RECONSTRUCTED DISCONTINUOUS APPROXIMATION TO STOKES EQUATION IN A SEQUENTIAL LEAST SQUARES FORMULATION

We propose a new least squares finite element method to solve the Stokes problem with two sequential steps.The approximation spaces are constructed by the patch reconstruction with one unknown per element.For the first step,we reconstruct an approximation space consisting of piecewise curl-free polynomials with zero trace.By this space,we minimize a least squares functional to obtain the numerical approximations to the gradient of the velocity and the pressure.In the second step,we minimize another least squares functional to give the solution to the velocity in the reconstructed piecewise divergence-free space.We derive error estimates for all unknowns under both L 2 norms and energy norms.Numerical results in two dimensions and three dimensions verify the convergence rates and demonstrate the great flexibility of our method.

A Reconstructed Discontinuous Approximation to Monge-Ampère Equation in Least Square Formulation

We propose a numerical method to solve the Monge-Ampère equation which admits a classical convex solution.The Monge-Ampère equation is reformulated into an equivalent first-order system.We adopt a novel reconstructed discontinuous approximation space which consists of piecewise irrotational polynomials.This space allows us to solve the first-order system in two sequential steps.In the first step,we solve a nonlinear system to obtain the approximation to the gradient.A Newton iteration is adopted to handle the nonlinearity of the system.The approximation to the primitive variable is obtained from the approximate gradient by a trivial least squares finite element method in the second step.Numerical examples in both two and three dimensions are presented to show an optimal convergence rate in accuracy.It is interesting to observe that the approximation solution is piecewise convex.Particularly,with the reconstructed approximation space,the proposed method numerically demonstrates a remarkable robustness.The convergence of the Newton iteration does not rely on the initial values.The dependence of the convergence on the penalty parameter in the discretization is also negligible,in comparison to the classical discontinuous approximation space.

Micropolar interface model of thin-layered interconnection components with heterogeneous internal microstructures

Being a wide variety of thin-layered interconnection components in electronics packaging with relatively small scale and heterogeneous materials, conventional numerical methods may be time consuming and even inefficacious to obtain an accurate prediction for the interface behavior under mechanical and/or thermal loading. Rather than resort to a fully spatial discretization in the vicinity of this interface zone, an interface model was proposed within the framework of micropolar theory by introducing discontinuous approximation. A fracture description was used to represent the microscopic failure progress inside the interface. The micropolar interface model was then numerically implemented with the finite element method. As an application, the interface behavior of a packaging system with anisotropic conductive adhesive (ACA) joint was analyzed, demonstrating its applicability and great efficiency.

Using Multiple Satellites to Search for Maritime Moving Targets Based on Reinforcement Learning

Searching for maritime moving targets using satellites is an attracting but rather difficult problem due to the satellites' orbits and discontinuous visible time windows.From a long term cyclic view,a non-myopic method based on reinforcement learning(RL)for multi-pass multi-targets searching was proposed.It learnt system behaviors step by step from each observation which resulted in a dynamic progressive way.Then it decided and adjusted optimal actions in each observation opportunity.System states were indicated by expected information gain.Neural networks algorithm was used to approximate parameters of control policy.Simulation results show that our approach with sufficient training performs significantly better than other myopic approaches which make local optimal decisions for each individual observation opportunity.

Dielectric Breakdown Model for an Electrically Semi-Permeable Penny-Shaped Crack in Three-Dimensional Piezoelectric Media

The dielectric breakdown（DB） model for a penny-shaped crack under a semipermeable boundary condition in a three-dimensional piezoelectric medium is studied.An approximate analytical solution is derived by using the boundary integral equation with extended displacement discontinuity,and the corresponding boundary element method with double iterative approaches is developed to analyze the semi-permeable crack.The effect of electric boundary conditions on crack faces is discussed on the basis of DB model.By comparing the DB model with the polarization saturation（PS） model for different piezoelectric materials,some interesting phenomena related to the electric yielding zone and local J-integral are observed.

On Poincare-Friedrichs Type Inequalities for the Broken Sobolev Space W^(2,1)

We are concerned with the derivation of Poincare-Friedrichs type inequalities in the broken Sobolev space W^(2,1)(Ω;T h)with respect to a geometrically conforming,simplicial triagulation T h of a bounded Lipschitz domainΩin R d,d∈N.Such inequalities are of interest in the numerical analysis of nonconforming finite element discretizations such as C^(0) Discontinuous Galerkin(C^(0)DG)approximations of minimization problems in the Sobolev space W^(2,1)(Ω),or more generally,in the Banach space BV^(2)(Ω)of functions of bounded second order total variation.As an application,we consider a C^(0) DG approximation of a minimization problem in BV^(2)(Ω)which is useful for texture analysis and management in image restoration.