The semiclassical Schrodinger equation with multiscale and random potentials often appears when studying electron dynamics in heterogeneous quantum systems. As time evolves, the wavefunction develops high-frequency oscillations in both the physical space and the random space, which poses severe challenges for numerical methods. We propose a multiscale reduced basis method, where we construct multiscale reduced basis functions using an optimization method and the proper orthogonal decomposition method in the physical space and employ the quasi-Monte Carlo method in the random space. Our method is verified to be efficient: the spatial grid size is only proportional to the semiclassical parameter and (under suitable conditions) almost first order convergence rate is achieved in the random space with respect to the sample number.
13 Sep 2019
3:30pm - 4:30pm
Where
Room 3472, Academic Building (Lifts 25-26)
Speakers/Performers
Prof. Jingrun CHEN
Soochow University
Organizer(S)
Department of Mathematics
Contact/Enquiries
mathsemnar@ust.hk
Payment Details
Audience
Alumni, Faculty and Staff, PG Students, UG Students
Language(s)
English
Other Events
14 Jul 2025
Seminar, Lecture, Talk
IAS / School of Science Joint Lecture - Boron Clusters
Abstract The study of carbon clusters led to the discoveries of fullerenes, carbon nanotubes, and graphene. Are there other elements that can form similar nanostructures? To answer this questio...
15 May 2025
Seminar, Lecture, Talk
IAS / School of Science Joint Lecture - Laser Spectroscopy of Computable Atoms and Molecules with Unprecedented Accuracy
Abstract Precision spectroscopy of the hydrogen atom, a fundamental two-body system, has been instrumental in shaping quantum mechanics. Today, advances in theory and experiment allow us to ext...