Dirichlet problems with nonsmooth boundary

Multisymplectic Schemes for the Complex Modified Korteweg-de Vries Equation AYDIN, AYHAN; Karasözen, Bülent (2008-09-20) In this paper, the multisymplectic formulation of the CMKdV(complex modified Korteweg-de Vries equation) is derived. Based on the multisymplectic formulation, the eight-point multisymplectic Preissman scheme and a linear-nonlinear multisymplectic splitting scheme are developed. Both methods are compared numerically with respect to the conservation of local and global quantities of the CMKdV equation.
Optimal control and reduced order modelling of Fitzhugh–Nagumo equation Küçükseyhan , Tuğba; Karasözen, Bülent; Uzunca, Murat; Department of Scientific Computing (2017) In this thesis, we investigate model order reduction and optimal control of FitzHugh-Nagumo equation (FHNE). FHNE is coupled partial differential equations (PDEs) of activator-inhibitor types. Diffusive FHNE is a model for the transmission of electrical impulses in a nerve axon, whereas the convective FHNE is a model for blood coagulation in a moving excitable media. We discretize these state FHNEs using a symmetric interior penalty Galerkin (SIPG) method in space and an average vector field (AVF) method in...
Recent results on Bayesian Cramér-Rao bounds for jump Markov systems Fritsche, Carsten; Orguner, Umut; Svensson, Lennart; Gustafsson, Fredrik (2016-07-08) In this paper, recent results on the evaluation of the Bayesian Cramer-Rao bound for jump Markov systems are presented. In particular, previous work is extended to jump Markov systems where the discrete mode variable enters into both the process and measurement equation, as well as where it enters exclusively into the measurement equation. Recursive approximations are derived with finite memory requirements as well as algorithms for checking the validity of these approximations are established. The tightnes...
FINITE DIFFERENCE APPROXIMATIONS OF VARIOUS STEKLOV EIGENVALUE PROBLEMS ÖZALP, MÜCAHİT; Bozkaya, Canan; Türk, Önder; Department of Mathematics (2022-8-26) In this thesis, the finite difference method (FDM) is employed to numerically solve differently defined Steklov eigenvalue problems (EVPs) that are characterized by the existence of a spectral parameter on the whole or a part of the domain boundary. The FDM approximation of the Laplace EVP is also considered due to the fact that the defining differential operator in a Steklov EVP is the Laplace operator. The fundamentals of FDM are covered and their applications on some BVPs involving Laplace operator are d...
Derivative free optimization methods for optimizing stirrer configurations Uğur, Ömür; SCHAEFER, M.; YAPICI, KEREM (2008-12-16) In this paper a numerical approach for the optimization of stirrer configurations is presented. The methodology is based on a flow solver, and a mathematical optimization tool, which are integrated into an automated procedure. The flow solver is based on the discretization of the incompressible Navier-Stokes equations by means of a fully conservative finite-volume method for block-structured, boundary-fitted grids, for allowing a flexible discretization of complex stirrer geometries. Two derivative free opt...

Citation Formats

A. Celebi, “Dirichlet problems with nonsmooth boundary,” 2002, vol. 147, p. 295, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/63329.