LETIZIA SCUDERI

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Confirmed Associate Professor

+39 0110907560 / 7560 (DISMA)

Scientific branch MAT/08 - ANALISI NUMERICA
(Area 0001 - Scienze matematiche e informatiche)
Identifiers ORCID: 0000-0002-1685-9608
Research topics Numerical solution of acoustic and elastic wave propagation problems, both in frequency and time domain, defined in bounded and unbounded domains and described by partial differential equations (PDEs). Problems, whose formulation can be reduced to boundary integral equations, are considered. Among the classical examples, it is worth mentioning: i) the propagation and the simple/multiple scattering of acoustic waves in non-viscous fluids, in presence of obstacles of arbitrary shape; ii) the propagation of elastic (seismic) waves in homogeneous or multi-layered media and that of electromagnetic waves. The presence of sources, even located far away from the spatial domain of interest, of non-trivial initial data, and of Dirichlet, Neumann or mixed boundary conditions are considered. By using a proper boundary integral formulation, it is possible to determine directly the solution of the problem at any desired point. The same integral formulation represents a non-reflecting boundary condition that can be defined on an artificial boundary of arbitrary shape, thus allowing to solve the problem on a bounded spatial domain of interest. The solution of the reformulated problem is obtained by coupling a boundary element discretization (BEM) of the above mentioned integral equation with a classical finite element method (FEM) or a finite difference method, or by means of the virtual element method (VEM). The applied numerical techniques entail:
 
 • collocation and Galerkin methods for the numerical solution of integral formulation of PDEs and efficient quadrature formulas for the computation of weakly and strongly singular integrals therein involved. This last issue is particularly important for the efficacy and the accuracy of the numerical method applied to the integral equation;
 
 • convolution quadrature formulas for space-time boundary element methods;
 
 • wavelet techniques for the sparsification of the matrices associated with linear systems arising from the space-time discretization of the integral operators involved in the integral reformulation of PDEs.
Skills and keywords

ERC sectors

PE1_20 - Application of mathematics in sciences PE1_17 - Numerical analysis

Keywords

Acoustic waves Advanced numerical methods Convolution integrals Elasticity Integral equation method Integral equations Sismology