Omar Ghattas

TL;DR: This work presents scalable algorithms for parallel adaptive mesh refinement and coarsening (AMR), partitioning, and 2:1 balancing on computational domains composed of multiple connected two-dimensional quadtrees or three-dimensional octrees, referred to as a forest of octrees.

TL;DR: This work addresses the solution of large-scale statistical inverse problems in the framework of Bayesian inference with a so-called Stochastic Monte Carlo method.

TL;DR: A model-constrained adaptive sampling methodology is proposed for the reduction of large-scale systems with high-dimensional parametric input spaces using an efficient adaptive algorithm that scales well to systems with a large number of parameters.

TL;DR: A system that helps automate the task of writing efficient portable unstrucmred mesh solvers for distributed memory parallel supercomputers and indicates that, despite the highly irregular structure of the problem, excellent performance and scalability are achieved.

TL;DR: A new method for steady-state PDE-constrained optimization, based on the idea of using a full space Newton solver combined with an approximate reduced space quasi-Newton SQP preconditioner is proposed, which is fully parallelizable, exploits the structure of available parallel algorithms for the PDE forward problem, and is locally quadratically convergent.