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Div-curl lemma revisited: Applications in electromagnetism

Marián Slodička, Ján Jr. Buša (2010)

Kybernetika

Two new time-dependent versions of div-curl results in a bounded domain Ω ⊂ ℝ 3 are presented. We study a limit of the product v k w k , where the sequences v k and w k belong to Ł 2 ( Ω ) . In Theorem 2.1 we assume that ∇ × v k is bounded in the L p -norm and ∇ · w k is controlled in the L r -norm. In Theorem 2.2 we suppose that ∇ × w k is bounded in the L p -norm and ∇ · w k is controlled in the L r -norm. The time derivative of w k is bounded in both cases in the norm of - 1 ( Ω ) . The convergence (in the sense of distributions) of v k w k to the product v w of weak limits...

EasyMSG : tools and techniques for an adaptive overlapping in SPMD programming

Pascal Havé (2002)

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

During the development of a parallel solver for Maxwell equations by integral formulations and Fast Multipole Method (FMM), we needed to optimize a critical part including a lot of communications and computations. Generally, many parallel programs need to communicate, but choosing explicitly the way and the instant may decrease the efficiency of the overall program. So, the overlapping of computations and communications may be a way to reduce this drawback. We will see a implementation of this techniques...

EasyMSG: Tools and techniques for an adaptive overlapping in SPMD programming

Pascal Havé (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

During the development of a parallel solver for Maxwell equations by integral formulations and Fast Multipole Method (FMM), we needed to optimize a critical part including a lot of communications and computations. Generally, many parallel programs need to communicate, but choosing explicitly the way and the instant may decrease the efficiency of the overall program. So, the overlapping of computations and communications may be a way to reduce this drawback. We will see a implementation of this...

Edge finite elements for the approximation of Maxwell resolvent operator

Daniele Boffi, Lucia Gastaldi (2002)

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

In this paper we consider the Maxwell resolvent operator and its finite element approximation. In this framework it is natural the use of the edge element spaces and to impose the divergence constraint in a weak sense with the introduction of a Lagrange multiplier, following an idea by Kikuchi [14]. We shall review some of the known properties for edge element approximations and prove some new result. In particular we shall prove a uniform convergence in the L 2 norm for the sequence of discrete operators....

Edge finite elements for the approximation of Maxwell resolvent operator

Daniele Boffi, Lucia Gastaldi (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper we consider the Maxwell resolvent operator and its finite element approximation. In this framework it is natural the use of the edge element spaces and to impose the divergence constraint in a weak sense with the introduction of a Lagrange multiplier, following an idea by Kikuchi [14]. We shall review some of the known properties for edge element approximations and prove some new result. In particular we shall prove a uniform convergence in the L2 norm for the sequence of discrete...

Finite element approximation for a div-rot system with mixed boundary conditions in non-smooth plane domains

Michal Křížek, Pekka Neittaanmäki (1984)

Aplikace matematiky

The authors examine a finite element method for the numerical approximation of the solution to a div-rot system with mixed boundary conditions in bounded plane domains with piecewise smooth boundary. The solvability of the system both in an infinite and finite dimensional formulation is proved. Piecewise linear element fields with pointwise boundary conditions are used and their approximation properties are studied. Numerical examples indicating the accuracy of the method are given.

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