Scalable Two-level Domain Decomposition Algorithms for Stochastic Systems

A Risk-averse Inventory-based Supply Chain Protection Problem with Adapted Stochastic Measures under Intentional Facility Disruptions: Decomposition and Hybrid Algorithms

Owing to rising intentional events, supply chain disruptions have been considered by setting up a game between two players, namely, a designer and an interdictor contesting on minimizing and maximizing total cost, respectively. The previous studies have found the equilibrium solution by taking transportation, penalty and restoration cost into account. To contribute further, we examine how incor...

UN CO RR EC TE D PR O O F 1 Domain Decomposition Methods of Stochastic PDEs 2

In conjunction with modern high performance computing systems, domain decomAQ1 8 position algorithms permit simulation of PDEs with extremely high resolution nu9 merical models. Such computational models substantially reduce discretization er10 rors. In realistic simulation of certain physical systems, it is however necessary to 11 consider the heterogeneities of the model parameters. Whenever ...

Domain decomposition method of stochastic PDEs: a two-level scalable preconditioner

A domain decomposition method of stochastic PDEs: An iterative solution techniques using a two-level scalable preconditioner

Recent advances in high performance computing systems and sensing technologies motivate computational simulations with extremely high resolution models with capabilities to quantify uncertainties for credible numerical predictions. A two-level domain decomposition method is reported in this investigation to devise a linear solver for the large-scale system in the Galerkin spectral stochastic fi...

Implicit Space-Time Domain Decomposition Methods for Stochastic Parabolic Partial Differential Equations

We introduce and study parallel space-time domain decomposition methods for solving deterministic and stochastic parabolic equations. Traditional parallel algorithms solve parabolic problems time step by time step. The parallelism is restricted to each time step, and the algorithms are purely sequential in time. In this paper, we develop some overlapping Schwarz methods whose subdomains cover b...