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Point Method (point + method)
Kinds of Point Method Selected AbstractsTransmission network expansion planning with security constraints based on bi-level linear programmingEUROPEAN TRANSACTIONS ON ELECTRICAL POWER, Issue 3 2009Hong Fan Abstract In deregulated power market, multiple conflicting objectives with many constraints should be balanced in transmission planning. The primary objective is to ensure the reliable supply to the demand as economically as possible. In this paper, a new bi-level linear programming model for transmission network expansion planning (TNEP) with security constraints has been proposed. The modeling improves traditional building style by adding reliability planning into economy planning as constraints, letting optimal planning strategy be more economic and highly reliable. A hybrid algorithm which integrates improved niching genetic algorithm and prime-dual interior point method is newly proposed to solve the TNEP based on bi-level programming. The advantages of the new methodology include (1) the highest reliability planning scheme can be acquired as economically as possible; (2) new model avoids the contradictions of conflicting objectives in TNEP, and explores new ideas for TNEP modeling; (3) the proposed hybrid algorithm is able to solve bi-level programming and fully manifests the merits of two algorithms as well. Simulation results obtained from two well-known systems and comparison analysis reveal that the proposed methodology is valid. Copyright © 2008 John Wiley & Sons, Ltd. [source] The modelling of anchors using the material point methodINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 9 2005C. J. Coetzee Abstract The ultimate capacity of anchors is determined using the material point method (MPM). MPM is a so-called meshless method capable of modelling large displacements, deformations and contact between different bodies. A short introduction to MPM is given and the derivation of the discrete governing equations. The analysis of a vertically loaded anchor and one loaded at 45° is presented. The load,displacement curves are compared to that obtained from experiments and the effect of soil stiffness and anchor roughness is investigated. The results of the vertically loaded anchor are also compared to an analytical solution. The displacement of the soil surface above the anchor was measured and compared to the numerical predictions. Convergence with mesh refinement is demonstrated and the effect of mesh size and dilatancy angle on the shear band width and orientation is indicated. The results show that MPM can model anchor pull out successfully. No special interface elements are needed to model the anchor,soil interface and the predicted ultimate capacities were within 10% of the measured values. Copyright © 2005 John Wiley & Sons, Ltd. [source] Decoupling and balancing of space and time errors in the material point method (MPM)INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2010Michael Steffen Abstract The material point method (MPM) is a computationally effective particle method with mathematical roots in both particle-in-cell and finite element-type methods. The method has proven to be extremely useful in solving solid mechanics problems involving large deformations and/or fragmentation of structures, problem domains that are sometimes problematic for finite element-type methods. Recently, the MPM community has focused significant attention on understanding the basic mathematical error properties of the method. Complementary to this thrust, in this paper we show how spatial and temporal errors are typically coupled within the MPM framework. In an attempt to overcome the challenge to analysis that this coupling poses, we take advantage of MPM's connection to finite element methods by developing a ,moving-mesh' variant of MPM that allows us to use finite element-type error analysis to demonstrate and understand the spatial and temporal error behaviors of MPM. We then provide an analysis and demonstration of various spatial and temporal errors in MPM and in simplified MPM-type simulations. Our analysis allows us to anticipate the global error behavior in MPM-type methods and allows us to estimate the time-step where spatial and temporal errors are balanced. Larger time-steps result in solutions dominated by temporal errors and show second-order temporal error convergence. Smaller time-steps result in solutions dominated by spatial errors, and hence temporal refinement produces no appreciative change in the solution. Based upon our understanding of MPM from both analysis and numerical experimentation, we are able to provide to MPM practitioners a collection of guidelines to be used in the selection of simulation parameters that respect the interplay between spatial (grid) resolution, number of particles and time-step. Copyright © 2009 John Wiley & Sons, Ltd. [source] Simple modifications for stabilization of the finite point methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2005B. Boroomand Abstract A stabilized version of the finite point method (FPM) is presented. A source of instability due to the evaluation of the base function using a least square procedure is discussed. A suitable mapping is proposed and employed to