Weak formulations in Analytical Dynamics are developed, paralleling the variational methods in elastostatics, and including a fundamental yet novel approach for treating constraints (both holonomic and nonholonomic). A general three-field approach is presented, in which the momentum balance conditions, the compatibility conditions between displacement and velocity, the constitutive relations an...

In this article we study a network design problem that arises in the exploitation of wind energy. We formulate this problem as a mixed integer programming problem, relate this formulation to other problems in combinatorial optimization, strengthen the formulation and propose cutting planes, and finally present experimental results for real-world instances of the collection network design problem.

algorithm: variable V-cycle Let mk be the number of smoothings and assume that β0mk ≤ mk−1 ≤ β1mk , where 1 < β0 ≤ β1. Algorithm Let B1 = Λ −1 1 . Assuming Bk−1 : Σk−1 → Σk−1 be defined, define Bk : Σk → Σk as follows. Let g ∈ Σk and τ 0 = 0. (1) τ l = τ l−1 + Rk(g −Λkτ ) for l = 1, · · · , mk; (2) σk = τk + IkBk−1I t k(g −Λkτ k); (3) σ = σ + Rk(g −Λkσ ) for l = mk + 1, · · · , 2mk ; Set Bkg = ...

We combine a dual-mixed finite element method with a Dirichletto-Neumann mapping (derived by the boundary integral equation method) to study the solvability and Galerkin approximations of a class of exterior nonlinear transmission problems in the plane. As a model problem, we consider a nonlinear elliptic equation in divergence form coupled with the Laplace equation in an unbounded region of th...

A design methodology based on a mixed adjoint approach for ow problems governed by the Incompressible Turbulent Navier Stokes equations is deduced and tested. The main feature of the algorithm is that instead of solving an exact discrete adjoint equation, it solves a fastconverging low-order adjoint formulation, saving an important amount of CPU time, and giving a smoothed approximation to the ...

We present an equivalent, compact reformulation of the `2,1 mixednorm minimization problem for joint sparse signal reconstruction from multiple measurement vectors (MMVs). The reformulation builds upon a compact parameterization, which models the rownorms of the sparse signal representation as parameters of interest, resulting in a significant reduction of the MMV problem size. Given the sparse...

In 2007, Vestal proposed Mixed-Criticality Scheduling (MCS) to increase utilisation despite imperfect timing evidence. Others have since refined the MCS problem formulation, proposed alternative scheduling approaches, and evaluated their performance. We assess existing MCS problem formulations from a safety assurance perspective and report problems found. Among these is the use of the word ‘cri...

We present a family of pairs of finite element spaces for the unaltered Hellinger–Reissner variational principle using polynomial shape functions on a single triangular mesh for stress and displacement. There is a member of the family for each polynomial degree, beginning with degree two for the stress and degree one for the displacement, and each is stable and affords optimal order approximati...

Most industrial model predictive controllers (MPC) use the traditional two-layer structure developed in the early 1980’s, where the upper layer defines optimal steady-state targets for inputs and outputs, while the lower layer calculates the control moves that drive the system towards these steady-state targets. Typically both layers use continuous quadratic programming (QP) formulations to der...

This paper presents a mixed variational framework and numerical examples to treat a bidimensional friction contact problem in large deformation. Two different contact algorithms with friction are developed using the 2D finite element code PLAST2. The first contact algorithm is the classical node-on-segment, and the second one corresponds to an extension of the mortar element method to a unilate...