The Experts below are selected from a list of 248508 Experts worldwide ranked by ideXlab platform
D Lesnic - One of the best experts on this subject based on the ideXlab platform.
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steady state nonlinear heat conduction in composite materials using the method of fundamental Solutions
2008Co-Authors: Andreas Karageorghis, D LesnicAbstract:The steady-state heat conduction in composite (layered) heat conductors with temperature dependent thermal conductivity and mixed boundary conditions involving convection and radiation is investigated using the method of fundamental Solutions with Domain decomposition. The locations of the singularities outside the Solution Domain are optimally determined using a non-linear least-squares procedure. Numerical results for non-linear bimaterials are presented and discussed.
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a three dimensional boundary determination problem in potential corrosion damage
2005Co-Authors: N S Mera, D LesnicAbstract:In this paper we consider the identification of the geometric structure of the boundary of the Solution Domain for the three-dimensional Laplace equation. We investigate the determination of the shape of an unknown portion of the boundary of a Solution Domain from Cauchy data on the remaining portion of the boundary. This problem arises in the study of quantitative non-destructive evaluation of corrosion in materials in which boundary measurements of currents and voltages are used to determine the material loss caused by corrosion. The Domain identification problem is considered as a variational problem to minimize a defect functional, which utilises some additional data on certain known parts of the boundary. A sequential quadratic programming (SQP) optimization algorithm is used in order to minimise the objective functional. The unknown boundary is parameterized using B-splines. The Laplace equation is discretised using the method of fundamental Solutions (MFS). Numerical results are presented and discussed for several test examples.
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the method of fundamental Solutions for the cauchy problem associated with two dimensional helmholtz type equations
2005Co-Authors: Liviu Marin, D LesnicAbstract:In this paper, the application of the method of fundamental Solutions to the Cauchy problem associated with two-dimensional Helmholtz-type equations is investigated. The resulting system of linear algebraic equations is ill-conditioned and therefore its Solution is regularized by employing the first-order Tikhonov functional, while the choice of the regularization parameter is based on the L-curve method. Numerical results are presented for both smooth and piecewise smooth geometries. The convergence and the stability of the method with respect to increasing the number of source points and the distance between the source points and the boundary of the Solution Domain, and decreasing the amount of noise added into the input data, respectively, are analysed.
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the method of fundamental Solutions for the cauchy problem in two dimensional linear elasticity
2004Co-Authors: Liviu Marin, D LesnicAbstract:In this paper, the application of the method of fundamental Solutions to the Cauchy problem in two-dimensional isotropic linear elasticity is investigated. The resulting system of linear algebraic equations is ill-conditioned and therefore its Solution is regularised by employing the first-order Tikhonov functional, while the choice of the regularisation parameter is based on the L-curve method. Numerical results are presented for both smooth and piecewise smooth geometries, as well as for constant and linear stress states. The convergence and the stability of the method with respect to increasing the number of source points and the distance between the source points and the boundary of the Solution Domain, and decreasing the amount of noise added into the input data, respectively, are analysed.
Liviu Marin - One of the best experts on this subject based on the ideXlab platform.
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an invariant method of fundamental Solutions for two dimensional steady state anisotropic heat conduction problems
2016Co-Authors: Liviu MarinAbstract:Abstract We investigate both theoretically and numerically the so-called invariance property, see e.g. Sun and Ma (2015a,b), of the Solution of boundary value problems associated with the anisotropic heat conduction equation (or Laplace–Beltrami’s equation) in two dimensions with respect to elementary transformations of the Solution Domain, e.g. dilations or contractions. We also show that the standard method of fundamental Solutions (MFS) does not satisfy the invariance property. Motivated by these reasons, we introduce, in a natural manner, a modified version of the MFS that remains invariant under elementary transformations of the Solution Domain and is referred to as the invariant MFS (IMFS). Five two-dimensional examples are thoroughly investigated to assess the numerical accuracy, convergence and stability of the proposed IMFS, in conjunction with the Tikhonov regularization method (Tikhonov and Arsenin, 1986) and Morozov’s discrepancy principle (Morozov, 1966), for Laplace–Beltrami’s equation with perturbed boundary conditions.
