The Experts below are selected from a list of 3798 Experts worldwide ranked by ideXlab platform

Y.z. Chen - One of the best experts on this subject based on the ideXlab platform.

  • evaluation of the t stress and stress intensity factor for a cracked plate in general case using Eigenfunction Expansion variational method
    Fatigue & Fracture of Engineering Materials & Structures, 2008
    Co-Authors: Y.z. Chen, X.y. Lin, Z. X. Wang
    Abstract:

    This paper investigates the T-stress and stress intensity factor for a cracked plate in general case. In the general case, the shape of boundary and the applied loading are arbitrary. The Eigenfunction Expansion variational method (EEVM) is developed to evaluate the T-stress and stress intensity factor. For the traction boundary value problem, the EEVM is equivalent to the theorem of least potential energy in elasticity. Therefore, the EEVM possesses a clear physical meaning and it does not depend on any boundary collocation scheme. Several numerical examples are presented, which include: (1) a line crack in circular plate and (2) a line crack in rectangular plate. Numerical examination for convergence in an example is carried out.

  • Eigenfunction Expansion variational method for stress intensity factor and T-stress evaluation of a circular cracked plate
    Acta Mechanica, 2007
    Co-Authors: Y.z. Chen, X.y. Lin
    Abstract:

    In this paper, the Eigenfunction Expansion variational method (Abbreviated as EEVM) is developed to solve the T-stress problem of the circular cracked plate. In the traction boundary value problem, EEVM is equivalent to the theorem of least potential energy in elasticity. Therefore, EEVM possesses a clear physical meaning. EEVM does not need any boundary collocation scheme. For the circular cracked plate, the following boundary value problems are solved: (a) with a uniform normal loading on the boundary, (b) with a partial loading on the boundary, (c) under mixed boundary condition. For the circular cracked plate with applied concentrated forces, after using the superposition principle and EEVM, the boundary value problem is solved. In the numerical examples, many computed results for stress intensity factor (SIF) and T-stress are presented. Some of computed results for T-stress are first presented in this paper.

  • Eigenfunction Expansion variational method for the solution of a cusp crack problem in a finite plate
    Acta Mechanica, 2004
    Co-Authors: Y.z. Chen
    Abstract:

    In this paper, the EEF (Eigenfunction Expansion form) for the cusp crack in a finite plate is obtained, and the EEVM (Eigenfunction Expansion variational method) is used to solve the cusp crack problem in a finite plate. Each term in the EEF satisfies the governing equation of elasticity and the traction free condition along the cusp crack. As a result of using EEVM, the final solution for complex potentials is obtainable. It is found that the slenderness of the cusp crack has a significant influence to the SIF (stress intensity factor) at the crack tip. Particular attention is paid to a compression loading applied in the direction of the cusp crack axis. This can make an explanation for the rupture of rock with cusp crack under compression. Finally, numerical examples with the calculated results are presented.

  • stress analysis of a cylindrical bar with a spherical cavity or rigid inclusion by the Eigenfunction Expansion variational method
    International Journal of Engineering Science, 2004
    Co-Authors: Y.z. Chen
    Abstract:

    Axisymmetric tension problem of a round bar containing a spherical cavity or a rigid inclusion is considered in this paper. The bar has a finite length. In order to solve the problem, an Eigenfunction Expansion form is suggested. The Eigenfunction always satisfies the governing equations of elasticity and the traction free condition on the surface of sphere, or the fixed displacement condition on the surface of sphere. The undetermined coefficients in the Eigenfunction Expansion form are determined by the use of the variational method in elasticity. The whole process of solution is called the Eigenfunction Expansion variational method (abbreviated as EEVM) in this paper. The solutions for two cases, one for the bar containing a spherical cavity, other for the bar containing a spherical inclusion, are obtained. Finally, some numerical examples are given and some stress concentration factors for the problem are presented.

  • Eigenfunction Expansion and higher order weight functions of interface cracks
    Journal of Applied Mechanics, 1994
    Co-Authors: Y.z. Chen, Norio Hasebe
    Abstract:

    In this paper the properties of the Eigenfunction Expansion form in the interface crack problem of plane elasticity are discussed in detail. After using the Betti’s reciprocal theorem to the cracked dissimilar bonded body, several path-independent integrals are obtained. All the coefficients in the Eigenfunction Expansion form, including the K1 and K2 values, and the J-integral can be related to corresponding path independent integrals. Possibility for formulating the weight function is also suggested.

