Date/Time : 04 Sep 2019 16:00
Venue : S17 #05-11 SR5
Speaker : Marko Hans Weber, National University of Singapore

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Date/Time : 28 Aug 2019 16:00
Venue : S17 #05-11 SR5
Speaker : Li-Lian Wang, Nanyang Technological University

Date/Time:28 Aug 2019 16:00 Venue: S17 #05-11 SR5 Speaker: Li-Lian Wang, Nanyang Technological University Fast Spectral Methods for PDEs with Integral Fractional Laplacian in Multiple Dimensions PDEs with fractional Laplacian have emerged as a powerful tool in modelling anomalous diffusion and nonlocal interactions, but their numerical solutions can be very difficult especially in multiple dimensions. Many nonlocal models are more physically motivated and naturally set in unbounded domains. In this talk, we shall present a superfast spectral-Galerkin method with two critical components (i) the Dunford-Taylor formulation of fractional Laplacian operator, and (ii) the use of Fourier-like bi-orthogonal mapped Chebyshev functions as basis functions. We shall also report some of our recent attempts for integral fractional Laplacian in bounded domains, which are deemed even more notoriously difficult for effective numerical discretisation. Along this line, we work with the formulation associated with the Fourier transformations, and derive a number of useful analytical formulas which are essential for the algorithm development. Add to calendar: 

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Date/Time : 21 Aug 2019 16:00
Venue : S17 #05-11 SR5
Speaker : Wang Weicheng, National Tsing Hua University, Taiwan

Date/Time:21 Aug 2019 16:00 Venue: S17 #05-11 SR5 Speaker: Wang Weicheng, National Tsing Hua University, Taiwan An Efficient Solver for Fractional Diffusion Equations The fractional order differential operators have attracted considerable attention recently as an essential tool for developing more sophisticated mathematical models that can accurately describe complex anomalous systems. Since the fractional order differential operators are nonlocal, the corresponding linear system involves a dense, structured Toeplitz matrix. Many research activities are devoted to developing robust and efficient solvers for such linear systems. In this talk, we propose a numerical method for the fractional diffusion equations based on a new preconditioner that can be used to develop direct and iterative solvers for fractional diffusion equations with total $O(N \log N)$ operations per time step. Numerical results suggests the new method is a competitive alternative to existing methods. Add to calendar: 

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Date/Time : 14 Aug 2019 16:00
Venue : 16:00 S17 #05-11 SR5
Speaker : Simon Etter, National University of Singapore

Date/Time:14 Aug 2019 16:00 Venue: S17 #05-11 SR5 Speaker: Simon Etter, National University of Singapore Polynomial and Rational Approximation for Electronic Structure Theory Density Functional Theory (DFT) and related electronic structure models are some of the largest consumers of computing power in supercomputing centres worldwide, and the bulk of this time is spent on evaluating functions of large, sparse matrices. Traditionally, such matrix functions have been computed by means of the eigenvalue decomposition, but the cubic scaling of standard eigensolvers with respect to the matrix size renders this ansatz prohibitively expensive in many applications. Several alternative algorithms have been developed in recent decades, among which the Pole Expansion and Selected Inversion (PEXSI) algorithm by Lin Lin and collaborators stands out for its ease of use and excellent parallel scaling. However, the runtime of the PEXSI scheme grows with $N^{3/2}$ for two-dimensional systems of $N$ atoms and with $N^2$ for three-dimensional systems, which is an important drawback of this method compared to most of its competitors. The first part of this talk will present a modification of the PEXSI algorithm which reduces its cost to linear in the system size regardless of the dimension. This modification is based on the observation that the LU factorisation of a sparse, well-conditioned matrix is localised, i.e. the magnitudes of the fill-in entries decay exponentially as we move away from the nonzero entries of the original matrix. The second part of this talk will discuss conductivity calculations, which introduce a new twist to the theory of electronic structure algorithms in that the matrix function to evaluate in this case is a bivariate one. The runtime of such calculations is proportional to the number of significant Chebyshev coefficients of the function $f(x,y) := 1/(x – y + s)$ with small imaginary $s$, and we will see that this number scales with only $|s|^{3/2}$ rather than $|s|^2$ as one might expect based on one-dimensional arguments. Add to calendar: 

