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Differential Equations Seminar

Francesca R. McFadden, Kevin Williamson, UMBC

Monday, December 5, 2016
11:00 AM - 12:00 PM
Mathematics/Psychology : 401
Speaker: Francesca R. McFadden

Title: Computational complexity of exact stochastic simulation algorithms for spatially-distributed reaction-diffusion systems

Abstract: In this talk, we discuss exact stochastic simulation algorithms for modeling progression of reaction-diffusion systems. We describe algorithms meant to improve the computational complexity for domains showing spatial variation, especially when the spatial domain is subdivided into a large number of numerical cells. Theoretical comparisons of different strategies to get better efficiency are discussed and computational comparisons are shown for a simple example in the quasi-1D domain. Application to 2D and 3D domains is discussed. Different algorithms used are from Hu, Kang, and Othmer (2014).

Speaker: Kevin Williamson

Title: Numerical Solution of the Stokes-Brinkman Equation Using Mixed Finite Elements

Abstract: Flow in porous media has numerous applications, to include reservoir simulation, nuclear waste disposal, and carbon sequestration. Simulations are complicated due to a heterogeneous domain (varying porosity) and the presence of fractures and vugs. The Stokes-Brinkman equation combines Darcy's law (which models the porous region) with Stokes (which models the free-flowing region). This talk will begin with an overview of Stokes-Brinkman and then describe the discretization of the system using mixed finite elements. The resulting linear system is ill-conditioned and requires a preconditioner to speed up convergence to a solution. Two simple preconditioners will be presented and compared.