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Numerical Analysis group

Group members, research topics and publications

Alessandra Aimi, PA (PhD, Associate Professor)

- Isogeometric Analysis and Boundary Element Method
- Study of elastic wave propagation problems in layered media, reformulated in terms of boundary integral equations (BIEs) in space-time domain. Introduction of a new weak formulation related to the energy of the differential model problem
- Energetic BEM-FEM coupling 
- Introduction and analysis of numerical quadrature schemes for double integrals with weakly singular, singular and hyper-singular kernels arising in the solution of BIEs with Galerkin BEM related to 2D and 3D problems
- Reformulation in discrete context of Decomposition in Subspaces Method, with the introduction of suitable restriction matrices

Publications of Alessandra AIMI

Mauro Diligenti, PO (Full Professor)

- Boundary integral equations and boundary elements method
- Analysis and applications of new numerical methods for integral models related to study of elastic waves propagation in multi-domains
- Numerical Integration
- Decomposition method
Chiara Guardasoni, RTD (Research Assistant)
- numerical methods for kinetic theory
- weak formulations for wave propagation problems
- numerical quadrature schemes
- “fast” techniques for the linear system resolution
- numerical methods for finance models


Main collaborators & visitors

Francesco Calabrò (Università di Cassino)
Angelo Carini (Università di Brescia)
Stéphanie Chaillat-Loseille (UMA-ENSTA, Parigi)
Luca Desiderio (UMA-ENSTA, Parigi)
Silvia Falletta (Politecnico di Torino)
Attilio Frangi (Politecnico di Milano)
Silvia Gazzola (University of Bath)
Giovanni Monegato (Politecnico di Torino)
Stefano Panizzi (Università di Parma)
Alberto Salvadori (Università di Brescia)
Maria Lucia Sampoli (Università di Siena)
Simona Sanfelici (Università di Parma)
Letizia Scuderi (Politecnico di Torino)
Alessandra Sestini (Università di Firenze)

Research projects
  • 2017 grant CARIPARMA Banking foundation  (responsible:  A. Aimi)
  • INdAM-GNCS 2017 (12 months): New numerical techniques for the solution of time-dependent problems by BEM (responsible:  A. Aimi, participants: M. Diligenti, C. Guardasoni)
  • GNCS 2016 (12 months): Isogeometric approach and quadrature techniques for 3D Boundary Element Method (participants: A.Aimi, M.Diligenti, C. Guardasoni)
  • INdAM-GNCS 2015 (12 months): Isogeometric Analysis and Boundary Element Method (responsible: A. Aimi, participants: C. Guardasoni, M. Diligenti)
  • FIL 2014 – Local Funds for Research based on peer-review: Boundary Element Method for barrier options in models with time-dependent parameters (responsible: C. Guardasoni; participants: S. Sanfelici, M. de Donno, A. Aimi; external collaborators: M. Rodrigo (University of Wallongong, Australia), J. Akahori (Ritsumeikan University, Japan), L.V. Ballestra (University of Bologna), D. Marazzina (Polytechnic of Milan).
  • INdAM-GNCS 2014 (12 months): From approximation to linear algebra: numerical methods for isogeometric analysis (participants: A. Aimi, M.Diligenti)
  • INdAM-GNCS 2013 (12 months): Fast methods for the numerical resolution of systems of integro-differential equations (responsible: A. Aimi, participant: C.Guardasoni)
  • INDAM_GNCS-Young Researchers (12 months): Integral equations approach for numerical resolution of Quantitative Finance problems; (responsible: C. Guardasoni; participants: S. Sanfelici; external collaborators: G. Sartorelli, A. Pallavicini (IMI Bank of Milan)).
  • INdAM-GNCS 2012 (12 months): Coupling of Numerical Methods for BIEs and PDEs related to external and multi-layers evolutionary problems (responsible: A. Aimi, participant: C. Guardasoni)
  • INdAM-GNCS 2011 (12 months): Numerical Methods for problems of elastic waves propagation in multi-domains (responsible: A. Aimi, participant: C. Guardasoni)
  • GNCS-2010 Research Fellow Program: Application of Restriction Matrices to Boundary Element Method for evolutionary problems (responsible: C.Guardasoni; participants: A. Aimi, M. Diligenti, S. Gazzola (University of Bath)).
  • PRIN 2009 (24 mesi): Boundary Element Method for elastic waves propagation problems, National responsible: Prof. G. Monegato (Politecnico di Torino); local responsible: Prof. M. Diligenti; participants: A. Aimi, C. Guardasoni.
  • PRIN 2007 (24 months): Boundary Element Method for elastic waves propagation problems,  National responsible: Prof. G. Monegato (Politecnico di Torino); local responsible: Prof. M. Diligenti; participants: A. Aimi, C. Guardasoni.
  • PRIN 2007 Italian Research Program: Advanced Numerical Methods for evolutionary equations and multi-scale problems;
    supervisors: Prof. A. Quarteroni (Polytechnic of Milan) and Prof. G. Naldi (University of Milan); participants: C. Guardasoni.