eliminate the ill-conditioning effect due to directional arrangement of the points. A step by step algorithm is given for finding the local rotated axes and the dimensions of the cloud using local average spacing and inertia moments of the points distribution. It is shown that the conventional version of FPM may lead to wrong results when the proposed mapping algorithm is not used. It is shown that another source for instability and non-monotonic convergence rate in collocation methods lies in the treatment of Neumann boundary conditions. Unlike the conventional FPM, in this work the Neumann boundary conditions and the equilibrium equations appear simultaneously in a weight equation similar to that of weighted residual methods. The stabilization procedure may be considered as an interpretation of the finite calculus (FIC) method. The main difference between the two stabilization procedures lies in choosing the characteristic length in FIC and the weight of the boundary residual in the proposed method. The new approach also provides a unique definition for the sign of the stabilization terms. The reasons for using stabilization terms only at the boundaries is discussed and the two methods are compared. Several numerical examples are presented to demonstrate the performance and convergence of the proposed methods. Copyright © 2005 John Wiley & Sons, Ltd. [source] A computational model for impact failure with shear-induced dilatancyINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 14 2003Z. Chen Abstract It has been observed in plate impact experiments that some brittle solids may undergo elastic deformation at the shock wave front, and fail catastrophically at a later time when they are shocked near but below the apparent Hugoniot elastic limit. Because this phenomenon appears to have features different from those of usual inelastic waves, it has been interpreted as the failure wave. To design an effective numerical procedure for simulating impact failure responses, a three-dimensional computational damage model is developed in this paper. The propagation of the failure wave behind the elastic shock wave is described by a non-linear diffusion equation. Macroscopic shear-induced dilatancy is assumed and treated as a one-to-one measure of the mean intensity of microcracking. The damage evolution in time is determined based on the assumption that the deviatoric strain energy in the elastically compressed material (undamaged) is converted, through the damaging process, into the volumetric potential energy in the comminuted and dilated material. For the ease in large-scale simulations, the coupled damage diffusion equation and the stress wave equation are solved via a staggered manner in a single computational domain. Numerical solutions by using both the finite element method and the material point method, i.e. with and without a rigid mesh connectivity, are presented and compared with the experimental data available. It is shown that the model simulations capture the essential features of the failure wave phenomenon observed in shock glasses, and that the numerical solutions for localized failure are not mesh-dependent. Copyright © 2003 John Wiley & Sons, Ltd. [source] A general non-linear optimization algorithm for lower bound limit analysisINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2003Kristian Krabbenhoft Abstract The non-linear programming problem associated with the discrete lower bound limit analysis problem is treated by means of an algorithm where the need to linearize the yield criteria is avoided. The algorithm is an interior point method and is completely general in the sense that no particular finite element discretization or yield criterion is required. As with interior point methods for linear programming the number of iterations is affected only little by the problem size. Some practical implementation issues are discussed with reference to the special structure of the common lower bound load optimization problem, and finally the efficiency and accuracy of the method is demonstrated by means of examples of plate and slab structures obeying different non-linear yield criteria. Copyright © 2002 John Wiley & Sons, Ltd. [source] Solving time-dependent PDEs using the material point method, a case study from gas dynamicsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 7 2010L. T. Tran Abstract The material point method (MPM) developed by Sulsky and colleagues is currently being used to solve many challenging problems involving large deformations and/or fragementations with some success. In order to understand the properties of this method, an analysis of the considerable computational properties of MPM is undertaken in the context of model problems from gas dynamics. The MPM method in the form used here is shown both theoretically and computationally to have first-order accuracy for a standard gas dynamics test problem. Copyright © 2009 John Wiley & Sons, Ltd. [source] A hybrid immersed boundary and material point method for simulating 3D fluid,structure interaction problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2008Anvar Gilmanov Abstract A numerical method is developed for solving the 3D, unsteady, incompressible Navier,Stokes equations in curvilinear coordinates containing immersed boundaries (IBs) of arbitrary geometrical complexity moving and deforming under forces acting on the body. Since simulations of flow in complex geometries with deformable surfaces require special treatment, the present approach combines a hybrid immersed boundary method (HIBM) for handling complex moving boundaries and a material point method (MPM) for resolving structural stresses and movement. This combined HIBM & MPM approach is presented as an effective approach for solving fluid,structure interaction (FSI) problems. In the HIBM, a curvilinear grid is defined and the variable values at grid points adjacent to a boundary are forced or interpolated to satisfy the boundary conditions. The MPM is used for solving the equations of solid structure and communicates with the fluid through appropriate interface-boundary conditions. The governing flow equations are discretized on a non-staggered grid layout using second-order accurate finite-difference formulas. The discrete equations are integrated in time via a second-order accurate dual time stepping, artificial compressibility scheme. Unstructured, triangular meshes are employed to discretize the complex surface of the IBs. The nodes of the surface mesh constitute a set of Lagrangian control points used for tracking the motion of the flexible body. The equations of the solid body are integrated in time via the MPM. At every instant in time, the influence of the body on the flow is accounted for by applying boundary conditions at stationary curvilinear grid nodes located in the exterior but in the immediate vicinity of the body by reconstructing the solution along the local normal to the body surface. The influence of the fluid on the body is defined through pressure and shear stresses acting on the surface of the body. The HIBM & MPM approach is validated for FSI problems by solving for a falling rigid and flexible sphere in a fluid-filled channel. The behavior of a capsule in a shear flow was also examined. Agreement with the published results is excellent. Copyright © 2007 John Wiley & Sons, Ltd. [source] A novel finite point method for flow simulationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2002M. Cheng Abstract A novel finite point method is developed to simulate flow problems. The mashes in the traditional numerical methods are supplanted by the distribution of points in the calculation domain. A local interpolation based on the properties of Taylor series expansion is used to construct an approximation for unknown functions and their derivatives. An upwind-dominated scheme is proposed to efficiently handle the non-linear convection. Comparison with the finite difference solutions for the two-dimensional driven cavity flow and the experimental results for flow around a cylinder shows that the present method is capable of satisfactorily predicting the flow separation characteristic. The present algorithm is simple and flexible for complex geometric boundary. The influence of the point distribution on computation time and accuracy of results is included. Copyright © 2002 John Wiley & Sons, Ltd. [source] A hybrid search combining interior point methods and metaheuristics for 0,1 programmingINTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH, Issue 6 2002Agnès Plateau Our search deals with methods hybridizing interior point processes and metaheuristics for solving 0,1 linear programs. This paper shows how metaheuristics can take advantage of a sequence of interior points generated by an interior point method. After introducing our work field, we present our hybrid search which generates a diversified population. Next, we explain the whole method combining the solutions encountered in the previous phase through a path relinking template. Computational experiments are reported on 0,1 multiconstraint knapsack problems. [source] Maximum bite force after the replacement of complete denturesJOURNAL OF ORAL REHABILITATION, Issue 9 2002F. MÜLLER In complete denture wearers the maximum bite force (MBF) is known to be considerably lower than in dentate people. Low MBF might therefore be an indication of poor denture fit but there is limited evidence on this. Therefore, the aim of the present study was to investigate whether MBF can be improved by the replacement of complete dentures for elderly people. Nine edentulous volunteers, average age 74·2 ± 5·5 years and average denture experience 19·4 ± 19·5 years (1,50 years), had replacement dentures made. Functional impressions were taken after border moulding using zinc oxide eugenol paste. After a rehearsal session, MBF was recorded with the old dentures, and with the new dentures immediately at insertion, at 3, 8 days, 2,3 weeks, 1, 2, 3 and 6,10 months post-insertion (p.i.). The MBF was recorded with the central bearing point method using a full-bridge strain gauge with a confirmed linearity from 1 to 1000 N and an accuracy of ±1 N. Data were analysed off-line using the mean of two peak readings per patient per session. The results indicate that MBF tended to be impaired when replacement dentures were first fitted (n.s.). However, this trend reversed during the first month p.i. for patients with a ,moderate' lower ridge resorption of Atwood (1963) grade 3 or 4 (n=5). Patients with more severe lower ridge resorption (Atwood grade 5 or 