We apply a new industrial strength numerical approximation, called the “mesh-free adjoint method,” to solve the nonlinear filtering problem. This algorithm exploits the smoothness of the problem, unlike particle filters, and hence we expect that mesh-free adjoints are superior to particle filters for many practical applications. The nonlinear filter problem is equivalent to solving the Fokker-P...

The paper investigates boundary optimal controls and parameter estimates to the well-posedness nonlinear model of dehydratation of thermic problems. We summarize the general formulations for the boundary control for initial-boundary value problem for nonlinear partial differential equations modeling the heat transfer and derive necessary optimality conditions, including the adjoint equation, fo...

In this paper, we study the variational discretization and adaptive mixed finite element methods for optimal control problems governed by integro-differential equations. The state and the co-state are discretized by the lowest order Raviart-Thomas mixed finite element spaces and the control is not discretized. We derive a posteriori error estimates for the coupled state and control approximatio...

In this paper, we propose a splitting least-squares mixed finite element method for the approximation of elliptic optimal control problem with the control constrained by pointwise inequality. By selecting a properly least-squares minimization functional, we derive equivalent two independent, symmetric and positive definite weak formulation for the primal state variable and its flux. Then, using...

We consider 1+1-dimensional QCD coupled to Majorana fermions in the adjoint representation of the gauge group SU(N). Pair creation of partons (fermion quanta) is not suppressed in the large-N limit, where the glueball-like bound states become free. In this limit the spectrum is given by a linear light-cone Schrödinger equation, which we study numerically using the discretized light-cone quantiz...

1 Introduction Cartesian-mesh methods [I] are perhaps the most promising approach for addressing the issues of flow solution automation for aerodynamic design problems. In these methods, the discretization of the wetted surface is decoupled from that of the volume mesh. This not only enables fast &id robust mesh generation for geometry of arbitrary cQing&eziQ:> but &o facili@$es _accezs to geoa...

Deterministic chaotic dynamics presumes that the state space can be partitioned arbitrarily finely. In a physical system, the inevitable presence of some noise sets a finite limit to the finest possible resolution that can be attained. Much previous research deals with what this attainable resolution might be, all of it based on a global averages over stochastic flow. What is novel here is that...

In finance, hedging strategies are used to safeguard portfolios against risk associated with financial derivatives such as options. For an option with an underlying asset, the risk can be measured in terms of the so-called Greeks. In particular, the derivative of the option price with respect to the value of the asset is referred to as the Delta. An alternative to optimize hedges for options is...