Concept

Gaussian quadrature

Related publications (54)

Finite-element preconditioning of G-NI spectral methods

Several old and new finite-element preconditioners for nodal-based spectral discretizations of −laplace(u) = f in the domain

\Omega = (-1, 1)^d

(d = 2 or 3), with Dirichlet or Neumann boundary conditions, are considered and compared in terms of bothcondi ...

2009

Efficient computation of RCS from scatterers of uncertain shapes

Jan Sickmann Hesthaven

We propose a way of accounting for the lack of detailed knowledge about material shapes in computational time-domain electromagnetics. We use Legendre-Gauss-Lobatto, Stroud-2 and Stroud-3 quadrature formulas to solve the resulting stochastic equation and w ...

Institute of Electrical and Electronics Engineers2007

Calculation of multiple-scattering angular distributions of electrons and positrons

Rakesh Chawla, Cezarina Elena Negreanu

A robust numerical algorithm for the calculation of multiple-scattering angular distributions of high-energy electrons and positrons is described. This algorithm implements the multiple-scattering theories of Goudsmit-Saunderson, which disregards energy lo ...

Elsevier Ltd2005

Numerical analysis of a non-singular boundary integral method: Part II: The general case

Jacques Rappaz

In order to numerically solve the interior and the exterior Dirichlet problems for the Laplacian operator, we have presented in a previous paper a method which consists in inverting, on a finite element space, a non-singular integral operator for circular ...

2002

Nodal high-order discontinuous Galerkin methods for the spherical shallow water equations

Jan Sickmann Hesthaven

We present a high-order discontinuous Galerkin method for the solution of the shallow water equations on the sphere. To overcome well-known problems with polar singularities, we consider the shallow water equations in Cartesian coordinates, augmented with ...

Elsevier2002

Numerical analysis of a non-singular boundary integral method: Part I. The circular case

Jacques Rappaz

In order to numerically solve the interior and the exterior Dirichlet problems for the Laplacian operator, we present here a method which consists in inverting, on a finite element space, a non-singular integral operator. This operator is a geometrical per ...

2001

The LT phase of Cs3Bi2I9

Gervais Chapuis, Alla Arakcheeva

The low temperature (LT) modification of Cs3Bi2I9 has been refined to R(F) = 0.055 on the basis of X-ray diffraction measurements at T = 130 K from a twin crystal with six fractions connected by 3-fold axis and m-planes symmetry operations. Data were colle ...

2001

Stable spectral methods for conservation laws on triangles with unstructured grids

Jan Sickmann Hesthaven

This paper presents an asymptotically stable scheme for the spectral approximation of linear conservation laws defined on a triangle. Lagrange interpolation on a general two-dimensional nodal set is employed and, by imposing the boundary conditions weakly ...

ELSEVIER SCIENCE SA1999

A recursive method for solving unconstrained tangential interpolation problems

Ali H. Sayed

An efficient recursive solution is presented for the one-sided unconstrained tangential interpolation problem. The method relies on the triangular factorization of a certain structured matrix that is implicitly defined by the interpolation data. The recurs ...

IEEE1999

From electrostatics to almost optimal nodal sets for polynomial interpolation in a simplex

Jan Sickmann Hesthaven

The electrostatic interpretation of the Jacobi-Gauss quadrature points is exploited to obtain interpolation points suitable for approximation of smooth functions defined on a simplex. Moreover, several new estimates, based on extensive numerical studies, f ...

Society for Industrial and Applied Mathematics1998

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Finite-element preconditioning of G-NI spectral methods

Alfio Quarteroni

Several old and new finite-element preconditioners for nodal-based spectral discretizations of −laplace(u) = f in the domain

\Omega = (-1, 1)^d

(d = 2 or 3), with Dirichlet or Neumann boundary conditions, are considered and compared in terms of bothcondi ...

2009