6; n=4) showed a significantly lower MBF over the entire observation period (P=0·05) and took longer to regain bite strength. Only patients with moderate bone resorption exceeded their pre-insertion level of MBF within the observation period of 6,10 months p.i. In contrast to one report of immediate improvement of MBF at insertion of a new or relined denture (Leyka et al., 2000), the present study suggests that, at least for elderly patients with severe bone resorption, delayed improvement of MBF should be expected. [source] Proximal point method for optimal control processes governed by ordinary differential equations,ASIAN JOURNAL OF CONTROL, Issue 1 2010Vadim Azhmyakov Abstract This paper is concerned with the proximal-based approach to linear and finite-difference approximations of constrained convex optimal control problems. We consider control systems governed by ordinary differential equations in the presence of additional terminal/state inequalities and propose a numerical method derived from the proximal point algorithm. The aim of the paper is to study the convergence properties of the obtained conceptual algorithm and to show that it can be used to compute approximate optimal controls. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source] Joint inversion of multiple data types with the use of multiobjective optimization: problem formulation and application to the seismic anisotropy investigationsGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 2 2007E. Kozlovskaya SUMMARY In geophysical studies the problem of joint inversion of multiple experimental data sets obtained by different methods is conventionally considered as a scalar one. Namely, a solution is found by minimization of linear combination of functions describing the fit of the values predicted from the model to each set of data. In the present paper we demonstrate that this standard approach is not always justified and propose to consider a joint inversion problem as a multiobjective optimization problem (MOP), for which the misfit function is a vector. The method is based on analysis of two types of solutions to MOP considered in the space of misfit functions (objective space). The first one is a set of complete optimal solutions that minimize all the components of a vector misfit function simultaneously. The second one is a set of Pareto optimal solutions, or trade-off solutions, for which it is not possible to decrease any component of the vector misfit function without increasing at least one other. We investigate connection between the standard formulation of a joint inversion problem and the multiobjective formulation and demonstrate that the standard formulation is a particular case of scalarization of a multiobjective problem using a weighted sum of component misfit functions (objectives). We illustrate the multiobjective approach with a non-linear problem of the joint inversion of shear wave splitting parameters and longitudinal wave residuals. Using synthetic data and real data from three passive seismic experiments, we demonstrate that random noise in the data and inexact model parametrization destroy the complete optimal solution, which degenerates into a fairly large Pareto set. As a result, non-uniqueness of the problem of joint inversion increases. If the random noise in the data is the only source of uncertainty, the Pareto set expands around the true solution in the objective space. In this case the ,ideal point' method of scalarization of multiobjective problems can be used. If the uncertainty is due to inexact model parametrization, the Pareto set in the objective space deviates strongly from the true solution. In this case all scalarization methods fail to find the solution close to the true one and a change of model parametrization is necessary. [source] Inverse Modeling of Coastal Aquifers Using Tidal Response and Hydraulic TestsGROUND WATER, Issue 6 2007Andrés Alcolea Remediation of contaminated aquifers demands a reliable characterization of hydraulic connectivity patterns. Hydraulic diffusivity is possibly the best indicator of connectivity. It can be derived using the tidal response method (TRM), which is based on fitting observations to a closed-form solution. Unfortunately, the conventional TRM assumes homogeneity. The objective of this study was to overcome this limitation and use tidal response to identify preferential flowpaths. Additionally, the procedure requires joint inversion with hydraulic test data. These provide further information on connectivity and are needed to resolve diffusivity into transmissivity and storage coefficient. Spatial variability is characterized using the regularized pilot points method. Actual application may be complicated by the need to filter tidal effects from the response to pumping and by the need to deal with different types of data, which we have addressed using maximum likelihood methods. Application to a contaminated artificial coastal fill leads to flowpaths that are consistent with the materials used during construction and to solute transport predictions that compare well with observations. We conclude that tidal response can be used to identify connectivity patterns. As such, it should be useful when designing measures to control sea water intrusion. [source] | |||||||||||||