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New efficient numerical method for 3D point cloud surface reconstruction by using level set methods

Kósa, Balázs, Haličková-Brehovská, Jana, Mikula, Karol (2017)

Proceedings of Equadiff 14

In this article, we present a mathematical model and numerical method for surface reconstruction from 3D point cloud data, using the level-set method. The presented method solves surface reconstruction by the computation of the distance function to the shape, represented by the point cloud, using the so called Fast Sweeping Method, and the solution of advection equation with curvature term, which creates the evolution of an initial condition to the final state. A crucial point for efficiency is...

New trends in coupled simulations featuring domain decomposition and metacomputing

Philippe d'Anfray, Laurence Halpern, Juliette Ryan (2002)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In this paper we test the feasibility of coupling two heterogeneous mathematical modeling integrated within two different codes residing on distant sites. A prototype is developed using Schwarz type domain decomposition as the mathematical tool for coupling. The computing technology for coupling uses a CORBA environment to implement a distributed client-server programming model. Domain decomposition methods are well suited to reducing complex physical phenomena into a sequence of parallel subproblems...

New trends in coupled simulations featuring domain decomposition and metacomputing

Philippe d'Anfray, Laurence Halpern, Juliette Ryan (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper we test the feasibility of coupling two heterogeneous mathematical modeling integrated within two different codes residing on distant sites. A prototype is developed using Schwarz type domain decomposition as the mathematical tool for coupling. The computing technology for coupling uses a CORBA environment to implement a distributed client-server programming model. Domain decomposition methods are well suited to reducing complex physical phenomena into a sequence of parallel subproblems...

Nonlinear conjugate gradient methods

Lukšan, Ladislav, Vlček, Jan (2015)

Programs and Algorithms of Numerical Mathematics

Modifications of nonlinear conjugate gradient method are described and tested.

Non-monotoneous parallel iteration for solving convex feasibility problems

Gilbert Crombez (2003)

Kybernetika

The method of projections onto convex sets to find a point in the intersection of a finite number of closed convex sets in an Euclidean space, sometimes leads to slow convergence of the constructed sequence. Such slow convergence depends both on the choice of the starting point and on the monotoneous behaviour of the usual algorithms. As there is normally no indication of how to choose the starting point in order to avoid slow convergence, we present in this paper a non-monotoneous parallel algorithm...

Numerical analysis of the MFS for certain harmonic problems

Yiorgos-Sokratis Smyrlis, Andreas Karageorghis (2004)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

The Method of Fundamental Solutions (MFS) is a boundary-type meshless method for the solution of certain elliptic boundary value problems. In this work, we investigate the properties of the matrices that arise when the MFS is applied to the Dirichlet problem for Laplace’s equation in a disk. In particular, we study the behaviour of the eigenvalues of these matrices and the cases in which they vanish. Based on this, we propose a modified efficient numerical algorithm for the solution of the problem...

Numerical analysis of the MFS for certain harmonic problems

Yiorgos-Sokratis Smyrlis, Andreas Karageorghis (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The Method of Fundamental Solutions (MFS) is a boundary-type meshless method for the solution of certain elliptic boundary value problems. In this work, we investigate the properties of the matrices that arise when the MFS is applied to the Dirichlet problem for Laplace's equation in a disk. In particular, we study the behaviour of the eigenvalues of these matrices and the cases in which they vanish. Based on this, we propose a modified efficient numerical algorithm for the solution of the problem...

Numerical approximation of the non-linear fourth-order boundary-value problem

Svobodová, Ivona (2008)

Programs and Algorithms of Numerical Mathematics

We consider functionals of a potential energy ℙ ψ ( u ) corresponding to 𝑎𝑛 𝑎𝑥𝑖𝑠𝑦𝑚𝑚𝑒𝑡𝑟𝑖𝑐 𝑏𝑜𝑢𝑛𝑑𝑎𝑟𝑦 - 𝑣𝑎𝑙𝑢𝑒 𝑝𝑟𝑜𝑏𝑙𝑒𝑚 . We are dealing with 𝑎 𝑑𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑜𝑛 𝑜𝑓 𝑎 𝑡ℎ𝑖𝑛 𝑎𝑛𝑛𝑢𝑙𝑎𝑟 𝑝𝑙𝑎𝑡𝑒 with 𝑁𝑒𝑢𝑚𝑎𝑛𝑛 𝑏𝑜𝑢𝑛𝑑𝑎𝑟𝑦 𝑐𝑜𝑛𝑑𝑖𝑡𝑖𝑜𝑛𝑠 . Various types of the subsoil of the plate are described by various types of the 𝑛𝑜𝑛𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡𝑖𝑎𝑏𝑙𝑒 nonlinear term ψ ( u ) . The aim of the paper is to find a suitable computational algorithm.

Numerical modelling of river flow (numerical schemes for one type of nonconservative systems

Brandner, Marek, Egermaier, Jiří, Kopincová, Hana (2008)

Programs and Algorithms of Numerical Mathematics

In this paper we propose a new numerical scheme to simulate the river flow in the presence of a variable bottom surface. We use the finite volume method, our approach is based on the technique described by D. L. George for shallow water equations. The main goal is to construct the scheme, which is well balanced, i.e. maintains not only some special steady states but all steady states which can occur. Furthermore this should preserve nonnegativity of some quantities, which are essentially nonnegative...

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