Narrow Results

In this paper a family of hybrid methods with minimal phase-lag are developed for the numerical solution of periodic initial-value problems. The methods are of eighth algebraic order and have large intervals of periodicity. The efficiency of the new methods is presented by their application to the wave equation and to coupled differential equations of the Schrödinger type.

In this paper a dissipative trigonometrically-fitted two-step explicit hybrid method is developed. This method is based on a dissipative explicit two-step method developed recently by Papageorgiou, Tsitouras and Famelis.⁶ Numerical examples show that the procedure of trigonometrical fitting is the only way in one to produce efficient dissipative methods for the numerical solution of second order initial value problems (IVPs) with oscillating solutions.

In this work we introduce a hybrid ab initio-classical simulation methodology designed to incorporate the chemistry into the description of phenomena that, intrinsically, require very large systems to be properly described. This hybrid approach allows us to conduct large-scale atomistic simulations with a simple classical potential (embedded atom method (EAM), for instance) while simultaneously using a more accurate ab initio approach for critical embedded regions. The coupling is made through shared atomic shells where the two atomistic modeling approaches are relaxed in an iterative, self-consistent manner. The magnitude of the incompatibility forces arising in the shared shell is analyzed, and possible terminations for the embedded region are discussed, as a way to reduce such forces. As a test case, the formation energy of a single vacancy in aluminum at different distances from an edge dislocation is studied. Results obtained using the hybrid approach are compared to those obtained using classical methods alone, and the range of validity for the classical approach is evaluated.

An eighth order exponentially fitted method is developed for the numerical integration of the Schrödinger equation. The formula considered contains certain free parameters which allow it to be fitted automatically to exponential functions. This is the first eighth order exponentially fitted method in the literature. Numerical results also indicate that the new method is much more accurate than other classical and exponentially fitted methods.

Supervised classification has already been the subject of numerous studies in the fields of Statistics, Pattern Recognition and Artificial Intelligence under various appellations which include discriminant analysis, discrimination and concept learning. Many practical applications relating to this field have been developed. New methods have appeared in recent years, due to developments concerning Neural Networks and Machine Learning. These "hybrid" approaches share one common factor in that they combine symbolic and numerical aspects. The former are characterized by the representation of knowledge, the latter by the introduction of frequencies and probabilistic criteria. In the present study, we shall present a certain number of hybrid methods, conceived (or improved) by members of the SYMENU research group. These methods issue mainly from Machine Learning and from research on Classification Trees done in Statistics, and they may also be qualified as "rule-based". They shall be compared with other more classical approaches. This comparison will be based on a detailed description of each of the twelve methods envisaged, and on the results obtained concerning the "Waveform Recognition Problem" proposed by Breiman et al.,⁴ which is difficult for rule based approaches.

In this paper, we consider the Weak Trefftz Discontinuous Galerkin (WTDG) method, which enables one to use at the same time the Finite Element Method (FEM) or Variational Theory of Complex Rays (VTCR) discretizations (polynoms and waves), for vibration problems. It has already been developed such that the FEM and the VTCR can be used in different adjacent subdomains in the same problem. Here, it is revisited and extended in order to allow one to use the two discretizations in the same subdomain, at the same time. Numerical examples illustrate the performances of such an approach.

A basket default swap (BDS) is a credit derivative with contingent payments that are triggered by a combination of default events of the reference entities. A forward-starting basket default swap (FBDS) is a BDS starting at a specified future time. Existing analytic or semi-analytic methods for pricing FBDS are time consuming due to the large number of possible default combinations before the BDS starts. This paper develops a fast approximation method for FBDS based on the conditional independence framework. The method converts the pricing of a FBDS to an equivalent BDS pricing problem and combines Monte Carlo simulation with an analytic approach to achieve an effective method. This hybrid method is a novel technique which can be viewed either as a means to accelerate the convergence of Monte Carlo simulation or as a way to estimate parameters in an analytic method that are difficult to compute directly. Numerical results demonstrate the accuracy and efficiency of the proposed hybrid method.

Traditionally, ocean acoustic propagation models assume the sea surface can be treated as an idealized pressure release boundary. For flat surfaces, this can easily be accomplished through a variety of modeling techniques. Rough surfaces, however, introduce additional complexities in numerical models which assume a pressure release condition. An alternative approach is to model the physical water/air interface in a manner analogous to the water/sediment interface of the bottom. However, the ocean surface boundary introduces a much larger interface discontinuity than the bottom interface. In this work, a previously developed hybrid split-step Fourier/finite-difference approach is implemented at the water/air interface. Results are compared with standard SSF smoothing approaches. Normal mode and finite element models are utilized to provide benchmark solutions. Tradeoffs between accuracy and stability are discussed, as well as the model’s ability to accurately compute transmission across the water/air interface.

A hybrid has two or more components that produce the same or better results, for example, a vehicle powered by both an electric motor and an internal combustion engine as sources of power for the drive train. We apply the hybrid algorithm of the particle swarm optimization (PSO) and Nelder–Mead (NM) simplex method for finite element model (FEM) updating. The results observed showed that on average the hybrid gave results that were more accurate, followed by the PSO and then the NM simplex method.