hp-DGFEM for Partial Differential Equations with Nonnegative Characteristic Form

Presented as Invited Lecture at the International Symposium on Discontinuous Galerkin Methods: Theory, Computation and Applications, in Newport, RI, USA.\ud \ud We develop the error analysis for the hp-version of a discontinuous finite element approximation to second-order partial differential equations with nonnegative characteristic form. This class of equations includes classical examples of second-order elliptic and parabolic equations, first-order hyperbolic equations, as well as equations of mixed type. We establish an a priori error bound for the method which is of optimal order in the mesh size h and 1 order less than optimal in the polynomial degree p. In the particular case of a first-order hyperbolic equation the error bound is optimal in h and 1/2 an order less than optimal in p

Electrical Network-Based Time-Dependent Model of Electrical Breakdown in Water

A time-dependent, two-dimensional, percolative approach to model dielectric breakdown based on a network of parallel resistor–capacitor elements having random values, has been developed. The breakdown criteria rely on a threshold electric field and on energy dissipation exceeding the heat of vaporization. By carrying out this time-dependent analysis, the development and propagation of streamers and prebreakdown dynamical evolution have been obtained directly. These model simulations also provide the streamer shape, characteristics such as streamer velocity, the prebreakdown delay time, time-dependent current, and relationship between breakdown times, and applied electric fields for a given geometry. The results agree well with experimental data and reports in literature. The time to breakdown (tbr) for a 100 μm water gap has been shown to be strong function of the applied bias, with a 15–185 ns range. It is also shown that the current is fashioned not only by dynamic changes in local resistance, but that capacitive modifications arising from vaporization and streamer development also affect the transient behavior

An investigation of heuristic decomposition to tackle workforce scheduling and routing with time-dependent activities constraints

This paper presents an investigation into the application of heuristic decomposition and mixed-integer programming to tackle workforce scheduling and routing problems (WSRP) that involve timedependent activities constraints. These constraints refer to time-wise dependencies between activities. The decomposition method investigated here is called repeated decomposition with con ict repair (RDCR) and it consists of repeatedly applying a phase of problem decomposition and sub-problem solving, followed by a phase dedicated to con ict repair. In order to deal with the time-dependent activities constraints, the problem decomposition puts all activities associated to the same location and their dependent activities in the same sub-problem. This is to guarantee the satisfaction of time-dependent activities constraints as each sub-problem is solved exactly with an exact solver. Once the assignments are made, the time windows of dependent activities are fixed even if those activities are subject to the repair phase. The paper presents an experimental study to assess the performance of the decomposition method when compared to a tailored greedy heuristic. Results show that the proposed RDCR is an effective approach to harness the power of mixed integer programming solvers to tackle the diffcult and highly constrained WSRP in practical computational time. Also, an analysis is conducted in order to understand how the performance of the different solution methods (the decomposition, the tailored heuristic and the MIP solver) is accected by the size of the problem instances and other features of the problem. The paper concludes by making some recommendations on the type of method that could be more suitable for different problem sizes

Tractability in Constraint Satisfaction Problems: A Survey

International audienceEven though the Constraint Satisfaction Problem (CSP) is NP-complete, many tractable classes of CSP instances have been identified. After discussing different forms and uses of tractability, we describe some landmark tractable classes and survey recent theoretical results. Although we concentrate on the classical CSP, we also cover its important extensions to infinite domains and optimisation, as well as #CSP and QCSP