Analysis of Double Sweep Optimized Schwarz Methods: the Positive Definite Case

2020 ◽  
pp. 53-64
Author(s):  
Martin J. Gander ◽  
Hui Zhang
Keyword(s):  
Positive Definite ◽  
Schwarz Methods ◽  
Definite Case ◽  
Optimized Schwarz Methods

Asynchronous optimized Schwarz methods with and without overlap

2017 ◽  
Vol 137 (1) ◽  
pp. 199-227 ◽  
Author(s):  
Frédéric Magoulès ◽  
Daniel B. Szyld ◽  
Cédric Venet
Keyword(s):  
Schwarz Methods ◽  
Optimized Schwarz Methods

Optimized Schwarz Methods with Elliptical Domain Decompositions

2021 ◽  
Vol 86 (2) ◽  
Author(s):  
Xin Chen ◽  
Martin J. Gander ◽  
Yingxiang Xu
Keyword(s):  
Schwarz Methods ◽  
Optimized Schwarz Methods

scholarly journals On the converse of Weyl’s conformal and projective theorems

2013 ◽  
Vol 94 (108) ◽  
pp. 55-65 ◽  
Author(s):  
Graham Hall
Keyword(s):  
Positive Definite ◽  
The Other ◽  
Dimensional Problem ◽  
Projective Tensor ◽  
Definite Case

This note investigates the possibility of converses of the Weyl theorems that two conformally related metrics on a manifold have the same Weyl conformal tensor and that two projectively related connections on a manifold have the same Weyl projective tensor. It shows that, in all relevant cases, counterexamples to each of Weyl?s theorems exist except for his conformal theorem in the 4-dimensional, positive definite case, where the converse actually holds. This (conformal) 4-dimensional problem is then solved completely for the other possible signatures.

scholarly journals A Classification of Symmetric (1, 1)-Coherent Pairs of Linear Functionals

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 213
Author(s):  
Herbert Dueñas Ruiz ◽  
Francisco Marcellán ◽  
Alejandro Molano
Keyword(s):  
Positive Definite ◽  
Linear Functionals ◽  
Definite Case ◽  
Coherent Pairs

In this paper, we study a classification of symmetric ( 1 , 1 ) -coherent pairs by using a symmetrization process. In particular, the positive-definite case is carefully described.

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