We consider natural convection in flow saturated porous media with random porosity. The porosity is treated as a random field and a stochastic finite element method is developed. The stochastic projection method is considered for the solution of the high-dimensional stochastic Navier-Stokes equations since it leads to the uncoupling of the velocity and pressure degrees of freedom. Because of th...

Whether a disturbance will trigger unexpected protection operation to exacerbate the normal operation state or even lead to the unstable state depends on the transient energy that the system gains during the fault period. The paper presents a new gradient projection approach to calculate the critical energy for transient stability assessment of the power system with the protection operation. Th...

We investigate projected scaled gradient (PSG) methods for convex minimization problems. These methods perform a descent step along a diagonally scaled gradient direction followed by a feasibility regaining step via orthogonal projection onto the constraint set. This constitutes a generalized algorithmic structure that encompasses as special cases the gradient projection method, the projected N...

In this paper we present a simple method for handling projections on the hemisphere. The proposed method defines a coordinate system on the hemisphere surface that effectively converts the hemisphere to an infinite plane tangent to the top of the hemisphere, which is called the gradient space. Using this coordinate system, projections onto the hemisphere are replaced by simple perspective proje...

Most real options models are American-type options involving a free boundary problem which can be modeled in the form of variational inequalities. In this paper, we provide a viable mathematical formulation and promising computational approach for the valuation of real options. We study an equivalent optimization problem with an inequality constraint and boundary conditions, whose necessary con...