Abstract: In this paper we resume some results concerned our work about least-squares approximation on GaussLobatto points. We present explicit formulas for discrete orthogonal polynomials and give the three-term recurrence relation to construct such polynomials. We also show that the normal matrix on this set of nodes can be factorized as the sum of two symmetric matrices: a full rank matrix w...

We present a well-balanced nodal discontinuous Galerkin (DG) scheme for compressible Euler equations with gravity. The DG scheme makes use of discontinuous Lagrange basis functions supported at GaussLobatto-Legendre (GLL) nodes together with GLL quadrature using the same nodes. The well-balanced property is achieved by a specific form of source term discretization that depends on the nature of ...

This paper analyses a Chebyshev pseudospectral collocation semidiscrete (continuous in time) discretization of a variable coefficient parabolic problem. Optimal stability and convergence estimates are given. The analysis is based on an approximation property concerning the GaussLobatto-Chebyshev interpolation operator.

The mass matrix for Gauss-Lobatto grid points is usually approximated by GaussLobatto quadrature because this leads to a diagonal matrix that is easy to invert. The exact mass matrix and its inverse are full. We show that the exact mass matrix and its inverse differ from the approximate diagonal ones by a simple rank-1 update (outer product). They can thus be applied to an arbitrary vector in O...

introduction: lymphoscintigraphy is imaging of the lymphatic system and has been integrated into the sentinel node mapping procedures. lymphoscintigraphy usually encompasses early or delayed static images. however, immediate dynamic imaging of the lymphatic basins and tumors has also been used as an adjunct lymphoscintigraphy imaging. the aim of this study was to assess the role of early dynami...

background: the purpose of this study was to evaluate nodal irradiation with conventional three-field's technique. materials and methods: fifty patients with breast cancer were enrolled in this study. computed tomography scans in the supine treatment position were imported into a treatment planning system. levels i-iii axillary and supraclavicular nodes were identified and their depths to ...

b a ckground: the management of internal mammary (im) nodes in breast cancer lacks a well-defined consensus. lymphoscintigraphy identifies up to one-third of breast cancer patients with extra-axillary drainage, which is mainly located in the im chain. our aim in this meta-analysis is to identify the lymphoscintigraphy technique variables that effect im node identification. m ethods: an internet...

We present a spectral-element discontinuous Galerkin lattice Boltzmann method for solving single-phase incompressible flows. Decoupling the collision step from the streaming step offers numerical stability at high Reynolds numbers. In the streaming step, we employ high-order spectral-element discretizations using a tensor product basis of one-dimensional Lagrange interpolation polynomials based...

background: the axillary and supraclavicular nodal volume treatment results in improvement of local control and survival after breast conserving surgery (bcs) or modified radical mastectomy (mrm). studies on the depth of these nodes have questioned the consistent use of standard fields for all patients. this study was done to assess the dose delivery to these lymph nodes with conventional treat...

The Karhunen-Loève expansion of a Gaussian process, a common tool on finite element methods for differential equations with stochastic coefficients, is based on the spectral decomposition of its covariance function. The eigenpairs of the covariance are expressed as a Fredholm integral equation of second kind, which can be readily approximated with piecewise-constant finite elements. In this wor...