these expressions have been incorporated within the FRW framework. A unique advantage of this algorithm is that it requires no discretization of either the volume or the surface of the problem domains. Furthermore, each random walk is independent, so that the computational procedure is highly parallelizable. In our previous work, we have presented preliminary calculations for one-dimensional and quasi-one-dimensional benchmark problems. In this paper, we present the detailed formulation of a two-dimensional algorithm, along with extensive finite-difference validation on fully two-dimensional benchmark problems. The solution of the NPB equation has many interesting applications, including the modelling of plasma discharges, semiconductor device modelling and the modelling of biomolecular structures and dynamics. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Mapped infinite elements for three-dimensional multi-region boundary element analysis

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2004
W. Moser
Abstract A formulation for an infinite boundary element (BE) is presented, which allows the modelling of infinite surfaces. The concept is that the finite surface is mapped to an infinite surface using special mapping functions. Using such mapping functions together with linear and quadratic interpolation for the displacements and the tractions, respectively, the desired decay behaviour can be modelled. The implementation of the proposed infinite elements becomes straightforward, since the Cauchy principal value, as well as the free term, are evaluated for the finite and infinite BEs with exactly the same techniques. The element developed can be used in a multi-region BE analysis of piecewise homogeneous domains, or for domains with joints and faults. The accuracy of the element is tested on some benchmark problems. Finally, a practical application in tunnelling is shown. Copyright © 2004 John Wiley & Sons, Ltd. [source]

Fully coupled non-linear analysis of piezoelectric solids involving domain switching

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2003
Wenjun Zeng
Abstract Domain switching is the cause of significant non-linearity in the response of piezoelectric materials to mechanical and electrical effects. In this paper, the response of piezoelectric solids is formulated by coupling thermal, electrical, and mechanical effects. The constitutive equations are non-linear. Moreover, due to the domain switching phenomenon, the resulting governing equations become highly non-linear. The corresponding non-linear finite element equations are derived and solved by using an incremental technique. The developed formulation is first verified against a number of benchmark problems for which a closed-form solution exists. Next, a cantilever beam made of PZT-4 is studied to evaluate the effect of domain switching on the overall force,displacement response of the beam. A number of interesting observations are made with respect to the extent of non-linearity and its progressive spread as the load on the beam increases. Copyright © 2002 John Wiley & Sons, Ltd. [source]

Flow-induced vibrations of non-linear cables.

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2002
Part 1: Models, algorithms
Abstract In this paper, we develop governing equations for non-linear cables as well as a formulation for the coupled flow-structure problem. The structure is discretized with second-order accuracy while the flow is discretized using spectral/hp elements in the context of the arbitrary Lagrangian,Eulerian formulation (ALE). Several benchmark problems are considered and the computational implementation is detailed. In the second part of this work large-scale simulation examples are presented. Copyright © 2002 John Wiley & Sons, Ltd. [source]