Silvia Falletta

• 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.

ERC sectors

• SCIENZE MATEMATICHE, 2022/2023 (39. ciclo)
  Politecnico di TORINO

• Collegio di Ingegneria Civile. Componente
• Collegio di Ingegneria Elettronica, delle Telecomunicazioni e Fisica. Componente

PhD

• Time-domain boundary integral equations: a Convolution Quadrature perspective (didattica di eccellenza). A.A. 2020/21, MATEMATICA PURA E APPLICATA. Main teacher

Master of Science

• Finite element modelling. A.A. 2024/25, INGEGNERIA ELETTRONICA (ELECTRONIC ENGINEERING). Titolare del corso
• Finite element modelling. A.A. 2023/24, INGEGNERIA ELETTRONICA (ELECTRONIC ENGINEERING). Titolare del corso
• Finite element modelling. A.A. 2022/23, INGEGNERIA ELETTRONICA (ELECTRONIC ENGINEERING). Titolare del corso
• Finite element modelling. A.A. 2021/22, INGEGNERIA ELETTRONICA (ELECTRONIC ENGINEERING). Titolare del corso
• Finite element modelling. A.A. 2020/21, INGEGNERIA ELETTRONICA (ELECTRONIC ENGINEERING). Titolare del corso
• Finite element modelling. A.A. 2019/20, INGEGNERIA ELETTRONICA (ELECTRONIC ENGINEERING). Titolare del corso
• Calcolo numerico. A.A. 2019/20, INGEGNERIA CHIMICA E DEI PROCESSI SOSTENIBILI. Collaboratore del corso
• Finite element modelling. A.A. 2018/19, INGEGNERIA ELETTRONICA (ELECTRONIC ENGINEERING). Collaboratore del corso
• Metodi numerici. A.A. 2018/19, INGEGNERIA ELETTRONICA (ELECTRONIC ENGINEERING). Collaboratore del corso

Bachelor of Science

• Calcolo numerico: metodi e software. A.A. 2024/25, INGEGNERIA AEROSPAZIALE. Titolare del corso
• Calcolo numerico: metodi e software. A.A. 2023/24, INGEGNERIA AEROSPAZIALE. Titolare del corso
• Calcolo numerico: metodi e software. A.A. 2022/23, INGEGNERIA AEROSPAZIALE. Titolare del corso
• Calcolo numerico: metodi e software. A.A. 2021/22, INGEGNERIA AEROSPAZIALE. Titolare del corso
• Calcolo numerico: metodi e software. A.A. 2020/21, INGEGNERIA AEROSPAZIALE. Titolare del corso
• Calcolo numerico: metodi e software. A.A. 2019/20, INGEGNERIA AEROSPAZIALE. Titolare del corso
• Algebra lineare e geometria. A.A. 2018/19, INGEGNERIA AEROSPAZIALE. Collaboratore del corso
• Calcolo numerico: metodi e software. A.A. 2018/19, INGEGNERIA AEROSPAZIALE. Titolare del corso

• (DISMA)
• BEM FEM methods for PDEs (DISMA)
• Integral and integro-differential equations (DISMA)

• Numerical Analysis and Scientific Computing (DISMA)

• Matteo Ferrari. Programme in Matematica Pura E Applicata (36^th cycle, 2020-2024)
  Thesis: The non-symmetric coupling of virtual and boundary elements for wave propagation problems in unbounded domains
  
  Numerical Analysis
  Numerical Analysis

• Falletta, Silvia; Ferrari, Matteo; Scuderi, Letizia (2024)
  A virtual element method for the solution of 2D time-harmonic elastic wave equations via scalar potentials. In: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, vol. 441. ISSN 0377-0427
  Contributo su Rivista
• Desiderio, Luca; Falletta, Silvia; Ferrari, Matteo; Scuderi, Letizia (2023)
  CVEM-BEM Coupling for the Simulation of Time-Domain Wave Fields Scattered by Obstacles with Complex Geometries. In: COMPUTATIONAL METHODS IN APPLIED MATHEMATICS, vol. 23, pp. 353-372. ISSN 1609-4840
  Contributo su Rivista
• Desiderio, L; Falletta, S; Ferrari, M; Scuderi, L (2022)
  CVEM-BEM Coupling with Decoupled Orders for 2D Exterior Poisson Problems. In: JOURNAL OF SCIENTIFIC COMPUTING, vol. 92. ISSN 0885-7474
  Contributo su Rivista
• Desiderio, Luca; Falletta, Silvia; Ferrari, Matteo; Scuderi, Letizia (2022)
  On the Coupling of the Curved Virtual Element Method with the One-Equation Boundary Element Method for 2D Exterior Helmholtz Problems. In: SIAM JOURNAL ON NUMERICAL ANALYSIS, vol. 60, pp. 2099-2124. ISSN 0036-1429
  Contributo su Rivista
• Falletta, Silvia; Monegato, Giovanni; Scuderi, Letizia (2022)
  An overview on a time discrete convolution—space collocation BEM for 2D exterior wave propagation problems. In: ANNALI DELL'UNIVERSITÀ DI FERRARA. SEZIONE 7: SCIENZE MATEMATICHE, vol. 68, pp. 311-336. ISSN 0430-3202
  Contributo su Rivista
• Falletta, S.; Monegato, G.; Scuderi, L. (2022)
  Two FEM-BEM methods for the numerical solution of 2D transient elastodynamics problems in unbounded domains. In: COMPUTERS & MATHEMATICS WITH APPLICATIONS, vol. 114, pp. 132-150. ISSN 0898-1221
  Contributo su Rivista
• Desiderio, L.; Falletta, S.; Scuderi, L. (2021)
  A Virtual Element Method coupled with a Boundary Integral Non Reflecting condition for 2D exterior Helmholtz problems. In: COMPUTERS & MATHEMATICS WITH APPLICATIONS, vol. 84, pp. 296-313. ISSN 0898-1221
  Contributo su Rivista
• Colombi, Annachiara; Falletta, Silvia; Scianna, Marco; Scuderi, Letizia (2021)
  An integro-differential non-local model for cell migration and its efficient numerical solution. In: MATHEMATICS AND COMPUTERS IN SIMULATION, vol. 180, pp. 179-204. ISSN 0378-4754
  Contributo su Rivista
• Desiderio, Luca; Falletta, Silvia (2020)
  Efficient Solution of Two-Dimensional Wave Propagation Problems by CQ-Wavelet BEM: Algorithm and Applications. In: SIAM JOURNAL ON SCIENTIFIC COMPUTING, vol. 42, pp. B894-B920. ISSN 1064-8275
  Contributo su Rivista
• Falletta, Silvia; Bertoluzza, Silvia (2019)
  FEM solution of exterior elliptic problems with weakly enforced integral non reflecting boundary conditions. In: JOURNAL OF SCIENTIFIC COMPUTING, vol. 81, pp. 1019-1049. ISSN 0885-7474
  Contributo su Rivista