Narrow Results

The importance of circuit simulation in the design of VLSI circuits has channelised research work in the direction of finding methods to speedup this highly compute-intensive problem. On one hand, attempts have been made to find better algorithms and use faster hardware; and on the other hand, to use parallel architectures for accelerating the circuit simulation task. In this paper, we examine the various issues involved in parallelizing two well-known circuit simulation approaches – direct methods and relaxation methods. A number of parallel computer architectures which have been used for this purpose are also surveyed.

Many direct methods of solution are available for solving nonlinear Volterra integral and integro-differential equations. All of these methods are inherently serial and therefore have not received much attention for use on a vector or parallel computer. It is possible, however, to make modest gains in speedup by employing some novel approaches to existing methods. These modifications are discussed and numerical examples illustrate the results.

We study the existence of minimizers of a regularized non-convex functional in the context of variable exponent Sobolev spaces by application of the direct method in the calculus of variations. The results are new even in the framework of classical Lebesgue spaces.

This paper is concerned with the active control of sound fields in enclosures. Specifically, the numerical problem of determining the optimum locations of control sensors and actuators is addressed. A new method for determining the optimum secondary sources strength is proposed, based on the explicit prediction of the sound field, which makes the simulation of realistic acoustical applications feasible, in terms of the enclosure's boundary conditions. The irregular geometry of a car cabin with complex boundary conditions is used in order to demonstrate the application of the new method to a test case where the existing methods cannot theoretically apply without resolving to significant numerical error. The new method of determining the secondary sources strength is combined with a modified genetic and a gradient optimization algorithm so as to locate the optimum positions of active noise control transducers for global sound field control. The overall algorithm, constituting of the method for calculating the secondary sources' strength and the optimization algorithms, is adjusted with computational improvements for better performance.

Jumps can be seen in many natural processes. Classical deterministic modeling approach explains the dynamical behavior of such systems by using impulsive differential equations. This modeling strategy assumes that the dynamical behavior of the whole system is deterministic, continuous, and it adds jumps to the state vector at certain times. Although deterministic approach is satisfactory in many cases, it is a well-known fact that stochasticity or uncertainty has crucial importance for dynamical behavior of many others. In this study, we propose to include this abrupt change in the stochastic modeling approach, beside the deterministic one. In our model, we introduce jumps to chemical master equation and use the Gillespie direct method to simulate the evolutionary system. To illustrate the idea and distinguish the differences, we present some numerically solved examples.

The two point boundary value problems (BVPs) occur in a wide variety of applications especially in sciences such as chemistry and biology. In this paper, we propose two point direct method of order six for solving nonlinear two point boundary value problems directly. This method is presented in a simple form of Adams Mouton type and determines the approximate solution at two point simultaneously. The method will be implemented using constant step size via shooting technique adapted with three-step iterative method. Numerical results are given to compare the efficiency of the proposed method with the Runge-Kutta and bvp4c method.