Marie Graff, Department of Earth, Ocean and Atmospheric Sciences, The University of British Columbia
A nonlinear optimization method is proposed for the solution of inverse scattering problems in the frequency domain, when the scattered field is governed by the Helmholtz equation. The time-harmonic inverse medium problem is formulated as a PDE-constrained optimization problem and solved by an inexact truncated Newton-type iteration. Instead of a grid-based discrete representation, the unknown wave speed is projected to a particular finite-dimensional basis of eigenfunctions, which is iteratively adapted during the optimization.
Curt Da Silva, Seismic Laboratory for Imaging and Modelling, The University of British Columbia
Many useful and interesting optimization problems can be cast in a convex composite form min_x h(c(x)),
where h is a non-smooth but convex function and c is a smooth nonlinear or linear mapping. The non-smoothness of the
outer function prevents traditional methods such as the Gauss-Newton method from converging quickly, which is problematic
for large scale problems. In this talk, we will explore level set methods, aka the SPGL1 'trick', for solving this class of problem
when we can easily project on to the level sets of h(z).
Many chemical systems exhibit a regular pattern of precipitate bands known as Liesegang rings in tribute to the chemist Raphael E. Liesegang who demonstrated them using a reaction of silver nitrate and potassium dichromate. A variety of theories have been studied to try and understand how these patterns develop and one of the most seminal papers on the topic was a mathematical model developed by Keller and Rubinow using a supersaturation framework. This model predicted the formation of primary and secondary bands using heuristic arguments and assumptions about the underlying equations.
Chen Greif, Department of Computer Science, The University of British Columbia
We introduce SPMR, a new family of methods for iteratively solving saddle-point systems
using a minimum or quasi-minimum residual approach. No symmetry assumptions are made. The basic mechanism underlying the method is a novel simultaneous bidiagonalization procedure that yields a simplified saddle-point matrix on a projected Krylov-like subspace, and allows for a monotonic short-recurrence iterative scheme. We develop a few variants, demonstrate the advantages of our approach, derive optimality conditions, and discuss connections to existing methods.
Ben Adcock, Department of Mathematics, Simon Fraser University
Many problems in scientific computing require the approximation of
smooth, high-dimensional functions from limited amounts of data. For
instance, a typical problem in uncertainty quantification involves
identifying the parameter dependence of the output of a computational
Colin Macdonald, Department of Mathematics, The University of British Columbia
RIDC (revisionist integral deferred correction) methods are a class of time integrators well-suited to parallel computing. RIDC methods can achieve high-order accuracy in wall-clock time comparable to forward Euler. The methods use a predictor and multiple corrector steps. Each corrector is lagged by one time step; the predictor and each of the correctors can then be computed in parallel. This presentation introduces RIDC methods and demonstrates their effectiveness on some test problems.
Simone Brugiapaglia, Department of Mathematics, Simon Fraser University
We present the CORSING (COmpRessed SolvING) method for the numerical
approximation of PDEs. Establishing an analogy between the bilinear form
associated with the weak formulation of a PDE and the signal acquisition
process, CORSING combines the classical Petrov-Galerkin method with
David Gleich, Department of Computer Science, Purdue University
Higher-order methods that use multiway and multilinear correlations are necessary to identify important structures in complex data from biology, neuroscience, ecology, systems engineering, and sociology. We will study our recent generalization of spectral clustering to higher-order structures in depth. This will include a generalization of the Cheeger inequality (a concise statement about the approximation quality) to higher-order structures in networks including network motifs.
Martin Oberlack, Chair of Fluid Dynamics, TU Darmstadt
The development of the new discontinuous Galerkin (DG) framework BoSSS (bounded support spectral solver) starting in 2007. Solvers for incompressible as well as compressible single and multi-phase flows were implemented.
The code features a modern object-oriented design and is of course MPI-parallel. Within the development cycle, we use unit-testing to ensure software quality: this covers a wide range of tests, form very simple ones that test e.g.
We will present JuMP, a modeling language for mathematical optimization embedded in the Julia programming language. JuMP provides a natural, algebraic syntax for expressing a wide range of optimization problems, from linear programming to derivative-based nonconvex optimization. We will walk through Jupyter notebooks to demonstrate basic modeling examples. We will not assume a strong background in optimization. Participants are encouraged but not required to bring laptops.