The Infona portal uses cookies, i.e. strings of text saved by a browser on the user's device. The portal can access those files and use them to remember the user's data, such as their chosen settings (screen view, interface language, etc.), or their login data. By using the Infona portal the user accepts automatic saving and using this information for portal operation purposes. More information on the subject can be found in the Privacy Policy and Terms of Service. By closing this window the user confirms that they have read the information on cookie usage, and they accept the privacy policy and the way cookies are used by the portal. You can change the cookie settings in your browser.
Abstract A class of matrices (2-matrices) has recently been introduced for storing discretisations of elliptic problems and integral operators from the BEM. These matrices have the following properties: (i) They are sparse in the sense that only few data are needed for their representation. (ii) The matrix-vector multiplication is of linear complexity. (iii) In general, sums and products of these...
Abstract Interval arithmetic can be used to enclose the range of a real function over a domain. However, due to some weak properties of interval arithmetic, a computed interval can be much larger than the exact range. This phenomenon is called dependency problem. In this paper, Horners rule for polynomial interval evaluation is revisited. We introduce a new factorization scheme based on well-known...
Abstract This short note discusses performance bounds for Ahrens algorithm, that can generate random variates from continuous distributions with monotonically decreasing density. This rejection algorithm uses constant hat-functions and constant squeezes over many small intervals. The choice of these intervals is important. Ahrens has demonstrated that the equal area rule that uses strips of constant...
Abstract In this note, we investigate the time complexity of non-preemptive shop scheduling problems with two jobs. First we study mixed shop scheduling where one job has a fixed order of operations and the operations of the other job may be executed in arbitrary order. This problem is shown to be binary NP-complete with respect to all traditional optimality criteria even if distinct operations of...
AbstractOne of the most popular pairs of finite elements for solving mixed formulations of the Stokes and NavierStokes problem is the QkPk1disc element. Two possible versions of the discontinuous pressure space can be considered: one can either use an unmapped version of the Pk1disc space consisting of piecewise polynomial functions of degree at most k1 on each cell or define a mapped version where...
Abstract The boundary concentrated FEM, a variant of the hp-version of the finite element method, is proposed for the numerical treatment of elliptic boundary value problems. It is particularly suited for equations with smooth coefficients and non-smooth boundary conditions. In the two-dimensional case it is shown that the Cholesky factorization of the resulting stiffness matrix requires O(Nlog4N)...
Abstract In the present paper a new numerical method for the Boltzmann equation is developed. The gain part of the collision integral is written in a form which allows its numerical computation on the uniform grid to be carried out efficiently. The amount of numerical work is shown to be of the order O(n6log(n)) for the most general model of interaction and of the order O(n6) for the Variable Hard...
AbstractThe subject of this article are third-order differential equations that may be linearized by a variable change. To this end, at first the equivalence classes of linear equations are completely described. Thereafter it is shown how they combine into symmetry classes that are determined by the various symmetry types. An algorithm is presented allowing it to transform linearizable equations by...
AbstractA subcoloring is a vertex coloring of a graph in which every color class induces a disjoint union of cliques. We derive a number of results on the combinatorics, the algorithmics, and the complexity of subcolorings. On the negative side, we prove that 2-subcoloring is NP-hard for comparability graphs, and that 3-subcoloring is NP-hard for AT-free graphs and for complements of planar graphs...
Abstract A short Matlab implementation for P1 and Q1 finite elements (FE) is provided for the numerical solution of 2d and 3d problems in linear elasticity with mixed boundary conditions. Any adaptation from the simple model examples provided to more complex problems can easily be performed with the given documentation. Numerical examples with postprocessing and error estimation via an averaged stress...
Abstract This paper considers a singularly perturbed reaction diffusion problem. It is investigated whether adaptive approaches are successful to design robust solution procedures. A key ingredient is the a posteriori error estimator. Since robust and mathematically analysed error estimation is possible in the energy norm, the focus is on this choice of norm and its implications. The numerical performance...
Abstract The paper is concerned with solving the periodically perturbed nonconservative systems, which will be differentiably imbedded into an one-parameter family of operators. The solution of the systems is then found by continuing the solution curve of operator homotopy. When the Newton-Kantorovich's procedure is applied to the corresponding operator equations, an efficient algorithm is derived...
Abstract A cascadic multigrid (CMG) method for elliptic problems with strong material jumps is proposed and analyzed. Nonmatching grids at interfaces between subdomains are allowed and treated by mortar elements. The arising saddle point problems are solved by a subspace confined conjugate gradient method as smoother for the CMG. Details of algorithmic realization including adaptivity are elaborated...
Abstract In the standard step-by-step cubic spline collocation method for Volterra integral equations an initial condition is replaced by a not-a-knot boundary condition at the other end of the interval. Such a method is stable in the same region of collocation parameter as in the step-by-step implementation with linear splines. The results about stability and convergence are based on the uniform...
Abstract Dynamic type checking and method binding slows pure object-oriented programs such as those written in Smalltalk. Dynamic method lookup is needed to support method overriding and type-method conformance. We have developed a platform independent technique that implements method overriding efficiently for pure object-oriented languages. The technique involves binding non-overridden method calls...
Abstract It has been observed by E. Eberlein and U. Keller that the hyperbolic distribution fits logarithmic rates of returns of a stock much better than the normal distribution. We give a method for sampling from the hyperbolic distribution by the inversion method, which is suited for simulation using low discrepancy point sets. Instead of directly inverting the cumulative distribution function (CDF)...
Abstract The coefficients perturbation method (CPM) is a numerical technique for solving ordinary differential equations (ODE) associated with initial or boundary conditions. The basic principle of CPM is to find the exact solution of an approximation problem obtained from the original one by perturbing the coefficients of the ODE, as well as the conditions associated to it. In this paper we shall...
Abstract In this paper, we present a new approach to construct robust multilevel algorithms for elliptic differential equations. The multilevel algorithms consist of multiplicative subspace corrections in spaces spanned by problem dependent generalized prewavelets. These generalized prewavelets are constructed by a local orthogonalization of hierarchical basis functions with respect to a so-called...
Set the date range to filter the displayed results. You can set a starting date, ending date or both. You can enter the dates manually or choose them from the calendar.