We consider a Newton-Krylov approach for discretized compressible Euler equations. A good preconditioner in the Krylov subspace method is essential for obtaining an efficient solver in such an approach. In this paper we compare point-block-Gauss-Seidel, point-block-ILU and point-block-SPAI preconditioners. It turns out that the SPAI method is not satisfactory for our problem class. The point-bl...

“Dual composition”, a new method of constructing energy-preserving discretizations of conservative PDEs, is introduced. It extends the summation-by-parts approach to arbitrary differential operators and conserved quantities. Links to pseudospectral, Galerkin, antialiasing, and Hamiltonian methods are discussed.

Here is a proof for the demeaning method used in lfe, and a description of the methods used for solving the residual equations. As well as a toy-example. This is a preliminary version of [3]. This method, formulated as the Gauss-Seidel algorithm, was noted in [4] without the author noticing it in the first version of this paper.

The -pseudospectrum of a square matrix A is the set of eigenvalues attainable when A is perturbed by matrices of spectral norm not greater than . The pseudospectral abscissa is the largest real part of such an eigenvalue, and the pseudospectral radius is the largest absolute value of such an eigenvalue. We find conditions for the pseudospectrum to be Lipschitz continuous in the setvalued sense ...

The q-deformed commutation relation aa ? qa a = 1 1 for the harmonic os-cillator is considered with q 2 ?1; 1]. An explicit representation generalizing the Bargmann representation of analytic functions on the complex plane is constructed. In this representation the distribution of a + a in the vacuum state is explicitly calculated. This distribution is to be regarded as the natural q-deformatio...

Recently, we have presented’ a pseudospectral formulation of the full configuration interaction (FCI) problem. The method was accurate to a mhartree after corrections, but the size of the numerical grids required made it impossible to realize any computational advantage for systems feasible with today’s hardware. In this paper, we present the first application of the pseudospectral method to tr...

A class of computational methods for solving a wide variety of optimal control problems is presented; these problems include nonsmooth, nonlinear, switched optimal control problems, as well as standard multiphase problems. Methods are based on pseudospectral approximations of the differential constraints that are assumed to be given in the form of controlled differential inclusions including th...

The multigrid method for discontinuous Galerkin discretizations of advection-diffusion problems is presented. It is based on a block Gauss-Seidel smoother with downwind ordering honoring the advection operator. The cell matrices of the DG scheme are inverted in this smoother in order to obtain robustness for higher order elements. Employing a set of experiments, we show that this technique actu...