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a meshless method for solving the cauchy problem in three dimensional elastostatics
2005Co-Authors: Liviu MarinAbstract:The application of the method of fundamental Solutions to the Cauchy problem in three-dimensional isotropic linear elasticity is investigated. The resulting system of linear algebraic equations is ill-conditioned and therefore, its Solution is regularized by employing the first-order Tikhonov functional, while the choice of the regularization parameter is based on the L-curve method. Numerical results are presented for both under- and equally-determined Cauchy problems in a piece-wise smooth geometry. The convergence, accuracy, and stability of the method with respect to increasing the number of source points and the distance between the source points and the boundary of the Solution Domain, and decreasing the amount of noise added into the input data, respectively, are analysed.
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numerical Solution of the cauchy problem for steady state heat transfer in two dimensional functionally graded materials
2005Co-Authors: Liviu MarinAbstract:The application of the method of fundamental Solutions to the Cauchy problem for steady-state heat conduction in two-dimensional functionally graded materials (FGMs) is investigated. The resulting system of linear algebraic equations is ill-conditioned and, therefore, regularization is required in order to solve this system of equations in a stable manner. This is achieved by employing the zeroth-order Tikhonov functional, while the choice of the regularization parameter is based on the L-curve method. Numerical results are presented for both smooth and piecewise smooth geometries. The convergence and the stability of the method with respect to increasing the number of source points and the distance between the source points and the boundary of the Solution Domain, and decreasing the amount of noise added into the input data, respectively, are analysed.
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the method of fundamental Solutions for the cauchy problem associated with two dimensional helmholtz type equations
2005Co-Authors: Liviu Marin, D LesnicAbstract:In this paper, the application of the method of fundamental Solutions to the Cauchy problem associated with two-dimensional Helmholtz-type equations is investigated. The resulting system of linear algebraic equations is ill-conditioned and therefore its Solution is regularized by employing the first-order Tikhonov functional, while the choice of the regularization parameter is based on the L-curve method. Numerical results are presented for both smooth and piecewise smooth geometries. The convergence and the stability of the method with respect to increasing the number of source points and the distance between the source points and the boundary of the Solution Domain, and decreasing the amount of noise added into the input data, respectively, are analysed.
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the method of fundamental Solutions for the cauchy problem in two dimensional linear elasticity
2004Co-Authors: Liviu Marin, D LesnicAbstract:In this paper, the application of the method of fundamental Solutions to the Cauchy problem in two-dimensional isotropic linear elasticity is investigated. The resulting system of linear algebraic equations is ill-conditioned and therefore its Solution is regularised by employing the first-order Tikhonov functional, while the choice of the regularisation parameter is based on the L-curve method. Numerical results are presented for both smooth and piecewise smooth geometries, as well as for constant and linear stress states. The convergence and the stability of the method with respect to increasing the number of source points and the distance between the source points and the boundary of the Solution Domain, and decreasing the amount of noise added into the input data, respectively, are analysed.
Jian Lin - One of the best experts on this subject based on the ideXlab platform.
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backtracking search based hyper heuristic for the flexible job shop scheduling problem with fuzzy processing time
2019Co-Authors: Jian LinAbstract:Abstract Flexible job-shop scheduling problem (FJSP) is among the most investigated scheduling problems over the past decades. The uncertainty of the processing time is an important practical characteristic in manufacturing. By considering the processing time to be fuzzy variable, the FJSP with fuzzy processing time (FJSPF) is more close to the reality. This paper proposes an effective backtracking search based hyper-heuristic (BS-HH) approach to address the FJSPF. Firstly, six simple and efficient heuristics are incorporated into the BS-HH to construct a set of low-level heuristics. Secondly, a backtracking search algorithm is introduced as the high-level strategy to manage the low-level heuristics to operate on the Solution Domain. Additionally, a novel hybrid Solution decoding scheme is proposed to find an optimal Solution more efficiently. Finally, the performance of the BS-HH is evaluated on two typical benchmark sets. The results show that the proposed hyper-heuristic outperforms the state-of-the-art algorithms in solving the FJSPF.
