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

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

Natural preconditioning and iterative methods for saddle point systems

The solution of quadratic or locally quadratic extremum problems subject to linear(ized) constraints gives rise to linear systems in saddle point form. This is true whether in the continuous or the discrete setting, so saddle point systems arising from the discretization of partial differential equation problems, such as those describing electromagnetic problems or incompressible flow, lead to equations with this structure, as do, for example, interior point methods and the sequential quadratic programming approach to nonlinear optimization. This survey concerns iterative solution methods for these problems and, in particular, shows how the problem formulation leads to natural preconditioners which guarantee a fast rate of convergence of the relevant iterative methods. These preconditioners are related to the original extremum problem and their effectiveness---in terms of rapidity of convergence---is established here via a proof of general bounds on the eigenvalues of the preconditioned saddle point matrix on which iteration convergence depends

Thermospheric heating at high latitudes as observed from intercosmos-Bulgaria-1300 and dynamics explorer-B

This paper reports the results of the first direct comparison of near simultaneous measurements obtained by the INTERCOSMOS-BULGARIA-1300 and the DYNAMICS EXPLORER-B satellites. The ICB-1300 is in a near circular orbit at a mean height of about 850 km. The DE-B satellite in an elliptical orbit is sometimes directly below the ICB-1300 satellite providing an opportunity to investigate the response of the thermosphere to particle fluxes from the magnetosphere. Energy fluxes in the range 0.2-15 keV are obtained from an energetic particle analyzer on board the ICB-1300 satellite. The thermospheric composition and density are obtained by a neutral gas mass spectrometer (NACS) on the DE-B satellite. During the period 20 August-20 November, 1981, observations show tht the times and locations of maxima in magnetospheric energy deposition coincide with regions of maximum thermospheric upwelling characterized by composition changes.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/25883/1/0000446.pd

Finite element pressure stabilizations for incompressible flow problems

Discretizations of incompressible flow problems with pairs of finite element spaces that do not satisfy a discrete inf-sup condition require a so-called pressure stabilization. This paper gives an overview and systematic assessment of stabilized methods, including the respective error analysis