Browsing by Subject "Numerical analysis."

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Open Access
Kronecker-based infinite level-dependent QBDS : matrix analytic solution versus simulation
(2011) Orhan, Muhsin Can
Markovian systems with multiple interacting subsystems under the influence of a control unit are considered. The state spaces of the subsystems are countably in- finite, whereas that of the control unit is finite. A recent infinite level-dependent quasi-birth-and-death (LDQBD) model for such systems is extended by facilitating the automatic representation and generation of the nonzero blocks in its underlying infinitesimal generator matrix with sums of Kronecker products. Experiments are performed on systems of stochastic chemical kinetics having two or more countably infinite state space subsystems. Results indicate that, albeit more memory consuming, there are many cases where a matrix analytic solution coupled with Lyapunov theory yields a faster and more accurate steady-state measure compared to that obtained with simulation.
Open Access
Towards practice real-time water simulations : multiphase smoothed particle hydrodynamics (M-SPH)
(2008) Gökdoğan, Göktuğ F.
Simulation of water and other fluid phenomena have always been a popular topic in the computer graphics research area and many solutions provided in this topic covers many fluid simulation aspects. However, with the complex nature of physics of fluid dynamics, usually these solutions are not applicable to the real-time domain, especially interactive applications like computer games. The solutions that both target a realistic behavior and real-time CPU boundaries tend to solve the problem by utilizing Smoothed Particle Hydrodynamics (SPH) technique in the solution of Navier-Stokes equations. In this study, we introduce a novel approach for modeling of the water dynamics with multiple layers of SPH. This approach increases the level of detail in the constructed water surfaces while decreasing the required overall computation time. To achieve this, an extra SPH layer is introduced to use larger particles to fill most of the fluid volume which helps to simulate general fluid behavior in less numbers while utilizing other extra SPH layers with small particles to fill up in-betweens for finer detail in water surfaces. The performance gain can be up to several magnitudes with the increase of the water size while maintaining visually similar or more appealing results.