Optimized Schwarz methods (OSM) are very popular methods which were introduced in [11] for elliptic problems and in [3] for propagative wave phenomena. We build here a coarse space for which the convergence rate of the two-level method is guaranteed regardless of the regularity of the coefficients. We do this by introducing a symmetrized variant of the ORAS (Optimized Restricted Additive Schwar...

SCHWARZ, Roberto. Seja como for: entrevistas, retratos e documentos. São Paulo: Duas Cidades; Editora 34, 2019.

It is helpful to have available systematic ways to find a variety useful conformal mappings. Our text treats one such method: bilinear transformations. Here we study a second: Schwarz-Christoffel transformations. These are discussed in many references; I recommend particularly [1], a lovely book on complex variable theory which has a decided applied slant. The Schwarz-Christoffel transformation...

The N=4 gauged SU(2)×SU(1,1) supergravity in four-dimensional Euclidean space is obtained via a consistent dimensional reduction of the N=1, D=10 supergravity on S × AdS3. The dilaton potential in the theory is proportional to the difference of the two gauge coupling constants, which is due to the opposite signs of the curvatures of S and AdS3. As a result, the potential can be positive, negati...