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Computational Wave Propagation

English title Computational Wave Propagation
Applicant Moiola Andrea
Number 137294
Funding scheme Fellowships for prospective researchers
Research institution
Institution of higher education Institution abroad - IACH
Main discipline Mathematics
Start/End 01.03.2012 - 28.02.2013
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Keywords (11)

Rellich and Morawetz estimates; Maxwell equations; Wave-based methods; Adaptivity; Discontinuous Galerkin method; Linear elasticity; Helmholtz equation; Wave propagation; Plane waves; Trefftz methods; Finite element method

Lay Summary (Italian)

Lead
Computational wave propagation
Lay summary
La simulazione di fenomeni relativi ad onde acustiche o elettromagnetiche, incluse propagazione, risonanze e scattering, e` di fondamentale importanza in molte aree ingegneristiche e scientifiche quali l'imaging medico e sismico, la progettazione di antenne, lo scattering da parte di particelle atmosferiche, la modellazione di ultrasuoni, radar e sonar. Molti dei corrispondenti modelli matematici possono essere facilmenti formulati come problemi al bordo (BVP) o equazioni integrali al bordo (BIE); d'altro canto, dato il carattere oscillatorio delle soluzioni, a medie ed alte frequenze la loro simulazione al computer richiede un enorme sforzo computazionale.

In questo progetto, abbiamo introdotto una nuova formulazione variazionale per un'ampia classe di BVP acustici (scattering e cavita`). Questa nuova formulazione e` "sign-definite", al contrario della maggior parte delle formulazioni note. La sign-indefiniteness dei problemi time-harmonic e` spesso considerata una principale fonte di difficolta` computazionali, poiche' e` presente in ogni discretizzazione e richiede l'uso di un grande numero di gradi di liberta` per ottenere un'accuratezza accettabile.

Un'altra parte del progetto e` stato dedicato all'estensione del metodo "Trefftz-discontinuous Galerkin" (TDG), uno schema numerico per l'approssimazione di problemi time-harmonic. In particolare, abbiamo lavorato sulla cosidetta "versione hp" del metodo TDG, che combina diversi raffinamenti per ottenere convergenza esponenziale nel numero di gradi di liberta` usati.
Direct link to Lay Summary Last update: 04.04.2013

Responsible applicant and co-applicants

Publications

Publication
Is the Helmholtz Equation Really Sign-Indefinite?
Moiola Andrea, Spence Euan A. (2014), Is the Helmholtz Equation Really Sign-Indefinite?, in SIAM Review, 56(2), 274-312.
Trefftz discontinuous Galerkin methods for acoustic scattering on locally refined meshes,
Hiptmair Ralf, Moiola Andrea, Perugia Ilaria, Trefftz discontinuous Galerkin methods for acoustic scattering on locally refined meshes,, in Appl. Numer. Math..

Collaboration

Group / person Country
Types of collaboration
ETH Zurich Switzerland (Europe)
- in-depth/constructive exchanges on approaches, methods or results
- Publication
University of Bath Great Britain and Northern Ireland (Europe)
- in-depth/constructive exchanges on approaches, methods or results
- Publication
Unversity of Pavia Italy (Europe)
- in-depth/constructive exchanges on approaches, methods or results
- Publication
University of Reading Great Britain and Northern Ireland (Europe)
- in-depth/constructive exchanges on approaches, methods or results

Scientific events

Active participation

Title Type of contribution Title of article or contribution Date Place Persons involved
InnoWave conference Talk given at a conference Trefftz-discontinuous Galerkin methods for Maxwell’s equations 03.09.2012 Nottingham, UK, Great Britain and Northern Ireland Moiola Andrea;
ESCO2012, 3rd European Seminar on Computing Talk given at a conference Trefftz-DG methods for time-harmonic Maxwell’s equations 25.06.2012 Pilsen, Czech Republic, Czech Republic Moiola Andrea;


Abstract

Understanding and predicting the propagation and scattering of acoustic, electromagnetic and elastic waves is a fundamental requirement in numerous engineering and scientific fields. However, the numerical simulation of these phenomena remains a serious challenge, particularly for problems at high frequency where the solutions to be computed are highly oscillatory. An important and active current area of research in numerical analysis and scientific computing is the design of new approximation methods better able to represent these highly oscillatory solutions, leading to new algorithms which offer the potential for hugely reduced computational times. A key associated activity is the development of supporting mathematical foundations, including a rigorous numerical analysis explaining and justifying the improved behaviour of new approximation methods and algorithms proposed. My research during my Ph.D. at the ETH Zurich has made important contributions to aspects of this international research activity. I am applying for this fellowship to support a deepening and widening of my research training through a two year postdoctoral experience.The main directions of my work will be:--- The extension to new settings of the Trefftz discontinuous Galerkin method I developed jointly with my advisor R. Hiptmair and I. Perugia.In particular, I intend to consider acoustic and electromagnetic models with smoothly varying material coefficients, non-homogeneous equations, linear elasticity and reaction-diffusion problems.--- The development of complete self-adaptive finite element schemes for the discretization of acoustic and electromagnetic problems where the basis functions include plane waves whose propagation directions are chosen in a fully automatic fashion.This will reduce significantly the computational effort needed in the numerical simulation of scattering and propagation phenomena and open new exciting possibilities in the use of wave-based methods.--- The application of the Rellich and Morawetz-type identities for Maxwell's equations I developed during my Ph.D. to new open problems;for instance,the proof of frequency-independent stability bounds for different boundary value problems that are relevant in electromagnetism, the formulation of new combined field integral operators with desirable numerical properties, in particular coercivity, and the application of these results to the analysis and design of numerical techniques such as finite and boundary elements methods (FEM and BEM).After my Ph.D. dissertation, planned for autumn 2011, I intend to conduct my research based at the University of Reading (UK), which, with the University of Bath and University College London, has become a centre for international work in this area. I will work as part of a group, with large current UK research funding, which spans these three institutions, comprising Prof. S.N. Chandler-Wilde, D. Hewett, S. Langdon (Univ. of Reading), Prof. I. Graham, E. Spence (Univ. of Bath), Prof. V. Smyshlyaev, T. Betcke and J. Phillips (UCL).A collaboration with some members of the team has already been established through a visit to the UK and reciprocal visits to ETH.The fellowship is planned for two years, supported by the SNSF grant for the first year, and by the University of Reading in year two.
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