Classical Fourier Analysis over Homogeneous Spaces of Compact Groups

This paper introduces a unified operator theory approach to the abstract Fourier analysis over homogeneous spaces of compact groups. Let G be a compact group and H be a closed subgroup of G. Let G/H be the left coset space of H in G and μ be the normalized G-invariant measure on G/H associated to the Weil＇s formula. Then, we present a generalized abstract framework of Fourier analysis for the Hilbert function space L^2 （G / H, μ）.

CONVERGENCE OF THE NONCONFORMING WILSON'S BRICK FOR ARBITRARY HEXAHEDRAL MESHES

The nonconforming Wilson’s brick classically is restricted to regular hexahedral meshes. Lesaint and Zlamal[6] relaxed this constraint for the two-dimensional analonue of this element In this paper we extend their results to three dimensions and prove that and where u is the exact solution, u_h is the approximate solution and is the usual norm for the Sobolev space H^1(?).

Efficient Solution of a Generalized Eigenvalue Problem Arising in a Thermoconvective Instability

The aim of this paper is to develop an efficient numerical method to compute the eigenvalues of the stability analysis of a problem describing the motion of a fluid within a cylindrical container heated non-homogeneously from below.An axisymmetric stationary motion settles in,at certain values of the external parameters appearing in the set of partial differential equations modeling the problem.This basic solution is computed by discretizing the equations with a Chebyshev collocation method.Its linear stability is formulated with a generalized eigenvalue problem.The numerical approach(generalized Arnoldi method)uses the idea of preconditioning the eigenvalue problem with a modified Cayley transformation before applying the Arnoldi method.Previous works have dealt with transformations requiring regularity to one of the submatrices.In this article we extend those results to the case in which that submatrix is singular.This method allows a fast computation of the critical eigenvalues which determine whether the steady flow is stable or unstable.The algorithm based on this method is compared to the QZ method and is found to be computationally more efficient.The reliability of the computed eigenvalues in terms of stability is confirmed via pseudospectra calculations.

AFast Solver for an H_(1) Regularized PDE-Constrained Optimization Problem

In this paperwe consider PDE-constrained optimization problemswhich incorporate an H_(1)regularization control term.We focus on a time-dependent PDE,and consider both distributed and boundary control.The problems we consider include bound constraints on the state,and we use a Moreau-Yosida penalty function to handle this.We propose Krylov solvers and Schur complement preconditioning strategies for the different problems and illustrate their performance with numerical examples.