18 research outputs found
smt: a Matlab structured matrices toolbox
We introduce the smt toolbox for Matlab. It implements optimized storage and
fast arithmetics for circulant and Toeplitz matrices, and is intended to be
transparent to the user and easily extensible. It also provides a set of test
matrices, computation of circulant preconditioners, and two fast algorithms for
Toeplitz linear systems.Comment: 19 pages, 1 figure, 1 typo corrected in the abstrac
Wavelet boundary element methods â Adaptivity and goal-oriented error estimation
This article is dedicated to the adaptive wavelet boundary element method. It computes an approximation to the unknown solution of the boundary integral equation under consideration with a rate , whenever the solution can be approximated with this rate in the setting determined by the underlying wavelet basis. The computational cost scale linearly in the number of degrees of freedom. Goal-oriented error estimation for evaluating linear output functionals of the solution is also considered. An algorithm is proposed that approximately evaluates a linear output functional with a rate , whenever the primal solution can be approximated with a rate and the dual solution can be approximated with a rate , while the cost still scale linearly in . Numerical results for an acoustic scattering problem and for the point evaluation of the potential in case of the Laplace equation are reported to validate and quantify the approach
Spectral analysis of isogeometric discretizations of 2d curl-div problems with general geometry
We study the spectral distribution of matrices arising in Galerkin isogeometric methods for weighted curl-div operators defined on a general planar domain. It can be compactly described by means of a spectral symbol which depends on the characteristic parameters of the problem: the weight parameters, the basic curl and div operators, the degree of the B-spline approximation, and the geometry map used to represent the computational domain
Steady oscillations in aggregation-fragmentation processes
We report surprising steady oscillations in aggregation-fragmentation processes. Oscillating solutions are
observed for the class of aggregation kernels Ki,j = iΜ jΌ + j Μ iΌ homogeneous in masses i and j of merging
clusters and fragmentation kernels, Fij = λKij , with parameter λ quantifying the intensity of the disruptive
impacts. We assume a complete decomposition (shattering) of colliding partners into monomers. We show that
an assumption of a steady-state distribution of cluster sizes, compatible with governing equations, yields a
power law with an exponential cutoff. This prediction agrees with simulation results when Ξ âĄ Îœ â ÎŒ < 1. For
Ξ = Îœ â ÎŒ > 1, however, the densities exhibit an oscillatory behavior. While these oscillations decay for not very
small λ, they become steady if Ξ is close to 2 and λ is very small. Simulation results lead to a conjecture that for
Ξ < 1 the system has a stable fixed point, corresponding to the steady-state density distribution, while for any
Ξ > 1 there exists a critical value λc, such that for λ<λc, the system has an attracting limit cycle. This is rather
striking for a closed system of Smoluchowski-like equations, lacking any sinks and sources of mass
Block locally toeplitz sequences: Construction and properties
The theory of block locally Toeplitz (LT) sequences\u2014along with its generalization known as the theory of block generalized locally Toeplitz (GLT) sequences\u2014is a powerful apparatus for computing the spectral distribution of matrices arising from the discretization of differential problems. In this paper we develop the theory of block LT sequences, whereas the theory of block GLT sequences is the subject of the complementary paper (Chap. 3 of this book)