An adaptive mesh refinement method for solving optimal control problems is developed. The method employs orthogonal collocation at Legendre-Gauss-Radau points, and adjusts both the mesh size and the degree of the approximating polynomials in the refinement process. A previously derived convergence rate is used to guide the refinement process. The method brackets discontinuities and improves sol...

Mesh generation by Delaunay refinement is a widely used technique for constructing guaranteed quality triangular and tetrahedral meshes. The quality guarantees are usually provided in terms of the bounds on circumradius-to-shortest-edge ratio and on the grading of the resulting mesh. Traditionally circumcenters of skinny elements and middle points of boundary faces and edges are used for the po...

Modern numerical process simulators are becoming increasingly complicated in both physical models and domain shape. Grid generation is difficult for these simulators because of the inherent transient nature of the problems being solved. This paper addresses adaptive grid refinement for use in solving diffusion problems. It additionally investigates higher order approximations to the discretized...

Finite element analysts and designers need to feel confident in the results of their analyses before sending a product to prototype or production. Mesh discretization can greatly influence the desired results. In this paper we present framework for adaptive mesh refinement to obtain FEA results with a desired accuracy. The process involves adaptively refining the mesh based on solution error no...

We present an improved algorithm for the progressive simplification of quad meshes, which adapts the resolution of the mesh to details of the modeled shape. We extend previous work [TPC∗10], by simplifying the approach and combining it with the concept of Fitmaps introduced in [PPT∗10]. The new algorithm has several advantages: it is simpler and more robust; it does not need a parametrization o...

The attempt to match asset price characteristics such as the risk-free interest rate, equity premium and the Sharpe ratio with data for models with instantaneous consumption decisions and time separable preferences has not been very successful. Many recent versions of asset pricing models have, in order to match those financial characteristics better with the data, employed habit formation wher...

The refinement of tetrahedral meshes is a significant task in many numerical and discretizations methods. The computational aspects for implementing refinement of meshes with complex geometry need to be carefully considered in order to have real-time and optimal results. In this paper we study some computational aspects of a class of tetrahedral refinement algorithms. For local adaptive refinem...

plied and theoretical physics is to fully understand and predict the behavior of systems far from thermodynamic equilibrium,1–4 including those systems driven by an external force or experiencing a sudden change in environment (such as pressure or temperature). They also include systems transitioning from one metastable or long-lived state to another. The need to accurately model and numericall...

The attempt to match asset price characteristics such as the risk-free interest rate, equity premium and the Sharpe ratio with data for models with instantaneous consumption decisions and time separable preferences has not been very successful. Many recent versions of asset pricing models have, in order to match those financial characteristics better with the data, employed habit formation wher...