This paper is concerned with parallel computation in solving the convection-diffusion equation and the incompressible Navier-Stokes equation via Newton-Schwarz method, a nonlinear domain decomposition (DD) method. Various preconditioners are investigated here. An interface problem is tackled as a preconditioner for nonlinear block Jacobi DD approach, with an optional fine level interface proble...

In this paper we study a class of modules over infinite-dimensional Lie (super)algebras, which we call conformal modules. In particular we classify and construct explicitly all irreducible conformal modules over the Virasoro and the N=1 Neveu-Schwarz algebras, and over the current algebras. 0. Introduction Conformal module is a basic tool for the construction of free field realization of infini...

Multitrace formulations (MTFs) are based on a decomposition of the problem domain into subdomains, and thus domain decomposition solvers are of interest. The fully rigorous mathematical MTF can however be daunting for the non-specialist. We introduce in this paper MTFs on a simple model problem using concepts familiar to researchers in domain decomposition. This allows us to get a new understan...

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...

This paper presents a preconditioner based on solving approximate Schur complement systems with overlapping restricted additive Schwarz methods (RAS). The construction of the preconditoner, called SchurRAS, is as simple as in the standard RAS. The communication requirements for each application of the preconditioning operation are similar with those of the standard RAS approach. In the particul...

Accurate simulation of glass melting furnaces requires the solution of very large linear algebraic systems of equations. To solve these equations efficiently a Schwarz domain decomposition (multi-block) method can be used. However, it can be observed that the convergence of the Schwarz method deteriorates when a large number of subdomains is used. This is due to small eigenvalues arising from t...

In this paper we introduce a boundary value problem involving powers of the p-Laplace operator. We will then prove a variant of Talenti inequality which shows that the Schwarz symmetrization of the solution of the boundary value problem is majorized by the solution of the appropriately symmetrized version of the problem. The case of equality is also investigated. Finally, as an application, we ...

—We present a new high-performance Convex Cauchy– Schwarz Divergence (CCS-DIV) measure for Independent Component Analysis (ICA) and Blind Source Separation (BSS). The CCS-DIV measure is developed by integrating convex functions into the Cauchy–Schwarz inequality. By including a convexity quality parameter, the measure has a broad control range of its convexity curvature. With this measure, a ne...