Coarse spaces play a crucial role in making Schwarz type domain decomposition methods scalable with respect to the number of subdomains. In this paper, we consider coarse spaces based on a class of partition of unity (PU) for some domain decomposition methods including the classical overlapping Schwarz method, and the new Schwarz method with harmonic overlap. PU has been used as a very powerful...

W'e develop a new class of overlapping Schwarz type algorithms for solving scalar convectiondiffusion equations discretized by finite element or finite difference methods. The preconditioners consist of two components, namely, the usual two-level additive Schwarz preconditioner and the sum of some quadratic terms constructed by using products of ordered neighboring subdomain preconditioners. Th...

The main purpose of this paper is to develop some methods investigate the Schwarz type lemmas holomorphic mappings and pluriharmonic in Banach spaces. Initially, we extend classical spaces, then apply these extensions establish a sharp Bloch theorem for on homogeneous unit balls ℂn obtain boundary Furthermore, improve generalize planar harmonic into forms present applications Additionally, usin...

During the last few years, an algebraic formulation of Schwarz methods was developed. In this paper this algebraic formulation is used to prove new convergence results for multiplicative Schwarz methods when applied to consistent singular systems of linear equations. Coarse grid corrections are also studied. In particular, these results are applied to the numerical solutions of Markov chains.

We prove two new reverse Cauchy–Schwarz inequalities of additive and multiplicative types in a space equipped with a positive sesquilinear form with values in a C *-algebra. We apply our results to get some norm and integral inequalities. As a consequence, we improve a celebrated reverse Cauchy–Schwarz inequality due to G. Pólya and G. Szegö.

We evaluated and compared Nuclear International, Schwarz/Mann, and Squibb kit methods for measurement of serum gastrin with respect to intra-run precision, analytical recovery of added gastrin, and values obtained for healthy fasting adults and for selected patients. As a result of this study, the Schwarz/Mann kit was chosen for use in our laboratory.

Schwarz methods use a decomposition of the computational domain into subdomains and need to impose boundary conditions on subdomain boundaries. In truncation one restricts unbounded bounded must also put both fields there are vast bodies literature research is very active ongoing. It turns out be fruitful think in as onto subdomains. Seminal precursors this fundamental idea papers by Hagstrom, ...