No abstract

Optimization problems constrained by nonlinear partial differential equations have been the focus of intense research in scientific computing lately. Current methods for the parallel numerical solution of such problems involve sequential quadratic programming (SQP), with either reduced or full space approaches. In this paper we propose and investigate a class of parallel full space SQP Lagrange-Newton-Krylov-Schwarz (LNKSz) algorithms. In LNKSz, a Lagrangian functional is formed and differentiated to obtain a Karush-Kuhn-Tucker (KKT) system of nonlinear equations. Inexact Newton method with line search is then applied. At each Newton iteration the linearized KKT system is solved with a Schwarz preconditioned Krylov subspace method. We apply LNKSz to the parallel numerical solution of some boundary control problems of two-dimensional incompressible Navier-Stokes equations. Numerical results are reported for different combinations of Reynolds number, mesh size and number of parallel processors. We also compare the application of LNKSz method to flow control problems against the application of NKSz method to flow simulation problems.

We address general approaches to the rational selection and validation of mathematical and computational models of tumor growth using methods of Bayesian inference. The model classes are derived from a general diffuse-interface, continuum mixture theory and focus on mass conservation of mixtures with up to four species. Synthetic data are generated using higher-order base models. We discuss general approaches to model calibration, validation, plausibility, and selection based on Bayesian-based methods, information theory, and maximum information entropy. We also address computational issues and provide numerical experiments based on Markov chain Monte Carlo algorithms and high performance computing implementations.

QUESO is a collection of statistical algorithms and programming constructs supporting research into the uncertainty quantification (UQ) of models and their predictions. It has been designed with three objectives: it should (a) be sufficiently abstract in order to handle a large spectrum of models, (b) be algorithmically extensible, allowing an easy insertion of new and improved algorithms, and (c) take advantage of parallel computing, in order to handle realistic models. Such objectives demand a combination of an object-oriented design with robust software engineering practices. QUESO is written in C++, uses MPI, and leverages libraries already available to the scientific community. We describe some UQ concepts, present QUESO, and list planned enhancements.