Browsing by Subject "Approximation theory."

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Open Access
Approximate dynamic programming approach for sequential change diagnosis problem
(2013) Akbulut, Elif
We study sequential change diagnosis problem which is the combination of change diagnosis and multi-hypothesis testing problem. One observes a sequence of independent and identically distributed random variables. At a sudden disorder time, the probability distribution of the random variables change. The disorder time and its cause are unavailable to the observer. The problem is to detect this abrupt change in the distribution of the random process as quickly as possible and identify its cause as accurately as possible. Dayanık et al. [Dayanık, Goulding and Poor, Bayesian sequential change diagnosis, Mathematics of Operations Research, vol. 45, pp. 475-496, 2008] reduce the problem to a Markov optimal stopping problem and provide an optimal sequential decision strategy. However, only a small subset of the problems is computationally feasible due to curse of dimensionality. The subject of this thesis is to search for the means to overcome the curse of dimensionality. To this end, we propose several approximate dynamic programming algorithms to solve large change diagnosis problems. On several numerical examples, we compare their performance against the performance of optimal dynamic programming solution.
Open Access
Low-temperature thermodynamics of finite and discrete quartic quantum oscillator in one dimension
(1999) Sıddıki, Afif
I.' this work we examined a quartic Hamiltonian using two different approaches. We first introduced a mean-field Gaussian approximation in order to handle this Hamiltonian analytically and observed that this approximation is insufficient for all coupling strengths. Hence we applied second and third order non-degenerate time-independent perturbation and obtained third or- ■ ler correcHo
Open Access
A three-dimensional nonlinear finite element method implementation toward surgery simulation
(2011) Gülümser, Emir
Finite Element Method (FEM) is a widely used numerical technique for finding approximate solutions to the complex problems of engineering and mathematical physics that cannot be solved with analytical methods. In most of the applications that require simulation to be fast, linear FEM is widely used. Linear FEM works with a high degree of accuracy with small deformations. However, linear FEM fails in accuracy when large deformations are used. Therefore, nonlinear FEM is the suitable method for crucial applications like surgical simulators. In this thesis, we propose a new formulation and finite element solution to the nonlinear 3D elasticity theory. Nonlinear stiffness matrices are constructed by using the Green-Lagrange strains (large deformation), which are derived directly from the infinitesimal strains (small deformation) by adding the nonlinear terms that are discarded in infinitesimal strain theory. The proposed solution is a more comprehensible nonlinear FEM for those who have knowledge about linear FEM since the proposed method directly derived from the infinitesimal strains. We implemented both linear and nonlinear FEM by using same material properties with the same tetrahedral elements to examine the advantages of nonlinear FEM over the linear FEM. In our experiments, it is shown that nonlinear FEM gives more accurate results when compared to linear FEM when rotations and high external forces are involved. Moreover, the proposed nonlinear solution achieved significant speed-ups for the calculation of stiffness matrices and for the solution of a system as a whole.