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Michael Gaiewski

Publications and source records attributed to Michael Gaiewski.

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Reverse Stress Testing for Supply Chain Resilience

Supply chains' increasing globalization and complexity have recently produced unpredictable disruptions, ripple effects, and cascading resulting failures. Proposed practices for managing these concerns include the advanced field of forward stress testing, where threats and predicted impacts to the supply chain are evaluated to harden the system against the most damaging scenarios. Such approaches are limited by the almost endless number of potential threat scenarios and cannot capture residual risk. In contrast to forward stress testing, this paper develops a reverse stress testing (RST) methodology that allows to predict which changes, with probabilistic certainty, across the supply chain network are most likely to cause a specified level of disruption at a specific entity in the network. The methodology was applied to the case of copper wire imports into the USA, a simple good which may have significant implications for national security. Results show that Canada, Chile, and Mexico are predicted to consistently be sources of disruptions at multiple loss levels. Other countries (e.g., Papua New Guinea) may contribute to small disruptions but be less important for the catastrophic losses of concern for decision makers. Other countries' disruptions would be catastrophic (e.g., Chile). The proposed methodology is the first case of reverse stress testing application in complex multilayered supply chains and can be used to address both risk and resilience.

physics.data-an

An H1-Conforming Solenoidal Basis for Velocity Computation on Powell-Sabin Splits for the Stokes Problem

A solenoidal basis is constructed to compute velocities using a certain finite element method for the Stokes problem. The method is conforming, with piecewise linear velocity and piecewise constant pressure on the Powell-Sabin split of a triangulation. Inhomogeneous Dirichlet conditions are supported by constructing an interpolating operator into the solenoidal velocity space. The solenoidal basis reduces the problem size and eliminates the pressure variable from the linear system for the velocity. A basis of the pressure space is also constructed that can be used to compute the pressure after the velocity, if it is desired to compute the pressure. All basis functions have local support and lead to sparse linear systems. The basis construction is confirmed through rigorous analysis. Velocity and pressure system matrices are both symmetric, positive definite, which can be exploited to solve their corresponding linear systems. Significant efficiency gains over the usual saddle-point formulation are demonstrated computationally.

math.NA