A novel nonlinear formulation of finite element and Galerkin methods is presented here, which leads to the Hadamard product expression of the resultant nonlinear algebraic analogue. The presented formulation attains the advantages of weak formulation in the standard finite element and Galerkin schemes and avoids the costly repeated numerical integration of the Jacobian matrix via the recently d...

We present a uni ed framework for studying interior point methods for linear programming. Within this framework, we compare three fundamental methods: (1) pathfollowing, (2) barrier, and (3) primal/dual a ne-scaling (our terminology di ers slightly from the commonly accepted terminology). The step directions for each of these methods are linear combinations of three fundamental directions: (1) ...

Optimal sensor placement for detecting contamination events in water distribution systems is a well explored problem in water distribution systems security. We study herein the problem of sensor placement in water networks to minimize the consumption of contaminated water prior to contamination detection. For any sensor placement, the average consumption of contaminated water prior to event det...

The DG algorithm is a powerful method for solving pdes, especially for evolution equations in conservation form. Since the algorithm involves integration over volume elements, it is not immediately obvious that it will generalize easily to arbitrary time-dependent curved spacetimes. We show how to formulate the algorithm in such spacetimes for applications in relativistic astrophysics. We also ...

We consider a stabilized finite element formulation for the Reissner-Mindlin plate bending model. The method uses standard bases functions for the deflection and the rotation vector. We apply a standard multigrid algorithm to obtain a preconditioner. We prove that the condition number of the preconditioned system is uniformly bounded with respect to the multigrid level and the thickness paramet...

astigmatism’s defect has not yet been formulated in physics and medical physics books theoretically. in this paper, we are trying to formulate the astigmatism’s defect. the results of formulation show that “the degree of astigmatism is negative reverse the distance that vision’s condition of astigmatism’s chart lines change conditions in dimness angle from dimness condition at infinite distance...

This paper describes the fundamental motivation and ideas surrounding current developments in available energy-based methods for vehicle design, which are a class of methods allowing direct estimation of the total cost chargeable to each loss mechanism in any general vehicle design (land, sea, air, or space). It is shown that losses can be expressed in terms of chargeable fuel weight. These are...

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The numerical simulation problem of tree-structured multibody systems, such as robot manipulators, is usually treated as two separate problems: (i) the forward dynamics problem for computing system accelerations, and (ii) the numerical integration problem for advancing the state in time. The interaction of these two problems can be important and has led to new conclusions about the overall eeci...

Many changes are occurring in the practice of medicine for the 21st century, one of the more positive being the emphasis on treating patients in a holistic way and involving them in their treatment 1� 2� 3� 4� planning. Most doctors agree with this aim, but in practice it can be a daunting prospect, adding a new dimension to the skills required of a practitioner. At its root is the need to be a...