수요 응용수학 세미나
연사 : Shi Jin 교수 (위스콘신 대학교 수학과)
제목 : "Hamiltonian Systems and Liouville Equations with Discontinuous
Hamiltonians: Computation of High Frequency Waves in
Heterogeneous Media"
일시 : 2007. 5. 2(수), 17:00
장소 : 수리과학과 산업경영학동 3221호실
요약 : We introduce Eulerian methods that are efficient in computing high frequency waves through heterogeneous media. The method is based on the classical Liouville equation in phase space, with discontinuous Hamiltonians (or singular coefficients) due to the barriers or material interfaces. We provide physically relevant interface conditions consistent with the correct transmissions and reflections, and then build the interface conditions into the numerical fluxes. This method allows the resolution of high frequency waves without numerically resolving the small wave lengths, and capture the correct transmissions and reflections at the interface. Moreover, we extend the method to include diffraction, and quantum barriers, by incorporating diffraction effects and quantum scattering information at the interface.
Applications to semiclassical limit of linear Schrodinger equation, geometrical optics, elastic waves, and semiconductor device modeling, will be discussed.
연사 : Shi Jin 교수 (위스콘신 대학교 수학과)
제목 : "Hamiltonian Systems and Liouville Equations with Discontinuous
Hamiltonians: Computation of High Frequency Waves in
Heterogeneous Media"
일시 : 2007. 5. 2(수), 17:00
장소 : 수리과학과 산업경영학동 3221호실
요약 : We introduce Eulerian methods that are efficient in computing high frequency waves through heterogeneous media. The method is based on the classical Liouville equation in phase space, with discontinuous Hamiltonians (or singular coefficients) due to the barriers or material interfaces. We provide physically relevant interface conditions consistent with the correct transmissions and reflections, and then build the interface conditions into the numerical fluxes. This method allows the resolution of high frequency waves without numerically resolving the small wave lengths, and capture the correct transmissions and reflections at the interface. Moreover, we extend the method to include diffraction, and quantum barriers, by incorporating diffraction effects and quantum scattering information at the interface.
Applications to semiclassical limit of linear Schrodinger equation, geometrical optics, elastic waves, and semiconductor device modeling, will be discussed.
