Idempotent filtering in spectral and spectral element methods

Authors:
Alex Kanevsky;Mark H. Carpenter;Jan S. Hesthaven
Affiliations:
Division of Applied Mathematics, Brown University, Box F, Providence, RI 02912, USA;Aeronautics and Aeroacoustic Methods Branch, NASA Langley Research Center, Hampton, VA 23681-0001, USA;Division of Applied Mathematics, Brown University, Box F, Providence, RI 02912, USA
Venue:
Journal of Computational Physics
Year:
2006

Citing 9
Cited 3

Family of spectral filters for discontinuous problems

Journal of Scientific Computing
On the Gibbs phenomenon I: recovering exponential accuracy from the Fourier partial sum of a nonperiodic analytic function

Journal of Computational and Applied Mathematics - Orthogonal polynomials and numerical methods
On the Gibbs Phenomenon and Its Resolution

SIAM Review
From Electrostatics to Almost Optimal Nodal Sets for Polynomial Interpolation in a Simplex

SIAM Journal on Numerical Analysis
Spectral methods for hyperbolic problems

Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. VII: partial differential equations
Nodal high-order discontinuous Galerkin methods for the spherical shallow water equations

Journal of Computational Physics
Nodal high-order methods on unstructured grids

Journal of Computational Physics
Additive Runge-Kutta schemes for convection-diffusion-reaction equations

Applied Numerical Mathematics
Numerical Convergence Study of Nearly Incompressible, Inviscid Taylor-Green Vortex Flow

Journal of Scientific Computing

Application of implicit-explicit high order Runge-Kutta methods to discontinuous-Galerkin schemes

Journal of Computational Physics
The use of a Legendre pseudospectral viscosity technique to solve a class of nonlinear dynamic Hamilton-Jacobi equations

Computers & Mathematics with Applications
The Chebyshev spectral viscosity method for the time dependent Eikonal equation

Mathematical and Computer Modelling: An International Journal

Quantified Score

Hi-index	31.45

Visualization

Abstract

The comparison of numerical results for implicit-explicit and fully explicit Runge-Kutta time integration methods for a nozzle flow problem shows that filtering can significantly degrade the accuracy of the numerical solution for long-time integration problems. We demonstrate analytically and numerically that filtering-in-time errors become additive for @?u"N(x,t+k@Dt)-u"N(x,t)@?@?@?u"N(x,t)@? when nonidempotent filters are used, and suggest the development and implementation of idempotent filters.