In this work, we analyse the Galerkin Infinite Element method for option pricing. The Infinite Element method is a very simple and efficient modification of the more common Finite Element method. It keeps the best features of Finite Elements, i.e. bandedness, easiness of programming, accuracy, and it is particularly useful when solving problems in unbounded domains. Three main aspects are consi...

Rapid development of engineering activities expands through a variety of rock engineering processes such as drilling, blasting, mining and mineral processing. These activities require rock dynamic fracture mechanics method to characterize the rock behavior. Dynamic fracture toughness is an important parameter for the analysis of engineering structures under dynamic loading. Several experimental...

Analysis of the stresses, displacements, and horizontal strains of the ground subsidence due to underground excavation in rocks can be accomplished by means of a hybridized higher order indirect boundary element/finite difference (BE/FD) formulation. A semi-infinite displacement discontinuity field is discretized (numerically) using the cubic displacement discontinuity elements (i.e. each highe...

Numerical methods (finite element methods) for the approximate solution of elliptic partial differential equations on unbounded domains are considered, and error bounds, with respect to the number of unknowns which have to be determined, are proven.

The scattering problem from time-harmonic waves by a Neumann type crack in R is considered. A PML technique is used for solving the problem with a bounded domain instead of the infinite domain. A coupled finite-infinite element method is employed in the computation. Because of the singularity of the solution, the infinite element method is used near the crack tip. An error analysis is presented...

Because of random nature of many dependent variables in coastal engineering, treatment of effective parameters is generally associated with uncertainty. Numerical models are often used for dynamic analysis of complex structures, including mechanical systems. Furthermore, deterministic models are not sufficient for exact anticipation of structure’s dynamic response, but probabilistic models...

This work is devoted to a study and summary of different Infinite Element (IE) formulations for Helmholtz problems in arbitrary exterior domains. The theoretical setting for each of the different formulations is presented and related to the mathematical existence theory. The influences of a bilinear or a sesquilinear formulation are discussed as well as possible extensions to other elements. Th...

Results of “generation” (determination of dynamic stress-intensity factor variation with time, for a specified crack-propagation history) studies, as well as “prediction” (determination of crack-propagation history for specified dynamic fracture toughness vs crack-velocity relationships) studies of dynamic crack propagation in plane-stress/strain situations are presented and discussed in detail...