Model order reduction with novel discrete empirical interpolation methods in space-time

This work proposes novel techniques for the efficient numerical simulation of parameterized, unsteady partial differential equations. Projection-based reduced order models (ROMs) such as the reduced basis method employ a (Petrov-)Galerkin projection onto a linear low-dimensional subspace. In unsteady applications, space-time reduced basis (ST-RB) methods have been developed to achieve a dimension reduction both in space and time, eliminating the computational burden of time marching schemes. However, nonaffine parameterizations dilute any computational speedup achievable by traditional ROMs. Computational efficiency can be recovered by linearizing the nonaffine operators via hyper-reduction, such as the empirical interpolation method in matrix form. In this work, we implement new hyper-reduction techniques explicitly tailored to deal with unsteady problems and embed them in a ST-RB framework. For each of the proposed methods, we develop a posteriori error bounds. We run numerical tests to compare the performance of the proposed ROMs against high-fidelity simulations, in which we combine the finite element method for space discretization on 3D geometries and the Backward Euler time integrator. In particular, we consider a heat equation and an unsteady Stokes equation. The numerical experiments demonstrate the accuracy and computational efficiency our methods retain with respect to the high-fidelity simulations

Collaborate and die! Exploring different understandings of organisational cooperation within Scotland's uncertain North Sea oil and gas industry.

This study ethnographically explores how collaboration is enacted within two differently structured sub-sea engineering organisations local to the oil & gas industry in Aberdeen, Scotland. Literature suggests organisational collaboration practices are largely dependent on trust, historical cooperation, establishing interpersonal relations and information sharing networks. Such notions are suggested as readily enacted in Aberdeen. However, following changes in industry landscape, we uncover a variety of additional factors pertaining to macro-level local industry climate, and meso-level organisational cultures that shape different perceptions, understandings, and enactments of collaboration. To grow current scholarly thinking, we define how such diverse understandings actively prevent organisational collaboration in the restrictively competitive climate of Aberdeen’s oil & gas industry. Implications for expanding understandings of collaboration in employment sectors facing substantial industry destabilisation and reformation are discussed

Space-time reduced basis methods for parametrized unsteady Stokes equations

In this work, we analyse space-time reduced basis methods for the efficient numerical simulation of hemodynamics in arteries. The classical formulation of the reduced basis (RB) method features dimensionality reduction in space, while finite differences schemes are employed for the time integration of the resulting ordinary differential equation (ODE). Space-time reduced basis (ST-RB) methods extend the dimensionality reduction paradigm to the temporal dimension, projecting the full-order problem onto a low-dimensional spatio-temporal subspace. Our goal is to investigate the application of ST-RB methods to the unsteady incompressible Stokes equations, with a particular focus on stability. High-fidelity simulations are performed using the Finite Element (FE) method and BDF2 as time marching scheme. We consider two different ST-RB methods. In the first one - called ST-GRB - space-time model order reduction is achieved by means of a Galerkin projection; a spatio-temporal velocity basis enrichment procedure is introduced to guarantee stability. The second method - called ST-PGRB - is characterized by a Petrov--Galerkin projection, stemming from a suitable minimization of the FOM residual, that allows to automatically attain stability. The classical RB method - denoted as SRB-TFO - serves as a baseline for the theoretical development. Numerical tests have been conducted on an idealized symmetric bifurcation geometry and on the patient-specific one of a femoropopliteal bypass. The results show that both ST-RB methods provide accurate approximations of the high-fidelity solutions, while considerably reducing the computational cost. In particular, the ST-PGRB method exhibits the best performance, as it features a better computational efficiency while retaining accuracies in accordance with theoretical expectations.Comment: 30 pages (25 + 5 in appendix), 4 figures, 4 tables. To appear on SIAM Journal on Scientific Computing (SISC

Music Composition in the 17th and 18th centuries: A Historical Analysis of how Georg Frideric Handel Participated in “Borrowing”

The primary focus in this research paper is borrowing; this means borrowing from other composers, and self-borrowing from a previous composition. It is widely accepted in scholarship that Georg Frideric Handel participated in the action of borrowing. However, there is significantly more contention among scholars surrounding both the extent of Handel’s borrowing, as well as what the appropriate modern perspective is for these actions. In this research paper our primary focus will be on Handel’s borrowings, the benefits he received from these actions, and the historical lens of borrowing in the seventeenth and eighteenth centuries

Paraplegia Following Pneumonectomy and Descending Thoracic Aorta Mass Resection

We present a case of paraplegia following an en bloc resection of a lung mass with thoracic aorta involvement. This complex case poses the opportunity to discuss several perioperative issues: fluid management for pneumonectomy; fluid management for thoracic aorta cross-clamping; and spinal cord ischemia