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differential evolution based hyper heuristic for the flexible job shop scheduling problem with fuzzy processing time
2017Co-Authors: Jian Lin, Dike Luo, Kaizhou Gao, Yanan LiuAbstract:In this paper, a differential evolution based hyper-heuristic (DEHH) algorithm is proposed to solve the flexible job-shop scheduling problem with fuzzy processing time (FJSPF). In the DEHH scheme, five simple and effective heuristic rules are designed to construct a set of low-level heuristics, and differential evolution is employed as the high-level strategy to manipulate the low-level heuristics to operate on the Solution Domain. Additionally, an efficient hybrid machine assignment scheme is proposed to decode a Solution to a feasible schedule. The effectiveness of the DEHH is evaluated on two typical benchmark sets and the computational results indicate the superiority of the proposed hyper-heuristic scheme over the state-of-the-art algorithms.
Rafael Valero - One of the best experts on this subject based on the ideXlab platform.
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smolyak method for solving dynamic economic models lagrange interpolation anisotropic grid and adaptive Domain
2014Co-Authors: Kenneth L Judd, Lilia Maliar, Serguei Maliar, Rafael ValeroAbstract:We show how to enhance the performance of a Smolyak method for solving dynamic economic models. First, we propose a more efficient implementation of the Smolyak method for interpolation, namely, we show how to avoid costly evaluations of repeated basis functions in the conventional Smolyak formula. Second, we extend the Smolyak method to include anisotropic constructions that allow us to target higher quality of approximation in some dimensions than in others. Third, we show how to effectively adapt the Smolyak hypercube to a Solution Domain of a given economic model. Finally, we argue that in large-scale economic applications, a Solution algorithm based on Smolyak interpolation has substantially lower expense when it uses derivative-free fixed-point iteration instead of standard time iteration. In the context of one- and multi-agent optimal growth models, we find that the proposed modifications to the conventional Smolyak method lead to substantial increases in accuracy and speed.
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smolyak method for solving dynamic economic models lagrange interpolation anisotropic grid and adaptive Domain
2013Co-Authors: Kenneth L Judd, Lilia Maliar, Serguei Maliar, Rafael ValeroAbstract:First, we propose a more efficient implementation of the Smolyak method for interpolation, namely, we show how to avoid costly evaluations of repeated basis functions in the conventional Smolyak formula. Second, we extend the Smolyak method to include anisotropic constructions; this allows us to target higher quality of approximation in some dimensions than in others. Third, we show how to effectively adapt the Smolyak hypercube to a Solution Domain of a given economic model. Finally, we advocate the use of low-cost fixed-point iteration, instead of conventional time iteration. In the context of one- and multi-agent growth models, we find that the proposed techniques lead to substantial increases in accuracy and speed of a Smolyak-based projection method for solving dynamic economic models.
Serguei Maliar - One of the best experts on this subject based on the ideXlab platform.
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smolyak method for solving dynamic economic models lagrange interpolation anisotropic grid and adaptive Domain
2014Co-Authors: Kenneth L Judd, Lilia Maliar, Serguei Maliar, Rafael ValeroAbstract:We show how to enhance the performance of a Smolyak method for solving dynamic economic models. First, we propose a more efficient implementation of the Smolyak method for interpolation, namely, we show how to avoid costly evaluations of repeated basis functions in the conventional Smolyak formula. Second, we extend the Smolyak method to include anisotropic constructions that allow us to target higher quality of approximation in some dimensions than in others. Third, we show how to effectively adapt the Smolyak hypercube to a Solution Domain of a given economic model. Finally, we argue that in large-scale economic applications, a Solution algorithm based on Smolyak interpolation has substantially lower expense when it uses derivative-free fixed-point iteration instead of standard time iteration. In the context of one- and multi-agent optimal growth models, we find that the proposed modifications to the conventional Smolyak method lead to substantial increases in accuracy and speed.
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smolyak method for solving dynamic economic models lagrange interpolation anisotropic grid and adaptive Domain
2013Co-Authors: Kenneth L Judd, Lilia Maliar, Serguei Maliar, Rafael ValeroAbstract:First, we propose a more efficient implementation of the Smolyak method for interpolation, namely, we show how to avoid costly evaluations of repeated basis functions in the conventional Smolyak formula. Second, we extend the Smolyak method to include anisotropic constructions; this allows us to target higher quality of approximation in some dimensions than in others. Third, we show how to effectively adapt the Smolyak hypercube to a Solution Domain of a given economic model. Finally, we advocate the use of low-cost fixed-point iteration, instead of conventional time iteration. In the context of one- and multi-agent growth models, we find that the proposed techniques lead to substantial increases in accuracy and speed of a Smolyak-based projection method for solving dynamic economic models.
