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In this paper we will present an effective numerical method for the Black-Scholes equation with transaction costs for the limiting price u(s, t;a). The technique combines the Rothe method with a two-grid (coarse-fine) algorithm for computation of numerical solutions to initial boundary-values problems to this equation. Numerical experiments for comparison the accuracy ant the computational cost of the method with other known numerical schemes are discussed. [ABSTRACT FROM AUTHOR]

The paper shows the a-priori error estimates for the Fedorenko finite superelement method in application to physical problems with small-scale singularities. [ABSTRACT FROM AUTHOR]

Constitutive models for the crystal plasticity have the common objective which relates the behavior of microscopic single crystals in the crystallographic texture to the macroscopic continuum response. This paper presents the texture analysis of polycrystalline materials using the rate-dependent single crystal plasticity to develop a multi-scale description of the mechanism at the grain and aggregate levels. The texture analysis requires a numerical algorithm for integrating the constitutive equations. The implicit deformation gradient approach is employed to update the stresses and texture orientations as an integration algorithm. It considers elastic or plastic deformation gradient as the primary unknown variables and constructs the residual of the elastic and plastic velocity gradients as the governing equations. This algorithm is shown to be an efficient and robust algorithm in rather large time steps. The texture analysis of the asymmetric rolling process is also presented to show investigation of the effect of texture evolution based on the finite element analysis as a numerical example. The analysis result for texture evolution is investigated by comparing the pole figure before and after the asymmetric rolling process. © 2007 American Institute of Physics [ABSTRACT FROM AUTHOR]

The simplified (one step) method also called “inverse approach”(IA) for the numerical analysis of the stamping process has been continuously developed by the authors since the end of the eighties (1, 2, 3, 4). In the present paper we recall the main finite element formulation aspects of a robust IA analysis code, called FAST_STAMP, for an efficient estimation of the large elastoplastic strains (in particular the thickness strains) encountered in deep drawing operations. Our results will be presented and compared with others, obtained either from experiments or from incremental codes such as ABAQUS or STAMPACK. The presentation includes “math based” optimization algorithms and strategies for process parameter design. The cost functions and constraints are mainly express to reduce or control the thickness changes, the localized necking, the wrinkling tendency, the springback effects after forming. The design variables are describing the shape of the blank and the tools, the restraining forces due to drawbeads, material properties such as anisotropy coefficient and hardening exponent. Results will be presented to show the actual capabilities of the coupled analysis and optimization strategy with application to the design of stamping parameters. © 2007 American Institute of Physics [ABSTRACT FROM AUTHOR]

The solution of linear systems of equations is the most time-consuming part in large-scale implicit FE computations of wave propagation problems. Traditionally, direct solvers have been used but recent developments of iterative solvers and precondition techniques may impose a change. In particular, preconditioning by multigrid seems to be favorable for finite element (FE) applications since it has a natural interpretation and substantially improves the rate of convergence of the conventional iterative solvers. The multigrid preconditioner uses a sequence of grids on which the fine-grid residual forces are prolongated to coarser grids and computed corrections are interpolated back to the fine grid such that the fine-grid solution successively is improved. By this technique, large 3D problems, invincible for solvers based on direct methods, can be solved in acceptable time and at low memory requirements. The proposed adaptive multigrid FE-method combines adaptivity and multigrid solution strategy in a sophisticated manner. The sequence of computational grids is successively refined (adapted) and generated according to the guidance of a posteriori error estimates until the solution fulfils a predefined accuracy specification. In contrast to standard adaptive procedures where rejected grids are deleted, the adaptive multigrid algorithm uses previous solution and generated grids to speed up the solution process. A refinement strategy based on element splitting and introduction of hanging nodes requires special care since the constraint equations of the hanging nodes are incorporated in the system by usage of Lagrange multipliers. The approach leads to indefinite systems and hence a special preconditioner that enforces the constraint equations to be fulfilled while iterating has been developed. The paper presents results using the adaptive multigrid procedure on an elasto-plastic wave propagation problem. © 2006 American Institute of Physics [ABSTRACT FROM AUTHOR]

Over the past two decades, various finite element formulations and solution techniques for metal forming analysis have been developed. Most finite element codes for bulk metal forming used in the industry today are based on static implicit solution schemes wherein a non-linear system of equations is solved iteratively for each time increment. For simple 2D problems, static implicit analysis models are generally known to be more accurate and efficient than dynamic explicit analysis models. However, for complex 3D forming problems, the static implicit procedures encounter a number of inherent difficulties especially in incremental forming processes such as ring rolling in which several surface nodes repeatedly make contact with and separate from the dies. Static implicit finite element formulations require a very long computational time for the analysis of ring rolling. Several solution techniques have been developed to reduce the computational time of static implicit finite element analysis, namely the dual mesh technique, Arbitrary Lagrangian Eulerian (ALE) technique, etc. The dynamic explicit method on the other hand appears to be very effective in analyzing complex incremental forming problems. In this paper, a comparison of the analysis results obtained using dynamic explicit finite element method and static implicit method using a dual mesh approach is presented. © 2004 American Institute of Physics [ABSTRACT FROM AUTHOR]

The simulation of high-velocity impact and penetration is inhibited by complex material behavior and large deformations. Lagrangian formulations best model complex materials because history-dependent variables and material boundaries are not advected. However, Lagrangian finite elements are limited by large deformations. Recently, meshfree particle methods have been used to avoid such limitations, and have demonstrated greater accuracy than traditional erosion methods (wherein deformed elements are removed). Though the variable connectivity of particles enables them to model large deformations, it requires more computational effort than (fixed-connectivity) elements. Therefore, an algorithm was designed to convert deformed elements to particles, thus providing the ability to model large deformations where needed, while maintaining the efficiency of elements elsewhere. This combination is essential in three dimensions, where problem size demands efficiency. In this paper, the conversion algorithm is demonstrated for several three-dimensional simulations of high-velocity impact and penetration. © 2004 American Institute of Physics [ABSTRACT FROM AUTHOR]