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INTERNODES: an accurate interpolation-based method for coupling the Galerkin solutions of PDEs on subdomains featuring non-conforming interfaces

Publications associées (56)

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Nonparametric Least Squares Regression for Image Reconstruction on the Sphere

Pascal Frossard, Ivana Tosic, Tamara Tosic

This paper addresses the problem of interpolating signals defined on a 2-d sphere from non-uniform samples. We present an interpolation method based on locally weighted linear and nonlinear regression, which takes into account the differences in importance ...

2009

Numerical Models for Differential Problems

Alfio Quarteroni

In this text, we introduce the basic concepts for the numerical modelling of partial differential equations. We consider the classical elliptic, parabolic and hyperbolic linear equations, but also the diffusion, transport, and Navier-Stokes equations, as w ...

Springer2009

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

Sound Field Analysis Along a Circle and its Application to HRTF Interpolation

Martin Vetterli, Christof Faller, Luciano Sbaiz, Thibaut Ajdler

The sampling and interpolation of a sound field in two and three dimensions along a circle is discussed. The Fourier domain representation of the sound field is used, and an angular sampling theorem is developed for the sampling of the sound field along a ...

2008

Adaptive and Reduced Basis methods for optimal control problems in environmental applications

Luca Dede'

In this work we provide efficient numerical methods for the numerical solution of Partial Differential Equations (PDEs) and the computation of the associated outputs of interest, also in the frame of optimal control problems. With this aim, a goal-oriented ...

Politecnico di Milano2008

Geometrical reconstruction of curves and surfaces using NURBS

Sylvain Rouge

The aim of this project is the analysis of different approaches for curve and surface reconstruction and the development of a related MATLAB library. We initially study the Lagrange polynomial interpolation, then the Bezier, the B-splines and the NURBS cur ...

2008

The symmetric discontinuous Galerkin method does not need stabilization in 1D for polynomial orders p ≥ 2

Erik Burman, Benjamin Stamm

In this Note we prove that in one space dimension, the symmetric discontinuous Galerkin method for second order elliptic problems is stable for polynomial orders

p \ge 2

without using any stabilization parameter. The method yields optimal convergence rat ...

2007

Linear Interpolation Revitalized

Michaël Unser, Philippe Thévenaz, Thierry Blu

We present a simple, original method to improve piecewise-linear interpolation with uniform knots: we shift the sampling knots by a fixed amount, while enforcing the interpolation property. We determine the theoretical optimal shift that maximizes the qual ...

IEEE2004

New anisotropic a priori error estimates

Luca Formaggia

We prove a priori anisotropic estimates for the L2 and H1 interpolation error on linear finite elements. The full information about the mapping from a reference element is employed to separate the contribution to the elemental error c ...

2001

Stable spectral methods on tetrahedral elements

Jan Sickmann Hesthaven

A framework for the construction of stable spectral methods on arbitrary domains with unstructured grids is presented. Although most of the developments are of a general nature, an emphasis is placed on schemes for the solution of partial differential equa ...

SIAM PUBLICATIONS2000

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

The symmetric discontinuous Galerkin method does not need stabilization in 1D for polynomial orders p ≥ 2

Erik Burman, Benjamin Stamm

In this Note we prove that in one space dimension, the symmetric discontinuous Galerkin method for second order elliptic problems is stable for polynomial orders

p \ge 2

without using any stabilization parameter. The method yields optimal convergence rat ...

2007