Highly oscillatory problems

Workshop theme

Highly oscillatory phenomena occur in a wide range of mathematical applications: from fluid to solid mechanics, electromagnetics, acoustics, combustion, computerised tomography and imaging, molecular dynamics, quantum chemistry, plasma transport and electrical engineering. Such phenomena have attracted a great deal of mathematical attention, mainly in harmonic analysis, asymptotic analysis, homogenisation, differential geometry, theory of Hamiltonian systems and theory of integrable systems. They have an oft-undeserved reputation of being hopelessly difficult to analyse and to compute: the truth of the matter is that, once they have been understood from the mathematical standpoint, effective computational algorithms are bound to follow.

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Timetable

Monday 13th September 2010
08:45 to 08:50	Welcome from Sir David Wallace, INI Director	No Room Required
08:50 to 09:00	Welcome from the Chair, Arieh Iserles, the Co-Chair Claude Le Bris, and the ESF Rapporteur, Chus Sanz-Serna	No Room Required
08:55 to 09:00	Welcome by ESF Rapporteur	Room 1
09:00 to 10:00	Ilaria Perugia Università degli Studi di Pavia Non polynomial approximations of wave problems	Room 1
10:00 to 11:00	Computing Slowly Advancing Features in Fast-Slow Systems without Scale Separation - A Young Measure Approach	Room 1
11:00 to 11:30	Morning Coffee	No Room Required
11:30 to 12:30	Daan Huybrechs Fourier series on triangles and tetrahedra	Room 1
12:30 to 13:30	Lunch at Wolfson Court	No Room Required
14:00 to 14:30	Ludwig Gauckler Eberhard Karls Universität Tübingen Modulated Fourier expansions for the long-time analysis of Hamiltonian PDEs	Room 1
14:30 to 15:00	Reinout Quispel La Trobe University Integral-Preserving Integrators	Room 1
15:00 to 15:30	Hermann Brunner Memorial University of Newfoundland On the numerical solution of first-kind Volterra integral equations with highly oscillatory kernels	Room 1
15:30 to 16:00	Afternoon Tea	No Room Required
16:00 to 17:00	Irene Fonseca Carnegie Mellon University Multiple integrals under differential constraints: two-scale convergence and homogenization	Room 1
17:00 to 18:00	On Wigner and Bohmian Measures	Room 1
18:00 to 18:30	Ekaterina Karatsuba Pereslavl-Zalessky of the Russian Academy of Sciences On approximation of special oscillating series of quantum theory	Room 1
18:30 to 19:00	Welcome Wine Reception	No Room Required
19:15 to 19:45	Dinner at Fitzwilliam College	No Room Required

Tuesday 14th September 2010
09:00 to 10:00	Numerical integration for numerical homogenizations methods	Room 1
10:00 to 11:00	Yalchin Efendiev Texas A&M University Multi-scale spaces for multiscale high-contrast problems and their applications	Room 1
11:00 to 11:30	Morning Coffee	No Room Required
11:30 to 12:30	Computing expectation values for molecular quantum dynamics	Room 1
12:30 to 13:30	Lunch at Wolfson Court	No Room Required
14:00 to 14:30	Variance reduction in stochastic homogenization using antithetic variables	Room 1
14:30 to 15:00	Gil Ariel Bar-Ilan University Oscillatory systems with three separated timescales	Room 1
15:00 to 15:30	Matthew Dobson ENPC - École des Ponts ParisTech Developing Integrators for Highly Oscillatory Hamiltonian Systems Using Homogenization	Room 1
15:30 to 16:00	Afternoon Tea	No Room Required
16:00 to 16:30	Poster Session	No Room Required
16:30 to 17:00	Chris Stolk Universiteit van Amsterdam Preconditioning the Helmholtz equation using rapidly oscillating functions	Room 1
17:00 to 17:30	Coercivity, Nonnormality and Numerical Range of boundary integral operators in high-frequency scattering	Room 1
17:30 to 18:00	Fatih Ecevit Convergent high-frequency algorithms for single and multiple scattering	Room 1
18:00 to 18:30	Lehel Banjai Max-Planck-Institut für Mathematik, Leipzig Runga-Kutta convolution quadrature: convergence theory and applications to time-domain BIE of acoustic scattering	Room 1
18:45 to 19:15	Dinner at Fitzwilliam College	No Room Required