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Date/Time : 12 Jun 2019 10:00
Venue : S17 #04-05 SR2
Speaker : Tomasz Tkocz , Carnegie Mellon University

Date/Time:12 Jun 2019 11:00 Venue: S17 #04-05 SR2 Speaker: Tomasz Tkocz, Carnegie Mellon University Volume of intersections of convex bodies with their symmetric images and efficient coverings Let K be a convex body with volume one and barycentre at the origin. How small is the volume of the intersection of K and -K? I shall discuss such lower bounds and present applications to the Hadwidger covering/illumination conjecture. Based on joint work with H. Huang, B. Slomka and B. Vritsiou. Add to calendar: 

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Date/Time : 12 Jun 2019 16:00
Venue : S17 #04-04 SR3
Speaker : Simon Weissmann, University of Mannheim

Date/Time:12 Jun 2019 15:00 Venue: S17 #04-04 SR3 Speaker: Simon Weissmann, University of Mannheim On the incorporation of box-constraints for ensemble Kalman inversion The Bayesian approach to inverse problems is widely used in practice to infer un- known parameters from noisy observations. In this framework, the ensemble Kalman inversion has been successfully applied for the quantification of uncertainties in various areas of applica- tions. In recent years, a complete analysis of the method has been developed for linear inverse problems adopting an optimization viewpoint. However, many applications require the incorpo- ration of additional constraints on the parameters, e.g. arising due to physical constraints. We propose a new variant of the ensemble Kalman inversion to include box constraints on the un- known parameters motivated by the theory of projected preconditioned gradient flows. Based on the continuous time limit of the constrained ensemble Kalman inversion, we discuss a complete convergence analysis for linear forward problems. We adopt techniques from filtering which are crucial in order to improve the performance and establish a correct descent, such as variance inflation. These benefits are highlighted through a number of numerical examples on various inverse problems based on partial differential equations. Add to calendar: 

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Date/Time : 21 May 2019 10:00
Venue : S17 #04-06 SR1
Speaker : Wei Cai, Southern Methodist University

Date/Time:21 May 2019 10:00 Venue: S17 #04-06 SR1 Speaker: Wei Cai, Southern Methodist University Algorithms for Wave Scattering of Random Media: Fast multipole method in layered media and a phase shift deep neural network for wideband learning In this talk, we will present two algorithms and numerical results for solving electromagnetic wave scattering of random meta-materials. Firstly, a fast multipole method for 3-D Helmholtz equation for layered media will be presented based on new multipole expansion (ME) and multipole to local translation (M2L) operators for layered media Green’s functions. Secondly, a parallel phase shift deep neural network (PhaseDNN) is proposed for wideband data learning. In order to achieve uniform convergence for low to high frequency content of data, phase shifts are used to convert high frequency learning to low frequency learning. Due to the fast learning of many DNNs in the low frequency range, PhaseDNN is able to learn wideband data uniformly in all frequencies. Reference: [1] B.Wang, W.Z. Zhang, W. Cai, Fast Multipole Method For 3-D Helmholtz Equation In Layered Media, arXiv:1902.05132 [2] W. Cai, X.G. Li, L.Z. Liu, PhaseDNN – A Parallel Phase Shift Deep Neural Network for Adaptive Wideband Learning , arXiv:1905.01389 Add to calendar: 

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Date/Time : 17 Apr 2019 15:00
Venue : S17 #04-04 SR3
Speaker : Zeng Fanhai, National University of Singapore

Date/Time:17 Apr 2019 15:00 Venue: S17 #04-04 SR3 Speaker: Zeng Fanhai, National University of Singapore Fast time-stepping method for fractional integral and derivative operators We develop two fast time-stepping methods with linear complexity to calculate the discrete convolution for the approximation of the fractional integral and derivative operators. The effectiveness of the fast methods are verified through a series of numerical examples for long-time integration, including a numerical study of a fractional reaction-diffusion model. Add to calendar: 

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Date/Time : 27 Mar 2019 16:00
Venue : S17 #04-06 SR1
Speaker : Zhao Quan, National University of Singapore

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