Asynchronous Partial Update of Domain Decomposition Preconditioners to Solve Nonlinear CFD Problems

Domain decomposition preconditioners for multiscale problems

In this paper, we study domain decomposition preconditioners for multiscale elliptic problems in high contrast media. We construct preconditioners such that the condition number of the preconditioned system is independent of media contrast. For this purpose, multiscale spaces for the interpolation on the coarse grid is developed using a local weighted spectral problem. A main observation is tha...

Domain Decomposition Preconditioners for Hermite Collocation Problems

An adapted coarse space for Balancing domain decomposition method to solve nonlinear elastodynamic problems

This work is devoted to present a scalable domain decomposition method to solve nonlinear elastodynamic problems. Large non linear elastodynamic problems represent an appropriate application field for substructuring methods which are efficient on parallel computer with the proviso of using specific preconditioner techniques well adapted to the mechanical modeling. According to this reason, we d...

Multiscale Domain Decomposition Preconditioners for Anisotropic High-Contrast Problems

In this paper, we study robust two-level domain decomposition preconditioners for highly anisotropic multiscale problems. We give a construction of coarse spaces that employ initial multiscale basis functions and discuss techniques to achieve smaller dimensional coarse spaces without sacrificing the robustness of the preconditioner. We also present numerical results and discuss possible extensi...

Domain Decomposition Preconditioners for Linear–quadratic Elliptic Optimal Control Problems

We develop and analyze a class of overlapping domain decomposition (DD) preconditioners for linear-quadratic elliptic optimal control problems. Our preconditioners utilize the structure of the optimal control problems. Their execution requires the parallel solution of subdomain linear-quadratic elliptic optimal control problems, which are essentially smaller subdomain copies of the original pro...