Vadim Linetsky - One of the best experts on this subject based on the ideXlab platform.

  • discretely monitored first passage problems and barrier options an Eigenfunction Expansion approach
    Social Science Research Network, 2014
    Co-Authors: Vadim Linetsky
    Abstract:

    This paper develops an Eigenfunction Expansion approach to solve discretely monitored first passage time problems for a rich class of Markov processes, including diffusions and subordinate diffusions with jumps, whose transition or Feynman-Kac semigroups possess Eigenfunction Expansions in L2 spaces. Many processes important in finance are in this class, including OU, CIR, (JD)CEV diffusions and their subordinate versions with jumps. The method represents the solution to a discretely monitored first passage problem in the form of an Eigenfunction Expansion with Expansion coefficients satisfying an explicitly given recursion. A range of financial applications is given, drawn from across equity, credit, commodity, and interest rate markets. Numerical examples demonstrate that even in the case of frequent barrier monitoring, such as daily, approximating discrete first passage time problems with continuous solutions may result in unacceptably large errors in financial applications. This highlights the relevance of the method to financial applications.

  • optimal stopping in infinite horizon an Eigenfunction Expansion approach
    Statistics & Probability Letters, 2014
    Co-Authors: Vadim Linetsky
    Abstract:

    Abstract We develop an Eigenfunction Expansion based value iteration algorithm to solve discrete time infinite horizon optimal stopping problems for a rich class of Markov processes that are important in applications. We provide convergence analysis for the value function and the exercise boundary, and derive easily computable error bounds for value iterations. As an application we develop a fast and accurate algorithm for pricing callable perpetual bonds under the CIR short rate model.

  • Pricing options on scalar diffusions: an Eigenfunction Expansion approach
    2013
    Co-Authors: Dmitry Davydov, Vadim Linetsky
    Abstract:

    This paper develops an Eigenfunction Expansion approach to pricing options on scalar diffusion processes. All derivative securities are unbundled into portfolios of primitive securities termed eigensecurities. Eigensecurities are eigenvectors of the pricing operator (present value operator). Pricing is then immediate by the linearity property of the pricing operator and the eigenvector property of eigensecurities. To illustrate the computational power of the method, we develop two applications: pricing vanilla, single- and double-barrier options under the constant elasticity of variance (CEV) process and interest rate knock-out options in the Cox-Ingersoll-Ross (CIR) term-structure model

  • evaluating callable and putable bonds an Eigenfunction Expansion approach
    Journal of Economic Dynamics and Control, 2012
    Co-Authors: Dongjae Lim, Vadim Linetsky
    Abstract:

    Abstract We propose an efficient method to evaluate callable and putable bonds under a wide class of interest rate models, including the popular short rate diffusion models, as well as their time changed versions with jumps. The method is based on the Eigenfunction Expansion of the pricing operator. Given the set of call and put dates, the callable and putable bond pricing function is the value function of a stochastic game with stopping times. Under some technical conditions, it is shown to have an Eigenfunction Expansion in Eigenfunctions of the pricing operator with the Expansion coefficients determined through a backward recursion. For popular short rate diffusion models, such as CIR, Vasicek, 3/2, the method is orders of magnitude faster than the alternative approaches in the literature. In contrast to the alternative approaches in the literature that have so far been limited to diffusions, the method is equally applicable to short rate jump–diffusion and pure jump models constructed from diffusion models by Bochner's subordination with a Levy subordinator.

  • pricing options on scalar diffusions an Eigenfunction Expansion approach
    Operations Research, 2003
    Co-Authors: Dmitry Davydov, Vadim Linetsky
    Abstract:

    This paper develops an Eigenfunction Expansion approach to pricing options on scalar diffusion processes. All contingent claims are unbundled into portfolios of primitive securities calledeigensecurities. Eigensecurities are eigenvectors (Eigenfunctions) of the pricing operator (present value operator). All computational work is at the stage of finding eigenvalues and Eigenfunctions of the pricing operator. The pricing is then immediate by the linearity of the pricing operator and the eigenvector property of eigensecurities. To illustrate the computational power of the method, we develop two applications:pricing vanilla, single- and double-barrier options under the constant elasticity of variance (CEV) process and interest rate knock-out options in the Cox-Ingersoll-Ross (CIR) term-structure model.