Wednesday 15th September 2010
09:00 to 10:00	Christian Lubich Eberhard Karls Universität Tübingen Modulated Fourier expansions and the Fermi-Pasta-Ulam problem	Room 1
10:00 to 11:00	Tony Lelievre ENPC - École des Ponts ParisTech Metastability, rare events and sampling problems in molecular dynamics	Room 1
11:00 to 11:30	Morning Coffee and Group Picture	No Room Required
11:30 to 12:00	Andrea Moiola ETH Zürich Approximation by plane waves	Room 1
12:00 to 12:30	The generalised eigenfunction method and time-dependent linear water-wave impact on a vertical elastic plate	Room 1
12:30 to 13:30	Lunch at Wolfson Court	No Room Required
14:00 to 14:30	Peter Olver University of Minnesota Numerical solution of Riemann–Hilbert problems: Painlevé II	Room 1
14:30 to 15:00	Jens Geier Technische Universität Wien Efficient finite difference schemes for highly oscillatory linear ODE	Room 1
15:00 to 15:30	Marianna Khanamiryan University of Cambridge Highly Oscillatory Integrals and their Applications	Room 1
15:30 to 16:00	Afternoon Tea	No Room Required
16:00 to 17:00	Optimal Tuning of Hybrid Monte Carlo	Room 1
17:00 to 18:00	The Hybrid Monte Carlo Algorithm in High Dimensions	Room 1
18:00 to 18:30	Olof Runborg Error Estimates for Gaussian Beam Superposition	Room 1
19:30 to 22:00	Conference Dinner at Gonville & Caius College, Dining Hall	No Room Required

Thursday 16th September 2010
09:00 to 10:00	Houman Owhadi CALTECH (California Institute of Technology) Homogenization with non-separated scales and high contrast	Room 1
10:00 to 11:00	Athanssios Fokas University of Cambridge A new transform method and some of its numerical implementations	Room 1
11:00 to 11:30	Morning Coffee	No Room Required
11:30 to 12:00	Higher-order total variation for oscillating patterns	Room 1
12:00 to 12:30	Olena Mul Ternopil Ivan Pul'uj National Technical University Oscillation Analysis of Some Hybrid Dynamical Systems of Transmission Pipelines	Room 1
12:30 to 13:30	Lunch at Wolfson Court	No Room Required
14:00 to 14:30	Tensor product method for radiative transfer	Room 1
14:30 to 15:00	Wu Hao Université Paul Sabatier Toulouse III Bloch Decomposition-Based Gaussian Beam Method for the Schrodinger equation with Periodic Potentials	Room 1
15:00 to 15:30	Liviu Ignat Universidad Autonoma de Madrid Strichartz estimates for the Schroedinger equation on a tree and applications	Room 1
15:30 to 16:00	Afternoon Tea	No Room Required
16:00 to 16:30	Yen-Hsi Tsai Japan Atomic Energy Agency & University of Texas at Austin Upscaling of network models for porous media	Room 1
16:30 to 17:00	Ricardo Silva Universidade de São Paulo Thin domains with highly oscillating boundaries	Room 1
17:00 to 17:30	Oscillatory diffusion equation	Room 1
17:30 to 18:00	Qin Sheng Baylor University An Effective Finite Difference Approach for Optical Beam Propagations	Room 1
18:00 to 18:30	Pablo Alvarez-Caudevilla Scuola Normale Superiore di Pisa Global and Blow-up patterns of the Cauchy problem of a fourth-order thin film equation	Room 1
18:45 to 19:15	Dinner at Fitzwilliam College	No Room Required

Friday 17th September 2010
09:00 to 10:00	Applications of High Frequency Methods in Aeronautics: status and needs	Room 1
10:10 to 10:40	Joaquim Correia University of Évora Nonlinear hyperbolic conservation laws: diffusive-dispersive limits	Room 1
10:40 to 11:10	Euan Spence University of Bath Coercivity of boundary integral operators in high frequency scattering	Room 1
11:10 to 11:30	Morning Coffee	No Room Required
11:30 to 12:30	Existence of approximate solitary waves in simplectic algorithms of integration	Room 1
12:30 to 13:30	Lunch at Wolfson Court	No Room Required

Speakers

Pablo Alvarez-Caudevilla Scuola Normale Superiore di Pisa
Gil Ariel Bar-Ilan University
Lehel Banjai Max-Planck-Institut für Mathematik, Leipzig
Hermann Brunner Memorial University of Newfoundland
Joaquim Correia University of Évora
Matthew Dobson ENPC - École des Ponts ParisTech
Fatih Ecevit
Yalchin Efendiev Texas A&M University
Athanssios Fokas University of Cambridge
Irene Fonseca Carnegie Mellon University
Ludwig Gauckler Eberhard Karls Universität Tübingen
Jens Geier Technische Universität Wien
Wu Hao Université Paul Sabatier Toulouse III
Daan Huybrechs
Liviu Ignat Universidad Autonoma de Madrid
Ekaterina Karatsuba Pereslavl-Zalessky of the Russian Academy of Sciences
Marianna Khanamiryan University of Cambridge
Tony Lelievre ENPC - École des Ponts ParisTech
Christian Lubich Eberhard Karls Universität Tübingen
Andrea Moiola ETH Zürich
Olena Mul Ternopil Ivan Pul'uj National Technical University
Peter Olver University of Minnesota
Houman Owhadi CALTECH (California Institute of Technology)
Ilaria Perugia Università degli Studi di Pavia
Reinout Quispel La Trobe University
Olof Runborg
Qin Sheng Baylor University
Ricardo Silva Universidade de São Paulo
Euan Spence University of Bath
Chris Stolk Universiteit van Amsterdam
Yen-Hsi Tsai Japan Atomic Energy Agency & University of Texas at Austin

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