Domain decomposition methods are used for approximate solving boundary problems for partial differential equations on parallel computing systems. Specific features of unsteady problems are taken into account in the most complete way in iteration-free schemes of domain decomposition. Regionally-additive schemes are based on different classes of splitting schemes. In this paper we highlight a class of domain decomposition schemes which is based on the partition of the initial domain into subdomains with common boundary nodes. Using the partition of unit we have constructed and studied unconditionally stable schemes of domain decomposition based on two-component splitting: the problem within subdomain and the problem at their boundaries. As an example there is considered the Cauchy problem for evolutionary equations of first and second order with non-negative self-adjoint operator in a finite Hilbert space. The theoretical consideration is supplemented with numerical solving a model problem for the two-dimensional parabolic equation.
Two-level space-time domain decomposition methods for unsteady inverse problems
Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences（中国科学院深圳先进技术研究院）；University of Colorado Boulder（科罗拉多大学博尔德分校）；The Chinese University of Hong Kong（香港中文大学）
Speeding up an unsteady flow simulation by adaptive BDDC and Krylov subspace recycling
Institute of Mathematics of the Czech Academy of Sciences（捷克科学院数学研究所）；Faculty of Mechanical Engineering, Czech Technical University in Prague（布拉格捷克理工大学机械工程学院）
BDDC for Mixed-Hybrid Formulation of Flow in Porous Media with Combined Mesh Dimensions
Institute of Mathematics, Academy of Sciences of the Czech Republic（捷克科学院数学研究所）；Technical University of Liberec（利贝雷茨理工大学）；University of Maryland, Baltimore County（马里兰大学巴尔的摩县分校）
Stabilized Weighted Reduced Order Methods for Parametrized Advection-Dominated Optimal Control Problems governed by Partial Differential Equations with Random Inputs