D K Hoffman - One of the best experts on this subject based on the ideXlab platform.

  • distributed approximating functional approach to the fokker planck equation Eigenfunction Expansion
    Journal of Chemical Physics, 1997
    Co-Authors: D S Zhang, Guowei Wei, D J Kouri, D K Hoffman
    Abstract:

    The distributed approximating functional method is applied to the solution of the Fokker–Planck equations. The present approach is limited to the standard Eigenfunction Expansion method. Three typical examples, a Lorentz Fokker–Planck equation, a bistable diffusion model and a Henon–Heiles two-dimensional anharmonic resonating system, are considered in the present numerical testing. All results are in excellent agreement with those of established methods in the field. It is found that the distributed approximating functional method yields the accuracy of a spectral method but with a local method’s simplicity and flexibility for the eigenvalue problems arising from the Fokker–Planck equations.

Pang-shyan Kooi - One of the best experts on this subject based on the ideXlab platform.

  • Cylindrical vector Eigenfunction Expansion of Green dyadics for multilayered anisotropic media and its application to four-layered forest
    IEEE Transactions on Antennas and Propagation, 2004
    Co-Authors: Le-wei Li, Jin-Hou Koh, Tat Soon Yeo, Mook Seng Leong, Pang-shyan Kooi
    Abstract:

    A complete Eigenfunction Expansion of the dyadic Green's functions (DGFs) for planar, arbitrary multilayered anisotropic media using cylindrical vector wave functions is presented. These formulations are constructed based on the principle of scattering superposition. For the scattering dyadic Green's function in each layer, the scattering coefficients of TE and TM modes are determined from the boundary conditions matched at the planar interfaces. The explicit representation of the DGFs after reduction to the isotropic case agrees well with the existing results corresponding to the isotropic media. The general DGFs for multilayered anisotropic media are then reduced to those for a four-layered forest where the trunk layer is modeled as anisotropic medium. Application is further made for radio-wave propagation through forests of a four-layered geometry, whereas it is shown how these Green dyadic formulations are used in a practical way and how the field distributions due to a dipole can be obtained.

Sondipon Adhikari - One of the best experts on this subject based on the ideXlab platform.

  • stochastic finite element response analysis using random Eigenfunction Expansion
    Computers & Structures, 2017
    Co-Authors: S E Pryse, Sondipon Adhikari
    Abstract:

    Abstract A mathematical form for the response of the stochastic finite element analysis of elliptical partial differential equations has been established through summing products of random scalars and random vectors. The method is based upon the eigendecomposition of a system’s stiffness matrix. The computational reduction is achieved by only summing the dominant terms and by approximating the random eigenvalues and the random eigenvectors. An error analysis has been conducted to investigate the effect of the truncation and the approximations. Consequently, a novel error minimisation technique has been applied through the Galerkin error minimisation approach. This has been implemented by utilising the orthogonal nature of the random eigenvectors. The proposed method is used to solve three numerical examples: the bending of a stochastic beam, the flow through a porous media with stochastic permeability and the bending of a stochastic plate. The results obtained through the proposed random Eigenfunction Expansion approach are compared with those obtained by using direct Monte Carlo Simulations and by using polynomial chaos.

  • Uncertainty Propagation Using Random Eigenfunction Expansion Method
    54th AIAA ASME ASCE AHS ASC Structures Structural Dynamics and Materials Conference, 2013
    Co-Authors: Sondipon Adhikari
    Abstract:

    Uncertainty propagation through stochastic elliptic type of partial differential equations are considered. An alternative approach by projecting the solution of the discretized equation into a finite dimensional stochastic vector basis is investigated. It is shown that the solution can be obtained using a reduced series comprising random eigenvalues and eigenvectors of the underlying system matrix. Based on the projection in the stochastic vector basis, a Galerkin error minimization approach is proposed. The constants appearing in the Galerkin method are obtained exactly in closed-form in terms of the random eiegnsolutions. The random eigensolutions in turn are obtained by existing approaches available for the random matrix eigenvalue problems. A hybrid analytical and simulation based computational approach is proposed to obtain the moments and pdf of the solution. The method is illustrated using a stochastic beam problem. The results are compared with the direct Monte Carlo simulation results for different correlation lengths and strengths of randomness.