Chiara Guardasoni | University of Parma (original) (raw)

Papers by Chiara Guardasoni

Journal of Engineering Mathematics, 2021

The paper deals with the numerical solution of 2D wave propagation exterior problems including vi... more The paper deals with the numerical solution of 2D wave propagation exterior problems including viscous and material damping coefficients and equipped by Neumann boundary condition, hence modeling the hard scattering of damped waves. The differential problem, which includes, besides diffusion, advection and reaction terms, is written as a space–time boundary integral equation (BIE) whose kernel is given by the hypersingular fundamental solution of the 2D damped waves operator. The resulting BIE is solved by a modified Energetic Boundary Element Method, where a suitable kernel treatment is introduced for the evaluation of the discretization linear system matrix entries represented by space–time quadruple integrals with hypersingular kernel in space variables. A wide variety of numerical results, obtained varying both damping coefficients and discretization parameters, is presented and shows accuracy and stability of the proposed technique, confirming what was theoretically proved for ...

Wave propagation analysis with boundary element method

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016), 2016

Communications in Applied and Industrial Mathematics, 2011

Here we present an advanced implementation of a direct space-time Galerkin boundary element metho... more Here we present an advanced implementation of a direct space-time Galerkin boundary element method for the discretization of retarded potential boundary integral equa- tions related to Dirichlet-Neumann two-dimensional wave propagation problems defined on bi-domains. This technique, recently introduced for the case of a single-domain, is based on a natural energy identity satisfied by the solution of the corresponding differ- ential problem. Various numerical simulations are presented and, through comparisons with available literature results, accuracy and stability of the method applied to layered media are experimentally observed.

Structured Matrices in Numerical Linear Algebra, 2019

The energetic boundary element method (BEM) is a discretization technique for the numerical solut... more The energetic boundary element method (BEM) is a discretization technique for the numerical solution of wave propagation problems, introduced and applied in the last decade to scalar wave propagation inside bounded domains or outside bounded obstacles, in 1D, 2D, and 3D space dimension.

Abstract. Time-dependent problems modeled by hyperbolic partial differential equations (PDEs) can... more Abstract. Time-dependent problems modeled by hyperbolic partial differential equations (PDEs) can be reformulated in terms of boundary integral equations (BIEs) and solved via the boundary element method (BEM). In this context, the analysis of damping phenomena that occur in many physics and engineering problems is of particular interest. Starting from a recently developed energetic space-time weak formulation of BIEs related to wave propagation problems, we consider an extension for the damped wave equation and a coupling algorithm is presented, which allows a flexible use of FEM and BEM as local discretization techniques. PDEs associated to BIEs will be weakly reformulated by the energetic approach. This method has shown excellent stability properties, which are crucial in guaranteeing an efficient BEM-FEM coupling. Several numerical results on 1D model problems are presented and discussed.

Axioms, 2021

In this paper, we extend the SABO technique (Semi-Analytical method for Barrier Options), based o... more In this paper, we extend the SABO technique (Semi-Analytical method for Barrier Options), based on collocation Boundary Element Method (BEM), to the pricing of Barrier Options with payoff dependent on more than one asset. The efficiency and accuracy already revealed in the case of a single asset is confirmed by the presented numerical results.

Boundary Elements and other Mesh Reduction Methods XLIV, 2021

In this paper, we consider some elastodynamics problems in 2D unbounded domains, with soft scatte... more In this paper, we consider some elastodynamics problems in 2D unbounded domains, with soft scattering conditions at the boundary, and their solution by the Boundary Element Method (BEM). The displacement identifying the elastic wave propagation is represented by both direct and indirect boundary integral formulations, which depend on the traction or on the jump of the traction at the boundary of the propagation domain, respectively. We study the characteristic singularities of the single layer and the double layer integral operators, which are involved in the considered energetic weak forms. Some algorithmic considerations about the parallel implementation of the energetic BEM and the quadrature techniques applied to overcome the issues due to the weak and the strong singularities of the integration kernels are proposed. Numerical simulations follow, showing a comparison between the external displacements obtained by the indirect and the direct formulations.

Axioms, 2018

This paper aims to illustrate how SABO (Semi-Analytical method for Barrier Option pricing) is eas... more 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 R code is made available here.

Mathematical Methods in the Applied Sciences, 2018

IMA Journal of Management Mathematics, 2018

A barrier option is an exotic path-dependent option contract that, depending on terms, automatica... more A barrier option is an exotic path-dependent option contract that, depending on terms, automatically expires or can be exercised only if the underlying asset ever reaches a predetermined barrier price. Using a partial differential equation approach, we provide an integral representation of the barrier option price via the Mellin transform. In the case of knock-out barrier options, we obtain a decomposition of the barrier option price into the corresponding European option value minus a barrier premium. The integral representation formula can be expressed in terms of the solution to a system of coupled Volterra integral equations of the first kind. Moreover, we suggest some possible numerical approaches to the problem of barrier option pricing.

Applied and Industrial Mathematics in Italy II, 2007

We consider wave propagation problems with vanishing initial and mixed boundary condition reformu... more We consider wave propagation problems with vanishing initial and mixed boundary condition reformulated as space-time boundary integral equations. The energetic Galerkin boundary element method (BEM) used in the discretization phase, after a double analytic integration in time variables, has to deal with weakly singular, singular and hypersingular double integrals in space variables. Efficient numerical quadrature schemes for evaluation of these integrals are here proposed. Several numerical results are presented and discussed.

Time-dependent problems modeled by hyperbolic partial differential equations (PDEs) can be reform... more Time-dependent problems modeled by hyperbolic partial differential equations (PDEs) can be reformulated in terms of boundary integral equations (BIEs) and solved via the boundary element method (BEM). In this context, the analysis of damping phenomena that occur in many physics and engineering problems is of particular interest. Starting from a recently developed energetic space-time weak formulation for the coupling of BIEs and PDEs related to wave propagation problems [1, 2, 3], we consider here an extension for the damped wave equation in layered media. A coupling algorithm is presented, which allows a flexible use of FEM and BEM as local discretization techniques. Stability and convergence have been proved by energy arguments. These properties are crucial in guaranteeing accurate solutions for simulations on large time intervals. Several numerical results on 1D model problems, confirming theoretical results, are presented and discussed.

Applied and Industrial Mathematics in Italy III - Selected Contributions from the 9th SIMAI Conference, 2009

13 A Space-time Galerkin BEM for 2D Exterior Wave Propagation Problems Alessandra Aimi♮, Mauro Di... more 13 A Space-time Galerkin BEM for 2D Exterior Wave Propagation Problems Alessandra Aimi♮, Mauro Diligenti, Ilario Mazzieri, Stefano Panizzi Department of Mathematics, Universita di Parma, Italy ♮ E-mail: alessandra. aimi@ unipr. it Chiara Guardasoni∗ Department of ...

ABSTRACT We consider Dirichlet-Neumann problems for two-dimensional wave propagation analysis in ... more ABSTRACT We consider Dirichlet-Neumann problems for two-dimensional wave propagation analysis in piecewise homogeneous media reformulated in terms of boundary integral equations. The related weak problem is based on a space-time energetic formulation recently introduced for single-domain problems. The discretization phase is carried out by means of Galerkin boundary element method. Numerical results obtained with this procedure will be presented and analyzed.

Numerical Algorithms, 2010

Here we consider exterior Neumann wave propagation problems reformulated in terms of space-time h... more 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.