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Numerical solution of several models of internal transonic flow

Jaroslav Fořt, Karel Kozel (2003)

Applications of Mathematics

The paper deals with numerical solution of internal flow problems. It mentions a long tradition of mathematical modeling of internal flow, especially transonic flow at our department. Several models of flow based on potential equation, Euler equations, Navier-Stokes and Reynolds averaged Navier-Stokes equations with proper closure are considered. Some mathematical and numerical properties of the model are mentioned and numerical results achieved by in-house developed methods are presented.

Numerical solution of the Kiessl model

Josef Dalík, Josef Daněček, Jiří Vala (2000)

Applications of Mathematics

The Kiessl model of moisture and heat transfer in generally nonhomogeneous porous materials is analyzed. A weak formulation of the problem of propagation of the state parameters of this model, which are so-called moisture potential and temperature, is derived. An application of the method of discretization in time leads to a system of boundary-value problems for coupled pairs of nonlinear second order ODE’s. Some existence and regularity results for these problems are proved and an efficient numerical...

Numerical solution of the Maxwell equations in time-varying media using Magnus expansion

István Faragó, Ágnes Havasi, Robert Horváth (2012)

Open Mathematics

For the Maxwell equations in time-dependent media only finite difference schemes with time-dependent conductivity are known. In this paper we present a numerical scheme based on the Magnus expansion and operator splitting that can handle time-dependent permeability and permittivity too. We demonstrate our results with numerical tests.

Numerical stability of the intrinsic equations for beams in time domain

Klesa, Jan (2019)

Programs and Algorithms of Numerical Mathematics

Intrinsic equations represent promising approach for the description of rotor blade dynamics. They are the system of non-linear partial differential equations. Stability of numeric solution by the finite difference method is described. The stability is studied for various numerical schemes with different methods for the computation of spatial derivatives from time level n + 0 . 5 (i.e., mean values of old and new time step) to n + 1 (i.e., only from new time step). Stable solution was obtained only for schemes...

Numerical study by a controllability method for the calculation of the time-periodic solutions of the Maxwell and Vlasov-Maxwell systems

Mihai Bostan (2001)

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

The topic of this paper is the numerical analysis of time periodic solution for electro-magnetic phenomena. The Limit Absorption Method (LAM) which forms the basis of our study is presented. Theoretical results have been proved in the linear finite dimensional case. This method is applied to scattering problems and transport of charged particles.

Numerical study by a controllability method for the calculation of the time-periodic solutions of the Maxwell and Vlasov-Maxwell systems

Mihai Bostan (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The topic of this paper is the numerical analysis of time periodic solution for electro-magnetic phenomena. The Limit Absorption Method (LAM) which forms the basis of our study is presented. Theoretical results have been proved in the linear finite dimensional case. This method is applied to scattering problems and transport of charged particles.

Numerical study of self-focusing solutions to the Schrödinger-Debye system

Christophe Besse, Brigitte Bidégaray (2001)

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

In this article we implement different numerical schemes to simulate the Schrödinger-Debye equations that occur in nonlinear optics. Since the existence of blow-up solutions is an open problem, we try to compute such solutions. The convergence of the methods is proved and simulations seem indeed to show that for at least small delays self-focusing solutions may exist.

Numerical study of self-focusing solutions to the Schrödinger-Debye system

Christophe Besse, Brigitte Bidégaray (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this article we implement different numerical schemes to simulate the Schrödinger-Debye equations that occur in nonlinear optics. Since the existence of blow-up solutions is an open problem, we try to compute such solutions. The convergence of the methods is proved and simulations seem indeed to show that for at least small delays self-focusing solutions may exist.

