Numerical Analysis Group Internal Seminar

Please note that the list below only shows forthcoming events, which may not include regular events that have not yet been entered for the forthcoming term. Please see the past events page for a list of all seminar series that the department has on offer.

Past events in this series
Today
14:00
Thomas Roy
Abstract


In petroleum reservoir simulation, the standard preconditioner is a two-stage process which involves solving a restricted pressure system with AMG. Initially designed for isothermal models, this approach is often used in the thermal case. However, it does not incorporate heat diffusion or the effects of temperature changes on fluid flow through viscosity and density. We seek to develop preconditioners which consider this cross-coupling between pressure and temperature. In order to study the effects of both pressure and temperature on fluid and heat flow, we first consider a model of non-isothermal single phase flow through porous media. For this model, we develop a block preconditioner with an efficient Schur complement approximation. Then, we extend this method for multiphase flow as a two-stage preconditioner.

  • Numerical Analysis Group Internal Seminar
Today
14:30
Ricardo Ruiz Baier
Abstract

In this talk I will introduce a new mathematical model for the computational modelling of the active contraction of cardiac tissue using stress-assisted conductivity as the main mechanism for mechanoelectrical feedback. The coupling variable is the Kirchhoff stress and so the equations of hyperelasticity are written in mixed form and a suitable finite element formulation is proposed. Next I will introduce a simplified version of the coupled system, focusing on its analysis in terms of solvability and stability of continuous and discrete mixed-primal formulations, and the convergence of these methods will be illustrated through two numerical tests.

  • Numerical Analysis Group Internal Seminar
27 November 2018
14:00
Oliver Sheridan-Methven
Abstract

Employing the usual multilevel Monte Carlo estimator, we introduce a framework for estimating the solutions of SDEs by an Euler-Maruyama scheme. By considering the expected value of such solutions, we produce simulations using approximately normal random variables, and recover the estimate from the exact normal distribution by use of a multilevel correction, leading to faster simulations without loss of accuracy. We will also highlight this concept in the framework of reduced precision and vectorised computations.

  • Numerical Analysis Group Internal Seminar
27 November 2018
14:30
Patrick Farrell
Abstract

When approximating PDEs with the finite element method, large sparse linear systems must be solved. The ideal preconditioner yields convergence that is  algorithmically optimal and parameter robust, i.e. the number of Krylov iterations required to solve the linear system to a given accuracy does not grow substantially as the mesh or problem parameters are changed.

Achieving this for the stationary Navier-Stokes has proven challenging: LU factorisation is Reynolds-robust but scales poorly with degree of freedom count, while Schur complement approximations such as PCD and LSC degrade as the Reynolds number is increased.

Building on the work of Schöberl, Olshanskii and Benzi, in this talk we present the first preconditioner for the Newton linearisation of the stationary Navier--Stokes equations in three dimensions that achieves both optimal complexity and Reynolds-robustness. The scheme combines a novel tailored finite element discretisation, discrete augmented Lagrangian stabilisation, a custom prolongation operator involving local solves on coarse cells, and an additive patchwise relaxation on each
level. We present 3D simulations with over one billion degrees of freedom with robust performance from Reynolds number 10 to 5000.

  • Numerical Analysis Group Internal Seminar
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