Past SCAIM Seminars

Tue, 2016-10-25 12:30 - 14:00
Eldad Haber, EOAS UBC
Solving Maxwell's equations for earth science applications requires the discretization of large domains with sufficiently small mesh to capture local conductivity variation. Multiscale methods are discretization techniques that allow to use a coarse mesh and still obtain accuracy that is obtained through finer meshes. However, when considering the multiscale solution of vector equations, basic operator properties are not conserved. In this talk we will show how to extend multiscale methods for vector quantities and demonstrate their use for Maxwell's equations.
Tue, 2016-10-04 12:30 - 14:00
Jessica Bosch, Computer Science, UBC
The Cahn-Hilliard equation models the motion of interfaces between several phases. The underlying energy functional includes a potential for which different types were proposed in the literature. We consider smooth and nonsmooth potentials with a focus on the latter. In the nonsmooth case, we apply a function space-based algorithm, which combines a Moreau-Yosida regularization technique with a semismooth Newton method. We apply classical finite element methods to discretize the problems in space.
Tue, 2016-09-20 12:30 - 14:00
Fred Roosta, Statistics UC Berkeley
Many data analysis applications require the solution of optimization problems involving a sum of large number of functions. We consider the problem of minimizing a sum of n functions over a convex constraint set. Algorithms that carefully sub-sample to reduce n can improve the computational efficiency, while maintaining the original convergence properties. For second order methods, we first consider a general class of problems and give quantitative convergence results for variants of Newtons methods where the Hessian or the gradient is uniformly sub-sampled.
Tue, 2016-09-06 12:30 - 14:00
Andy Wathen, Mathematical Institute, Oxford University
Descriptive convergence estimates or bounds for Krylov subspace iterative methods for nonsymmetric matrix systems are keenly desired but remain elusive. In the case of symmetric (self-adjoint) matrices, bounds based on eigenvalues can be usefully descriptive of observed convergence; an important consequence is that there are rigorous criteria for what constitutes a good preconditioner for symmetric matrices.
Tue, 2016-04-05 12:30 - 14:00
Julie Nutini, UBC Computer Science
There has been significant recent work on the theory and application of randomized coordinate descent algorithms, beginning with the work of Nesterov, who showed that a random-coordinate selection rule achieves the same convergence rate as the Gauss-Southwell selection rule. This result suggests that we should never use the Gauss-Southwell rule, as it is typically much more expensive than random selection.
Tue, 2016-03-15 12:30 - 14:00
Michael Friedlander, CS UBC and UC Davis
Convex optimization problems in a variety of applications have favourable objectives but complicating constraints, and first-order methods, often needed for large problems, are not immediately applicable. We propose a level-set approach that exchanges the roles of the objective and constraint functions, and instead approximately solves a sequence of parametric problems. We describe the theoretical and practical properties of this approach for a range of problems, including low-rank semidefinite optimization, which arise in matrix-completion applications. Joint work with A. Aravkin, J.
Tue, 2016-02-23 12:30 - 14:00
Anthony Wachs
Particle-laden flows are ubiquitous in environmental, geophysical and engineering processes. The intricate dynamics of these two-phase flows is governed by the momentum, heat and mass transfer between the continuous fluid phase and the dispersed particulate phase. While some multi-phase processes may be successfully modelled at the continuum scale through closure approximations, an increasing number of applications require resolution across scales, e.g. dense suspensions, fluidized beds.
Tue, 2016-01-26 12:30 - 14:00
Nilima Nigam, SFU Mathematics
The response of the muscle-tissue unit (MTU) to activation and applied forces is affected by the architectural details as well as the material properties of this nearly-incompressible tissue. We will describe the (highly nonlinear) elastic equations governing this response for a fully three-dimensional, quasi-static, fully nonlinear and anisotropic MTU. We describe a three-field formulation for this problem, and present a DG discretization strategy. The scheme was implemented using {\tt deal.ii}.
Tue, 2015-11-24 12:30 - 14:00
Jonathan Bardsley, Math Department, University of Montana
Many solution techniques for inverse problems involve solving an optimization problem using a numerical method. For example, the Tikhonov regularized solution is commonly defined as the minimizer of a penalized least squares function. Uncertainty quantification (UQ), on the other hand, often requires sampling from the Bayesian posterior density function arising from the assumed physical model, measurement error model, and prior probability density function.
Tue, 2015-11-17 12:30 - 14:00
Alexandre Bouchard-Cote, Statistics UBC
Computational biology, spatio-temporal analysis, natural language processing and a range of other fields rely on increasingly complex probabilistic models to make predictions and take action. In practice, these models often need to incorporate high-dimensional latent variables, complex combinatorial spaces and various heterogeneous data-structures.
Templates provided by UBC Department of Physics & Astronomy

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