Numerical study of the Davey-Stewartson system

Christophe Besse, Norbert J. Mauser, Hans Peter Stimming (2004)

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

We deal with numerical analysis and simulations of the Davey-Stewartson equations which model, for example, the evolution of water surface waves. This time dependent PDE system is particularly interesting as a generalization of the 1-d integrable NLS to 2 space dimensions. We use a time splitting spectral method where we give a convergence analysis for the semi-discrete version of the scheme. Numerical results are presented for various blow-up phenomena of the equation, including blowup of defocusing,...

Numerical study of the Davey-Stewartson system

Christophe Besse, Norbert J. Mauser, Hans Peter Stimming (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We deal with numerical analysis and simulations of the Davey-Stewartson equations which model, for example, the evolution of water surface waves. This time dependent PDE system is particularly interesting as a generalization of the 1-d integrable NLS to 2 space dimensions. We use a time splitting spectral method where we give a convergence analysis for the semi-discrete version of the scheme. Numerical results are presented for various blow-up phenomena of the equation, including blowup of defocusing,...

Numerical study of two-level additive Schwarz preconditioner for discontinuous Galerkin method solving elliptic problems

Hammerbauer, Tomáš, Dolejší, Vít (2025)

Programs and Algorithms of Numerical Mathematics

The paper deals with the analysis and numerical study of the domain decomposition based preconditioner for algebraic systems arising from the discontinuous Galerkin (DG) discretization of the linear elliptic problems. We introduce the DG discretization of the model problem and present the spectral h p -bound of the corresponding linear algebraic systems. Moreover, we present the two-level additive Schwarz preconditioner together with the theoretical result related to the estimate of the condition number....

Numerical study on the blow-up rate to a quasilinear parabolic equation

Anada, Koichi, Ishiwata, Tetsuya, Ushijima, Takeo (2017)

Proceedings of Equadiff 14

In this paper, we consider the blow-up solutions for a quasilinear parabolic partial differential equation u t = u 2 ( u x x + u ) . We numerically investigate the blow-up rates of these solutions by using a numerical method which is recently proposed by the authors [3].

Numerical treatment of a time dependent inverse problem in photon transport

S. Pieraccini, R. Riganti, A. Belleni-Morante (2005)

Bollettino dell'Unione Matematica Italiana

The time-dependent intensity of a UV-photon source, located inside an interstellar cloud, is determined by formulating and solving an inverse problem for the integro-differential transport equation of photons in a one-dimensional slab. Starting from a discretizazion of the forward problem, an iterative procedure is used to compute the values of the source intensity at increasing values of the time.

Object oriented design philosophy for scientific computing

Philippe R. B. Devloo, Gustavo C. Longhin (2002)

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

This contribution gives an overview of current research in applying object oriented programming to scientific computing at the computational mechanics laboratory (LABMEC) at the school of civil engineering – UNICAMP. The main goal of applying object oriented programming to scientific computing is to implement increasingly complex algorithms in a structured manner and to hide the complexity behind a simple user interface. The following areas are current topics of research and documented within the...

Object oriented design philosophy for scientific computing

Philippe R.B. Devloo, Gustavo C. Longhin (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

This contribution gives an overview of current research in applying object oriented programming to scientific computing at the computational mechanics laboratory (LABMEC) at the school of civil engineering – UNICAMP. The main goal of applying object oriented programming to scientific computing is to implement increasingly complex algorithms in a structured manner and to hide the complexity behind a simple user interface. The following areas are current topics of research and documented within the...

Observability properties of a semi-discrete 1d wave equation derived from a mixed finite element method on nonuniform meshes

Sylvain Ervedoza (2010)

ESAIM: Control, Optimisation and Calculus of Variations

The goal of this article is to analyze the observability properties for a space semi-discrete approximation scheme derived from a mixed finite element method of the 1d wave equation on nonuniform meshes. More precisely, we prove that observability properties hold uniformly with respect to the mesh-size under some assumptions, which, roughly, measures the lack of uniformity of the meshes, thus extending the work [Castro and Micu, Numer. Math.102 (2006) 413–462] to nonuniform meshes. Our results...

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