scholarly journals Introducing the Target-Matrix Paradigm for Mesh Optimization via Node-Movement

2010 ◽  
pp. 67-83 ◽  
Author(s):  
Patrick Knupp
Keyword(s):  
Mesh Optimization ◽  
Target Matrix

scholarly journals Enhancing finite difference approximations for double barrier options: mesh optimization and repeated Richardson extrapolation

2021 ◽  
Author(s):  
Luca Vincenzo Ballestra
Keyword(s):  
Finite Difference ◽  
Optimization Procedure ◽  
Richardson Extrapolation ◽  
Mesh Optimization ◽  
Option Prices ◽  
Barrier Option ◽  
Double Barrier ◽  
Finite Difference Approximations ◽  
Barrier Option Pricing ◽  
Richardson Extrapolation Technique

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.

Research on Mesh Optimization of the Finite Element Calculation about Three-Dimensional Foundation Pit

2012 ◽  
Vol 487 ◽  
pp. 855-859
Author(s):  
Shi Lun Feng ◽  
Yu Ming Zhou ◽  
Pu Lin Li ◽  
Jun Li ◽  
Zhi Yong Li ◽  
...  
Keyword(s):  
Finite Element ◽  
Complex Geometry ◽  
Three Dimensional ◽  
Mesh Optimization ◽  
Design Calculation ◽  
Foundation Pit ◽  
3D Design ◽  
Finite Element Software ◽  
Core Language ◽  
Grid Division

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.

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