We introduce in this paper a new tool to prove the convergence of the overlapping optimized Schwarz methods with multisubdomains. The technique is based on some estimates of the errors on the boundaries of the overlapping strips. Our guiding example is an n-dimensional linear parabolic equation.
We present a scalable and efficient iterative solver for high-order hybridized discon-tinuous Galerkin (HDG) discretizations of hyperbolic partial differential equations. It is an interplay between domain decomposition methods and HDG discretizations. In particular, the method is a fixed-point approach that requires only independent element-by-element local… (More)
In this note, we introduce a new approach to study overlapping domain decomposition methods for optimal control systems governed by partial differential equations. The model considered in our paper is systems governed by wave equations. Our technique could be used for several other equations as well.