Brown Applied Mathematics Pattern Theory and Vision Seminar
Electrical Engineering and Computer Science MIT | |
Abstract: Recent interest in network coding sprang from the desire to establish in network connections infeasible through routing alone. The algebraic approach of Koetter and Medard has allowed a characterization of possible connections in networks but also opened many questions. Network codes can be viewed as a characterization of network behavior and thus encompass most functions of a network.
What is the role of network coding for recovery in networks? What is the relation between network management and network coding? What is the role of network coding in compression and can compression be integrated with network coding? What are the source-channel coding separation issues? Do coding theorems apply in the context of network coding and what form do they take? What relations exist between flows and network codes?
In this talk, we seek to present an overview of current results towards answering these questions. In particular, we propose network coding as a possible vehicle for an unified view of information transmission to encompass source coding, channel coding, routing and network management.
(Joint work with R. Koetter, M. Effros, D. Karger, T. Ho, S. Ray and J. Abounadi).
Scientific Computing Seminar
University of Illinois at Urbana-Champaign | |
Abstract: We have recently developed a new hybrid scheme for Maxwell's equations, combining the Finite-Difference Time-Domain (FDTD) scheme and the Finite Element Method (FEM). The hybrid scheme exploits the efficiency of the FDTD together with the ability of FEM to model complex boundaries. Our hybrid method is derived by applying Galerkin's method to the self-adjoint Maxwell's equations. The discretized curl-curl and identity operators are real symmetric semi-positive definite and positive definite matrices, respectively. Thus, the eigenvalues of the frequency domain eigenvalue problem are therefore real and non-negative, which makes stable time-stepping possible. The hybrid is proven to be stable for time steps up to the stability limit of the FDTD without added dissipation and the scheme is free from spurious solutions.
The hybrid scheme has been applied to problems involving scattering, antennas and microwave devices. Numerical results for a PEC sphere and the NASA almond will be shown during the seminar. Applications of interest to the microwave industry will also be presented.
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