AbstractWe show that the performances of the finite difference method for double barrier option pricing can be strongly enhanced by applying both a repeated Richardson extrapolation technique and a mesh optimization procedure. In particular, first we construct a space mesh that is uniform and aligned with the discontinuity points of the solution being sought. This is accomplished by means of a suitable transformation of coordinates, which involves some parameters that are implicitly defined and whose existence and uniqueness is theoretically established. Then, a finite difference scheme employing repeated Richardson extrapolation in both space and time is developed. The overall approach exhibits high efficacy: barrier option prices can be computed with accuracy close to the machine precision in less than one second. The numerical simulations also reveal that the improvement over existing methods is due to the combination of the mesh optimization and the repeated Richardson extrapolation.
Abaqus finite element software can implement three-dimensional excavation design calculation, so authors used Python of Abaqus core language made the 3D design of foundation pit supporting program come ture and also did intensive study of mesh optimization during the process. Authors also did intensive comparison and analysis about grid division of the complex geometry foundation pit, through a regularization partion about a variety of special-shaped pit, we made the automatic division about the structural grid of all kinds of shapes foundation pit successful. On this basis, we achieved better calculation effects of the model. The article will introduce problems about optimization of grid in procedure.
Abstract
This paper presents a finite element mesh generation algorithm (PREPAT) designed to automatically discretize two-dimensional domains. The mesh generation algorithm is a mapping scheme which creates a uniform isoparametric FE model based on a pre-partitioned domain of the component. The proposed algorithm provides a faster and more accurate tool in the pre-processing phase of a Finite Element Analysis (FEA).
A primary goal of the developed mesh generator is to create a finite element model requiring only essential input from the analyst. As a result, the generator code utilizes only a sketch, based on geometric primitives, and information relating to loading/boundary conditions. These conditions represents the constraints that are propagated throughout the model and the available finite elements are uniformly mapped in the resulting sub-domains.
Relative advantages and limitations of the mesh generator are discussed. Examples are presented to illustrate the accuracy, efficiency and applicability of PREPAT.
Enhancing finite difference approximations for double barrier options: mesh optimization and repeated Richardson extrapolation