We address the problem of propagating input uncertainties through a computational fluid dynamics model. Methods such as Monte Carlo simulation can require many thousands (or more) of computational fluid dynamics solves, rendering them prohibitively expensive for practical applications. This expense can be overcome with reduced-order models that preserve the essential flow dynamics. The specific contributions of this paper are as follows: first, to derive a linearized computational fluid dynamics model that permits the effects of geometry variations to be represented with an explicit affine function; second, to propose an adaptive sampling method to derive a reduced basis that is effective over the joint probability density of the geometry input parameters. The method is applied to derive efficient reduced models for probabilistic analysis of a two-dimensional problem governed by the linearized Euler equations. Reduced-order models that achieve 3-orders-of-magnitude reduction in the number of states are shown to accurately reproduce computational fluid dynamics Monte Carlo simulation results at a fraction of the computational cost.

Abstract. Indecomposable polynomials are a special class of absolutely irreducible polynomials. Some improvements of important effective results on absolute irreducibility have recently appeared using Ruppert’s matrix. In a similar way, we show in this paper that the use of a Jacobian matrix gives

A coarse grid three-dimensional global inverse model of the

Differences, Sparsity. 1 INTRODUCTION In many nonlinear optimization problems one often needs to estimate the Jacobian matrix of a nonlinear function F : R

The paper presents a method for estimating the inverse Jacobian matrix of a function, without computing the direct Jacobian matrix. The resulting inverse Jacobian matrix is shown to perform much better in modelling a relation # = f (x) than the classical Moore-Penrose inverse J f

Abstract—Newton-Raphson State Estimation method using bus admittance matrix remains as an efficient and most popular method to estimate the state variables. Elements of Jacobian matrix are computed from standard expressions which lack physical significance. In this paper, elements of the state

This paper improves both the computational efficiency and numerical stability of the through-thelens camera control [5]. A simple 2m \Theta 7 Jacobian matrix is derived. The matrix equation is then solved using an efficient weighted least squares method while employing the singular value

inverse residual demand function, i.e., the Jacobian matrix, based on a multi-parameter sensitivity analysis of the optimal power flow solution, and characterize some of its properties. This Jacobian matrix provides valuable information, such as in characterizing a generation firm’s profit maximizing

Permanent email: Abstract: This paper provides a general proof of a relationship theorem between nonlinear analogue polynomial equations and the corresponding Jacobian matrix, presented recently by the present author. This theorem is also verified generally effective for all nonlinear polynomial

The design of locally optimal fault-tolerant manipulators has been previously addressed via adding constraints on the bases of a desired null space to the design constraints of the manipulators. Then by algebraic or numeric solution of the design equations, the optimal Jacobian matrix is obtained