Chiara Guardasoni

On the energetic Galerkin boundary element method applied to interior wave propagation problems

We consider two-dimensional interior wave propagation problems with vanishing initial and mixed boundary conditions, reformulated as a system of two boundary integral equations with retarded potential. These latter are then set in a weak form, based on a natural energy identity satisfied by the solution of the differential problem, and discretized by the related energetic Galerkin boundary element method. Numerical results are presented and discussed.

Numerical integration schemes for space---time hypersingular integrals in energetic Galerkin BEM

Here we consider exterior Neumann wave propagation problems reformulated in terms of space–time hypersingular boundary integral equations. We deal with quadrature schemes required, in the discretization phase, by the energetic Galerkin boundary element method.

Energetic BEM for the numerical analysis of 2D Dirichlet damped wave propagation exterior problems

Abstract Time-dependent problems modeled by hyperbolic partial differential equations can be reformulated in terms of boundary integral equations and solved via the boundary element method. In this context, the analysis of damping phenomena that occur in many physics and engineering problems is a novelty. Starting from a recently developed energetic space-time weak formulation for 1D damped wave propagation problems rewritten in terms of boundary integral equations, we develop here an extension of the so-called energetic boundary element method for the 2D case. Several numerical benchmarks, whose numerical results confirm accuracy and stability of the proposed technique, already proved for the numerical treatment of undamped wave propagation problems in several dimensions and for the 1D damped case, are illustrated and discussed.

Efficient BEM-Based Algorithm for Pricing Floating Strike Asian Barrier Options (with MATLAB® Code)

This paper aims to illustrate how SABO (Semi-Analytical method for Barrier Option pricing) is easily applicable for pricing floating strike Asian barrier options with a continuous geometric average. Recently, this method has been applied in the Black–Scholes framework to European vanilla barrier options with constant and time-dependent parameters or barriers and to geometric Asian barrier options with a fixed strike price. The greater efficiency of SABO with respect to classical finite difference methods is clearly evident in numerical simulations. For the first time, a user-friendly MATLAB® code is made available here.

Energetic BEM for the numerical solution of 2D damped waves propagation exterior problems

The analysis of damping phenomena that occur in many physics and engineering problems, such as fluid dynamics, kinetic theory and semiconductors, is of particular interest. For this kind of problems, one needs accurate and stable approximate solutions even on large time intervals. These latter can be obtained reformulating time-dependent problems modeled by partial differential equations (PDEs) of hyperbolic type in terms of boundary integral equations (BIEs) solved via boundary element methods (BEMs). In this context, starting from a recently developed energetic weak formulation of the space-time BIE modeling, in particular, classical wave propagation exterior problems [2, 3], we consider here an extension for the damped wave equation in 2D space dimension, based on successful simulations for the 1D case [6, 7]. In fact, the related energetic BEM reveals a robust time stability property, which is crucial in guaranteeing accurate numerical solutions on large time intervals. Several benchmarks will be presented and discussed.

Numerical approximation of a BGK-type relaxation model for reactive mixtures

The kinetic modelling of chemically reacting gas mixtures represents a fundamental step in order to derive proper macroscopic description at hydrodynamic level. Useful model equations have been recently obtained following a consistent BGK approach. A common way to solve the BGK equations is based on the operator splitting, i.e. the solution in one time step is obtained by the sequence of collision-step and convection-step. Numerical approximation of such BGK equations for problems with axial symmetry is here adressed. Several results in the numerical resolution of the Riemann problem for gas mixtures, obtained with splitting methods of different orders, are presented. [ DOI : 10.1685/CSC06004] About DOI