Accuracy of least-squares methods for the Navier-Stokes equations

Recently there has been substantial interest in least-squares finite element methods for velocity-vorticity-pressure formulations of the incompressible Navier-Stokes equations. The main cause for this interest is the fact that algorithms for the resulting discrete equations can be devised which require the solution of only symmetric, positive definite systems of algebraic equations. On the other hand, it is well-documented that methods using the vorticity as a primary variable often yield very poor approximations. Thus, here we study the accuracy of these methods through a series of computational experiments, and also comment on theoretical error estimates. It is found, despite the failure of standard methods for deriving error estimates, that computational evidence suggests that these methods are, at the least, nearly optimally accurate. Thus, in addition to the desirable matrix properties yielded by least-squares methods, one also obtains accurate approximations

A framework for mimetic discretization of the rotating shallow-water equations on arbitrary polygonal grids

Copyright © 2012 Society for Industrial and Applied MathematicsAccurate simulation of atmospheric flow in weather and climate prediction models requires the discretization of the governing equations to have a number of desirable properties. Although these properties can be achieved relatively straightforwardly on a latitude-longitude grid, they are much more challenging on the various quasi-uniform spherical grids that are now under consideration. A recently developed scheme—called TRiSK—has these desirable properties on grids that have an orthogonal dual. The present work extends the TRiSK scheme into a more general framework suitable for grids that have a nonorthogonal dual, such as the equiangular cubed sphere. We also show that this framework fits within the wider framework of mimetic discretizations and discrete exterior calculus. One key ingredient is the definition of certain mapping operators that are discrete analogues of the Hodge star operator, enabling the definition of a compatible inner product. Discrete Coriolis terms are also included within the mimetic framework, and in such a way as to conserve energy and ensure that discrete geostrophic balance can be maintained; this requires the definition of a further mapping operator, with special properties, that transfers the discrete velocity field from the primal to the dual grid

A conservative, optimization-based semi-lagrangian spectral element method for passive tracer transport

We present a new optimization-based, conservative, and quasi-monotone method for passive tracer transport. The scheme combines high-order spectral element discretization in space with semi-Lagrangian time stepping. Solution of a singly linearly constrained quadratic program with simple bounds enforces conservation and physically motivated solution bounds. The scheme can handle efficiently a large number of passive tracers because the semi-Lagrangian time stepping only needs to evolve the grid points where the primitive variables are stored and allows for larger time steps than a conventional explicit spectral element method. Numerical examples show that the use of optimization to enforce physical properties does not affect significantly the spectral accuracy for smooth solutions. Performance studies reveal the benefits of high-order approximations, including for discontinuous solutions

An extended vector space model for information retrieval with generalized similarity measures : theory and applications.

Abstract Not Provide

Case Report of Advanced Childhood Nasopharyngeal Carcinoma: Is Radiotherapy Dose Deescalation the Right Way in Good Responders to Induction Chemotherapy

Objectives:. Treatment of childhood NPC similar to adults consists of radiotherapy and chemotherapy, but distant failure is often observed, which led to introducing the induction chemotherapy followed by radiation or chemoradiation. The improved survival rates raised the question of late toxicity. The options for lowering the toxicity rate is the application of advanced radiotherapy techniques like IMRT and VMAT, and deescalation of the radiation dose in good responders and early NPC.Case report: We report a case of13-years old male patient with a high-risk childhood undifferentiated NPC, stage cT4 cN2b M0. He presented with unilateral swallowing at the middle third of left muscle sterenocleidomastoideus, and headache, fever, sore throat and intermittent nasal bleeding for an year. Diagnostic MRI and PET/CT showed good concordance for primary tumor extension and lymph node involvement. Three coursesinduction chemotherapy were applied according to NPC2003-GPOH protocolwith good treatment response. The restaging PET/CT found no distant metastasis. Deescalated protocol of radiotherapy alone was delivered to 50.4 Gy total dose with IGRT, VMAT irradiation technique. At three month PET/CT follow up a solitary bone lesion was detected.Conclusion: The present case proved that in high risk patients more aggressive treatment strategies should be recommended with no omission of concurrent chemotherapy even after full response. Deescalation of radiotherapy dose probably is not appropriate in this group of patients. MRI and PET CT should be used as complementary imaging modalities for early detection of locoregional or distant metastasis