The finite-difference time-domain method is a simple but powerful numerical method for simulating full-wave acoustic propagation and scattering. However, the method can demand a large amount of computational resources. Traditionally, continuously curved boundaries are represented in a stair-step fashion and thus accurately modeling scattering from a boundary will require a finer discretization ...

Discretization is defined as the process that divides continuous numeric values into intervals of discrete categorical values. In this article, the concept of cost-based discretization as a pre-processing step to the induction of a classifier is introduced in order to obtain an optimal multi-interval splitting for each numeric attribute. A transparent description of the method and the steps inv...

Discretization error occurs during the approximate numerical solution of differential equations. Of the various sources of numerical error, discretization error is generally the largest and usually the most difficult to estimate. The goal of this paper is to review the different approaches for estimating discretization error and to present a general framework for their classification. The first...

In this paper, the reduced dierential transform method is investigated fora nonlinear partial dierential equation modeling nematic liquid crystals, itis called the Hunter-Saxton equation. The main advantage of this methodis that it can be applied directly to nonlinear dierential equations withoutrequiring linearization, discretization, or perturbation. It is a semi analytical-numerical method t...

The present study involves a novel computational technique, regarding simultaneous use of the pseudo particle method, Poisson integral method and a special-purpose computer originally designed for molecular dynamics simulations (MDGRAPE-3). In the present calculations, the dynamics of two colliding vortex rings have been studied using the vortex method. The present acceleration technique allows...

SUMMARY Continuous pen pressure can be used to operate multi-state widgets such as menus in pen based user interfaces. The number of levels into which the pen pressure space is divided determines the number of states in the multi-state widgets. To increase the optimal number of divisions of the pen pressure space and achieve greater pen pressure usabil-ity, we propose a new discretization metho...

The level-set method is a popular method for interface capturing. One of the advantages of the level-set method is that the curvature and the normal vector of the interface can be readily calculated from the level-set function. However, in cases where the level-set method is used to capture topological changes, the standard discretization techniques for the curvature and the normal vector do no...

To model periodic structures with oblique incident waves/scan angles in FDTD, the field transformation method is successfully used to analyze their characteristics. In the field transformation method, Maxwell’s equations are Floquet-transformed so that only a single period of infinite periodic structure can be modeled in FDTD by using periodic boundary conditions (PBCs). A new discretization me...

In this paper we target at developing discretization-invariant, namely dimension-independent, Markov chain Monte Carlo (MCMC) methods to explore PDEconstrained Bayesian inverse problems in infinite dimensional parameter spaces. In particular, we present two frameworks to achieve this goal: Metropolize-then-discretize and discretize-then-Metropolize. The former refers to the method of first prop...

We present an adaptive Rothe method for two{dimensional problems combining an embedded Runge{Kutta scheme in time and a multi-level nite element discretization in space. The spatial discretization error is controlled by a posteriori error estimates based on interpolation techniques. A computational example for a thermodiiusive ame propagation model illustrates the high accuracy that is possible...