Friday, 2:30-3:30pm, 458 Campbell Hall, tea to follow.

(unless otherwise noted)

contact: cnavasca@uab.edu

]]>(unless otherwise noted)

contact: cnavasca@uab.edu

Title. Designing Optimal Spectral Filters and Low-Rank Matrices for Inverse Problems

Abstract. Computing reliable solutions to inverse problems is important in many applications such as biomedical imaging, computer graphics, and security. Regularization by incorporating prior knowledge is needed to stabilize the inversion process. In this talk, we develop a new framework for solving inverse problems that incorporates probabilistic information in the form of training data. We provide theoretical results for the underlying Bayes risk minimization problem and discuss efficient approaches for solving the associated empirical Bayes risk minimization problem. Various constraints can be imposed to deal with large-scale problems. Here we describe methods for computing optimal spectral filters, for cases where the SVD is available, and methods for computing an optimal low-rank regularized inverse matrix, for cases where the forward model is not known.

This is joint work with Matthias Chung (Virginia Tech) and Dianne O'Leary (University of Maryland, College Park).

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Title. 3D Mixed Element Discontinuous Galerkin with Shock Capturing and RANS

Abstract. A parallel high-order Discontinuous Galerkin method is developed for mixed elements to solve the Navier-Stokes equations. A PDE-based artificial viscosity equation is implemented to smooth and stabilize shocks. To solve this system of non-linear equations a Newton solver is implemented and preconditioned flexible-GMRES is used to solve the linear system arising from the Jacobian matrix. The preconditioners that are implemented include Jacobi relaxation, Gauss-Seidel relaxation, line implicit Jacobi, and ILU(0). A wide variety of simulations are performed to demonstrate the capabilities of the DG solver. The inviscid simulations include a p-adapted subsonic flow over a cylinder, a p=0 h-adapted hypersonic flow over a sphere, and a large scale p=2 simulation of an aircraft with artificial viscosity to stabilize the shock formed on the wing. Two hypersonic viscous flows of a cylinder and sphere are simulated and compared to the NASA code LAURA. The solution matches closely to LAURA and the shock becomes more resolved as the polynomial degree is increased. The heating rate on the surface matches closely to LAURA at p=3. In the case of turbulent flows the Reynolds Averaged Navier-Stokes (RANS) equations are solved. The new negative-Spalart-Almaras model is implemented and used to solve turbulent flow over a NACA 0012 wing, RAE2822 wing, and a multi-element 30P30N wing. Finally, the parallel scalability is tested and good speed up is obtained using up to 2048 processor cores. As the polynomial degree increases the scalability improves. Although, an ideal speedup was not shown this was contributed to load balancing. These simulations demonstrate the capability of the DG solver to handle strong shocks, RANS, complex geometry, hp-adaption, and parallel scalability.

This is joint work with Dimitri J. Mavriplis.

Figure. M=17.605, Re=376,930 flow over a cylinder, contours of artificial viscosity (left) and contours of Mach number (right)]]>

Title. Universal computation by multi-particle quantum walk in 2D

Abstract. In this talk we discuss a model consisting of

Title. Additivity (or not) of the Fixed Point Property

Abstract. Let each of X, Y, and X intersect Y be a continuum with the fixed point property (fpp).We say that "the fpp is additive for X and Y" if X union Y has the fpp. If G is some class of continua with the fpp, we say that "the fpp is additive for G" provided that whenever X, Y, and X intersect Y are in G, the fpp is additive for X and Y.

Question. For what classes G of continua is the fpp additive?

We discuss the history of this question, reviewing both positive and negative results. We end with recent examples of Hagopian and Marsh that show the fpp is not additive for the class of tree-like continua.]]>