反问题理论研究与计算会议通知

由浙大数学院主办的反问题理论研究与计算会议拟于12月21日-12月22日在浙江大学玉泉校区召开。本次会议将围绕反问题理论中的研究与计算展开讨论。会议将邀请来自国内外反问题领域的专家出席会议并做报告。

时间：2017年12月21日-12月22日

地点：浙江大学玉泉校区逸夫工商楼2楼200-9报告厅

联系人：汪燕

电话：0571-87953947

浙江大学数学科学学院

2017年12月18日

简明日程：

部分摘要：

陆帅（复旦大学）

On parameter identification in linear stochastic differential equations by Gaussian statistics

Linear stochastic differential equations (SDE) arise in many contemporary sciences and engineering involving dynamical processes. These SDEs are governed by several parameters, for instance the damping coefficient, the volatility or diffusion coefficient and possibly an external forcing. Identification of these parameters allows a better understanding of the dynamical processes and its hidden statistics. By calculating the Gaussian statistics explicitly for the Ornstein--Uhlenbeck process with constant parameters and Langevin equations with periodic parameters, we propose a parameter identification approach recovering these parameters by minimizing the difference between the empirical statistics. The proposed approach is further extended to parameter identification of SDEs which is indirectly observed by another random variable.

李培军 (Pudure University)

Electromagnetic field enhancement in a subwavelength rectangular open cavity

Consider the transverse magnetic polarization of the electromagnetic scattering of a plane wave by a perfectly conducting plane surface, which contains a two-dimensional subwavelength rectangular cavity. The enhancement is investigated fully for the electric and magnetic fields arising in such an interaction. The cavity wall is assumed to be a perfect electric conductor, while the cavity bottom is allowed to be either a perfect electric conductor or a perfect magnetic conductor. We show that the significant field enhancement may be achieved in both nonresonant and resonant regimes. The proofs are based on variational approaches, layer potential techniques, boundary integral equations, and asymptotic analysis. Numerical experiments will be presented to confirm the theoretical findings.

武海军（南京大学）

FEM and CIP-FEM for Helmholtz Equation with High Wave Number and PML Truncation

The Helmholtz scattering problem with high wave number is truncated by the perfectly matched layer (PML) technique and then discretized by the linear continuous interior penalty finite element method (CIP-FEM). It is proved that the truncated PML problem satisfies the inf--sup condition with inf--sup constant of order $O(k^{-1})$. Stability and convergence of the truncated PML problem are discussed. In particular, the convergence rate is twice of the previous result. The preasymptotic error estimates in the energy norm of the linear CIP-FEM as well as FEM are proved to be $C_1kh+C_2k^3h^2$ under the mesh condition that $k^3h^2$ is sufficiently small. Numerical tests are provided to illustrate the preasymptotic error estimates and show that the penalty parameter in the CIP-FEM may be tuned to reduce greatly the pollution error.

杨扬（密歇根州立大学）

A coupled physics inverse problem in electro-seismic imaging

Electro-seismic imaging is a geophysical imaging modality where electromagnetic wave is used to induce seismic wave in porous media. The mathematical model was derived by S. Pride in 1994 as a coupled system of the Maxwell's equations and the Biot's equations. In this talk, we will discuss a coupled physics inverse problem arising in electro-seismic imaging. The problem consists of retrieval of source data in the Biot's equations and inversion of the Maxwell's equations from the internal measurement. We will describe a time reversal approach to reconstruct the source data, and then prove that some parameters in the Maxwell's equations can be uniquely and stably determined from such data. This is based on joint work with Jie Chen, Yixian Gao and Peijun Li.