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Event(s) on August 2008
- Wednesday, 6th August, 2008
Title: ICM Distinguished Computational Mathematics Lecture: Sublinear Algebra for Multidimensional Tensor Problems Speaker: Prof. Eugene Tyrtyshnikov, Institute of Numerical Mathematics, Russian Academy of Sciences, Russia Time/Place: 11:00 - 12:00
LT1, Cha Chi-Ming Science Tower, Ho Sin Hang Campus, HKBU
Abstract: By a tensor problem in general, we mean one where all data on input and output are given exactly or approximately in tensor formats defined by a small number of parameters compared to the total amount of data. For such problems we propose to seek for algorithms that work with data exclusively in tensor formats, the price we pay is a contamination of data through some approximation (recompression) at each operation. We show that a certain intentional corruption of data, under pretty mild assumptions, still preserves the convergence rate of superlinear iterations. Then, we discuss which tensor formats are best suitable and advocate to deal with the Tucker format for all operands. As an application, we present new approximate matrix inversion algorithms with linear and even sublinear complexity in the matrix size and recent suggestions for construction of eigenvalue solvers. Also, we discuss the gains of combination of tensor and typical Toeplitz-like structures. In particular, doubly Toeplitz (block Toeplitz with Toeplitz blocks) matrices of a wide class can be approximately inverted with the complexity of order of square root of the matrix size.
- Monday, 18th August, 2008
Title: Two-phase Viscoelastic Flow Simulation by Moving Finite Element Method Speaker: Mr. Yubo Zhang, MATH Dept., Hong Kong Baptist University, HKSAR, China Time/Place: 14:30 - 15:30
FSC1111, Fong Shu Chuen Library, HSH Campus
Abstract: We introduced the moving finite elements method for two-phase viscoelastic flow. Phase-field model was adopted to handle interfacial dynamics between different fluid phases. Numerical results show that the adaptive moving mesh technique based on harmonic mapping is effective for such problems by imposing a diffused monitor function which produces high quality mesh near the interface. When the interfacial width become thinner, it is almost impossible to solve using uniform mesh because of the huge amount of mesh nodes. On the other hand, moving mesh still work for much thinner interface and the mesh will automatically adapt the phase solution according to its singularity region. Both accuracy and performance were boosted up.