Search results for "Computational Mathematic"
showing 10 items of 987 documents
Computing Euclidean Steiner trees over segments
2020
In the classical Euclidean Steiner minimum tree (SMT) problem, we are given a set of points in the Euclidean plane and we are supposed to find the minimum length tree that connects all these points, allowing the addition of arbitrary additional points. We investigate the variant of the problem where the input is a set of line segments. We allow these segments to have length 0, i.e., they are points and hence we generalize the classical problem. Furthermore, they are allowed to intersect such that we can model polygonal input. As in the GeoSteiner approach of Juhl et al. (Math Program Comput 10(2):487–532, 2018) for the classical case, we use a two-phase approach where we construct a superse…
Multi-Dimensional Pattern Matching with Dimensional Wildcards: Data Structures and Optimal On-Line Search Algorithms
1997
We introduce a new multidimensional pattern matching problem that is a natural generalization of string matching, a well studied problem1. The motivation for its algorithmic study is mainly theoretical. LetA1:n1,?,1:nd be a text matrix withN=n1?ndentries andB1:m1,?,1:mr be a pattern matrix withM=m1?mrentries, whered?r?1 (the matrix entries are taken from an ordered alphabet ?). We study the problem of checking whether somer-dimensional submatrix ofAis equal toB(i.e., adecisionquery).Acan be preprocessed andBis given on-line. We define a new data structure for preprocessingAand propose CRCW-PRAM algorithms that build it inO(logN) time withN2/nmaxprocessors, wherenmax=max(n1,?,nd), such that …
A quantitative reverse Faber-Krahn inequality for the first Robin eigenvalue with negative boundary parameter
2021
The aim of this paper is to prove a quantitative form of a reverse Faber-Krahn type inequality for the first Robin Laplacian eigenvalueλβwith negative boundary parameter among convex sets of prescribed perimeter. In that framework, the ball is the only maximizer forλβand the distance from the optimal set is considered in terms of Hausdorff distance. The key point of our stategy is to prove a quantitative reverse Faber-Krahn inequality for the first eigenvalue of a Steklov-type problem related to the original Robin problem.
Time-harmonic solution for acousto-elastic interaction with controllability and spectral elements
2010
The classical way of solving the time-harmonic linear acousto-elastic wave problem is to discretize the equations with finite elements or finite differences. This approach leads to large-scale indefinite complex-valued linear systems. For these kinds of systems, it is difficult to construct efficient iterative solution methods. That is why we use an alternative approach and solve the time-harmonic problem by controlling the solution of the corresponding time dependent wave equation. In this paper, we use an unsymmetric formulation, where fluid-structure interaction is modeled as a coupling between pressure and displacement. The coupled problem is discretized in space domain with spectral el…
Fronts propagating with signal dependent speed in limited diffusion and related Hamilton-Jacobi formulations
2021
We consider a class of limited diffusion equations and explore the formation of diffusion fronts as the result of a combination of diffusive and hyperbolic transport. We analyze a new class of Hamilton-Jacobi equations arising from the convective part of general Fokker-Planck equations ruled by a non-negative diffusion coefficient that depends on the unknown and on the gradient of the unknown. We explore the main features of the solution of the Hamilton-Jacobi equations that contain shocks and propose a suitable numerical scheme that approximates the solution in a consistent way with respect to the solution of the associated Fokker-Planck equation. We analyze three model problems covering d…
Linearly implicit-explicit schemes for the equilibrium dispersive model of chromatography
2018
Abstract Numerical schemes for the nonlinear equilibrium dispersive (ED) model for chromatographic processes with adsorption isotherms of Langmuir type are proposed. This model consists of a system of nonlinear, convection-dominated partial differential equations. The nonlinear convection gives rise to sharp moving transitions between concentrations of different solute components. This property calls for numerical methods with shock capturing capabilities. Based on results by Donat, Guerrero and Mulet (Appl. Numer. Math. 123 (2018) 22–42), conservative shock capturing numerical schemes can be designed for this chromatography model. Since explicit schemes for diffusion problems can pose seve…
The simulation of morphology of dissimilar copper–steel electron beam welds using level set method
2010
Abstract In present work, the simulation of morphology and velocity field in dissimilar electron beam welds formed between the metals with limited solubility is described by the example of copper–stainless steel couple. Finite element software COMSOL Multiphysics 3.5 has been employed due to its flexibility in solving of coupled multiphysical problems. The domination of horizontal flows allows reducing the model to two dimensions. Level set method has been used to determine the position of the interface between immiscible components basing on coupled heat transfer and fluid flow pseudo-stationary solution. The evolution of the shape, fluid flow and mixing pattern in function of operational …
Locally Convex Quasi *-Algebras of Operators
2011
This note is mainly concerned with locally convex quasi C*-normed *-algebras which arise as completions of C*-algebras of operators under certain topologies. Their importance is made clear by the representation theory of abstract locally convex quasi C*-normed *-algebras, investigated in previous papers and whose basic aspects are also overviewed here.
An updated version of the computational package SIMPRE that uses the standard conventions for Stevens crystal field parameters
2014
The crystal field approach used by SIMPRE is analyzed, verifying the exactness of the results concerning energy levels and magnetic properties calculated by the package. To coincide with the prevailing conventions, we reformulate the presentation of the crystal field parameters, so that the results are now, also from a formal point of view, strictly correct. New calculations are presented to test the influence of neglecting the excited J states, a common but critical approximation employed by SIMPRE. For that, we examine the case of Er(trensal) complex (H3 trensal = 2,2',2″-tris(salicylideneimino)triethylamine) where the influence of this approximation is found to be minimal. A patched vers…
Modeling crowd dynamics through coarse-grained data analysis
2018
International audience; Understanding and predicting the collective behaviour of crowds is essential to improve the efficiency of pedestrian flows in urban areas and minimize the risks of accidents at mass events. We advocate for the development of crowd traffic management systems, whereby observations of crowds can be coupled to fast and reliable models to produce rapid predictions of the crowd movement and eventually help crowd managers choose between tailored optimization strategies. Here, we propose a Bi-directional Macroscopic (BM) model as the core of such a system. Its key input is the fundamental diagram for bi-directional flows, i.e. the relation between the pedestrian fluxes and d…