INdAM GNCS: Archvio Progetti di Ricerca


  • C. Guardasoni: winner of the INDAM-SIMAI-2010 prize for the best thesis in Applied Mathematics


Invited talks
  • 28 June 2016: Pricing of Financial Derivatives, University of Modena and Reggio Emilia, Speaker: C. Guardasoni
  • 27 Janaury 2016: IgA-SGBEM: an overview, Workshop “Design of Reliable, Exact, and Application-oriented techniques for geometric Modeling and numerical Simulations (DREAMS)”, University of Rome “Tor Vergata”, Speaker: A. Aimi
  • 3 July 2014: A boundary element method for pricing barriers options, Insurance & Finance day, University of Parma, Speaker: C. Guardasoni
  • 8 January 2014: Energetic BEM-FEM coupling for the numerical solution of wave propagation problems in unbounded multi-domains, Department of Mathematics and Computer Science, University of Florence, Speaker: A. Aimi
  • 27 May 2013: Energetic BEM-FEM coupling for wave propagation in unbounded media, MOX Seminars, Polytechnic of Milan, Speaker: A. Aimi
  • 23-25 November 2011: An energy approach to space-time Galerkin BEM for exterior wave propagation problems, INRIA, Monthly POEMS Seminars, Rocquencourt (Paris), Speaker: A. Aimi
  • 9 September 2010: An energy approach to space-time Galerkin BEM for wave propagation problems, Workshop “Space-time Boundary Integral Equation Methods for Wave Propagation Problems”, Turin Polythecnic, Speaker: A. Aimi



Seminars at SMFI Department
  • C. Manni (University of Florence): GB-splines: from modeling to simulation (with a linear algebra detour), September 2015
  • A. Buffa (University of Pavia): Electromagnetic scattering with isogeometric analysis, September 2015
  • Stefano Serra-Capizzano (University of Insubria): Autovalori e valori singolari di matrici provenienti dalla approssimazione di operatori integro-differenziali,  Colloquium, April 2014
  • Maria Lucia Sampoli (University of Siena): Un’introduzione all’analisi isogeometricaApril 2014
  • Stéphanie Chaillat-Loseille (ENSTA, ParisTech): A new Analytic Preconditioner for the Fast Multipole accelerated Boundary Element Method in 3-D elastodynamics, February 2014
  • Stéphanie Chaillat-Loseille (ENSTA, ParisTech): Fast Multipole Method for 3-D elastodynamic and elastodynamic Boundary Integral Equations, June 2011


Scientific Activities Organization
  • October 26th-27th, 2017: workshop related to Project INdAM-GNCS 2017: New numerical techniques for the solution of transient problems by BEM, Parma University (organizers: A. Aimi,  M. Diligenti, C. Guardasoni).
  • September 13th-16th, 2016: XIII SIMAI Congress, Milan; Minisymposium: Applications and numerical methods for Integral Equations,  (organizers: A. Aimi,  M. Diligenti, C. Guardasoni)  
  • September 13th-16th, 2016: XIII SIMAI Congress, Milan; Minisymposium: Advances in Quantitative Finance,  (organizers: C. Guardasoni, D. Marazzina, S. Sanfelici)  
  • September 17th, 2015: Scientific day related to Project INdAM-GNCS 2015 Isogeometric Analysis and Boundary Element Method, Parma University (organizers: A. Aimi,  M. Diligenti, C. Guardasoni)  
  • February 18th -19th 2013: Scientific days concluding Project INdAM-GNCS 2012 Coupling of Numerical Methods for BIEs and PDEs related to external and multi-layers evolutionary problems, Politecnico di Torino (organizers: A. Aimi,  M. Diligenti, C. Guardasoni, G. Monegato, S. Falletta, L. Scuderi) 
  • June 25th -28th, 2012: XI SIMAI Congress, Turin, Minisymposium Integral Equations: numerical methods and applications, (organizers: A. Aimi,  M. Diligenti, C. Guardasoni)  
  • January 31st 2011: Scientific day concluding Project INdAM-GNCS 2011 Numerical Methods for problems of elastic waves propagation in multi-domains, Parma University  (organizers: A. Aimi,  M. Diligenti, C. Guardasoni)
  • October 29th -30th, 2009: Workshop Integral Equations: recent numerical developments and new applications, Parma University (organizers: A. Aimi,  M. Diligenti, C. Guardasoni)  
  • September 27th -28th, 2007: Workshop Integral Equations: recent numerical developments and new applications, Parma University (organizers: A. Aimi,  M. Diligenti, C. Guardasoni)  
  • December 6th, 2002: Scientific Day  in honour of Prof. Lucilla Bassotti Rizza, Parma University (organizers: A. Aimi,  M. Diligenti)  
  • July 4th -7th, 2000: IABEM 2000, Symposium of the International Association for Boundary Element Methods, Brescia University, Members of the Local  Organizing Committee: A. Aimi, M. Diligenti  


Pubblicato Wednesday, 25 June, 2014 - 12:15 | ultima modifica Thursday, 14 June, 2018 - 17:25