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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...

Elementary proofs of some basic subtemperature theorems

Neil A. Watson (2002)

Colloquium Mathematicae

We present simple elementary proofs of several theorems about temperatures and subtemperatures. Most of these are concerned with mean values over heat spheres, heat balls, and modified heat balls, with applications to proving Harnack theorems and the monotone approximation of subtemperatures by smooth subtemperatures.

Embedding of open riemannian manifolds by harmonic functions

Robert E. Greene, H. Wu (1975)

Annales de l'institut Fourier

Let M be a noncompact Riemannian manifold of dimension n . Then there exists a proper embedding of M into R 2 n + 1 by harmonic functions on M . It is easy to find 2 n + 1 harmonic functions which give an embedding. However, it is more difficult to achieve properness. The proof depends on the theorems of Lax-Malgrange and Aronszajn-Cordes in the theory of elliptic equations.

Equality cases for condenser capacity inequalities under symmetrization

Dimitrios Betsakos, Stamatis Pouliasis (2012)

Annales UMCS, Mathematica

It is well known that certain transformations decrease the capacity of a condenser. We prove equality statements for the condenser capacity inequalities under symmetrization and polarization without connectivity restrictions on the condenser and without regularity assumptions on the boundary of the condenser.

Espaces harmoniques sans potentiel positif

Victor Anandam (1972)

Annales de l'institut Fourier

Dans cet article on étudie les fonctions surharmoniques dans un espace Ω muni de la théorie axiomatique des fonctions harmoniques avec les axiomes 1, 2, 3 de M. Brelot, en supposant que les constantes sont harmoniques dans Ω et qu’il n’existe pas de potentiel > 0 dans Ω . Ainsi, dans la théorie axiomatique, on se propose de chercher à étendre les particularités du cas plan et quelques résultats sur les surfaces de Riemann du type parabolique. On démontre premièrement, en utilisant une notion de flux...

Essential norms of the Neumann operator of the arithmetical mean

Josef Král, Dagmar Medková (2001)

Mathematica Bohemica

Let K m ( m 2 ) be a compact set; assume that each ball centered on the boundary B of K meets K in a set of positive Lebesgue measure. Let C 0 ( 1 ) be the class of all continuously differentiable real-valued functions with compact support in m and denote by σ m the area of the unit sphere in m . With each ϕ C 0 ( 1 ) we associate the function W K ϕ ( z ) = 1 σ m m K g r a d ϕ ( x ) · z - x | z - x | m x of the variable z K (which is continuous in K and harmonic in K B ). W K ϕ depends only on the restriction ϕ | B of ϕ to the boundary B of K . This gives rise to a linear operator W K acting from...

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