Search results for "Discretization"
showing 10 items of 237 documents
ON THE CALCULATION OF THE HEAT CAPACITY IN PATH INTEGRAL MONTE CARLO SIMULATIONS
1992
In Path Integral Monte Carlo simulations the systems partition function is mapped to an equivalent classical one at the expense of a temperature-dependent Hamiltonian with an additional imaginary time dimension. As a consequence the standard relation linking the heat capacity Cv to the energy fluctuations, <E2>−<E>2, which is useful in standard classical problems with temperature-independent Hamiltonian, becomes invalid. Instead, it gets replaced by the general relation [Formula: see text] for the intensive heat capacity estimator; β being the inverse temperature and the subscript P indicates the P-fold discretization in the imaginary time direction. This heatcapacity estimator…
A SYMMETRIC AND POSITIVE DEFINITE BEM FOR 2-D FORCED VIBRATIONS
1997
A BEM formulation for 2D elastodynamics in the time domain has been presented. The formulation gives a resolving system that involves boundary displacements only. The stiffness and mass matrices of the boundary discretized body are frequency independent, symmetric and positive definite
Finite-element design sensitivity analysis for non-linear potential problems
1990
Design sensitivity analysis is performed for the finite-element system arising from the discretization of non-linear potential problems using isoparametric Lagrangian elements. The calculated sensitivity formulae are given in a simple matrix form. Applications to the design of electromagnets and airfoils are given.
On stability issues for IMEX schemes applied to 1D scalar hyperbolic equations with stiff reaction terms
2011
The application of a Method of Lines to a hyperbolic PDE with source terms gives rise to a system of ODEs containing terms that may have very different stiffness properties. In this case, Implicit-Explicit Runge-Kutta (IMEX-RK) schemes are particularly useful as high order time integrators because they allow an explicit handling of the convective terms, which can be discretized using the highly developed shock capturing technology, together with an implicit treatment of the source terms, necessary for stability reasons. Motivated by the structure of the source term in a model problem introduced by LeVeque and Yee in [J. Comput. Phys. 86 (1990)], in this paper we study the preservation of ce…
Nonsmooth Optimization Methods
1999
From the previous chapters we know that after the discretization, elliptic and parabolic hemivariational inequalities can be transformed into substationary point type problems for locally Lipschitz superpotentials and as such will be solved. There is a class of mathematical programming methods especially developed for this type of problems. The aim of this chapter is to give an overview of nonsmooth optimization techniques with special emphasis on the first and the second order bundle methods. We present their basic ideas in the convex case and necessary modifications for nonconvex optimization. We shall use them in the next chapter for the numerical realization of several model examples. L…
Arbitrarily shaped plates analysis via Line Element-Less Method (LEM)
2018
Abstract An innovative procedure is introduced for the analysis of arbitrarily shaped thin plates with various boundary conditions and under generic transverse loading conditions. Framed into Line Element-less Method, a truly meshfree method, this novel approach yields the solution in terms of the deflection function in a straightforward manner, without resorting to any discretization, neither in the domain nor on the boundary. Specifically, expressing the deflection function through a series expansion in terms of harmonic polynomials, it is shown that the proposed method requires only the evaluation of line integrals along the boundary parametric equation. Further, minimization of appropri…
The Exponential Dichotomy under Discretization on General Approximation Scheme
2011
This paper is devoted to the numerical analysis of abstract parabolic problem 𝑢 ( 𝑡 ) = 𝐴 𝑢 ( 𝑡 ) ; 𝑢 ( 0 ) = 𝑢 0 , with hyperbolic generator 𝐴 . We are developing a general approach to establish a discrete dichotomy in a very general setting in case of discrete approximation in space and time. It is a well-known fact that the phase space in the neighborhood of the hyperbolic equilibrium can be split in a such way that the original initial value problem is reduced to initial value problems with exponential decaying solutions in opposite time direction. We use the theory of compact approximation principle and collectively condensing approximation to show that such a decomposition o…
Discovering representative models in large time series databases
2004
The discovery of frequently occurring patterns in a time series could be important in several application contexts. As an example, the analysis of frequent patterns in biomedical observations could allow to perform diagnosis and/or prognosis. Moreover, the efficient discovery of frequent patterns may play an important role in several data mining tasks such as association rule discovery, clustering and classification. However, in order to identify interesting repetitions, it is necessary to allow errors in the matching patterns; in this context, it is difficult to select one pattern particularly suited to represent the set of similar ones, whereas modelling this set with a single model could…
Operator splitting methods for American option pricing
2004
Abstract We propose operator splitting methods for solving the linear complementarity problems arising from the pricing of American options. The space discretization of the underlying Black-Scholes Scholes equation is done using a central finite-difference scheme. The time discretization as well as the operator splittings are based on the Crank-Nicolson method and the two-step backward differentiation formula. Numerical experiments show that the operator splitting methodology is much more efficient than the projected SOR, while the accuracy of both methods are similar.
On incorporating the paradigms of discretization and Bayesian estimation to create a new family of pursuit learning automata
2013
Published version of an article in the journal: Applied Intelligence. Also available from the publisher at: http://dx.doi.org/10.1007/s10489-013-0424-x There are currently two fundamental paradigms that have been used to enhance the convergence speed of Learning Automata (LA). The first involves the concept of utilizing the estimates of the reward probabilities, while the second involves discretizing the probability space in which the LA operates. This paper demonstrates how both of these can be simultaneously utilized, and in particular, by using the family of Bayesian estimates that have been proven to have distinct advantages over their maximum likelihood counterparts. The success of LA-…