A Balancing Domain Decomposition by Constraints Preconditioner for a $C^0$ Interior Penalty Method
Provides a scalable preconditioner for a discontinuous Galerkin method applied to fourth-order elliptic problems, addressing a computational bottleneck in domain decomposition.
Developed a BDDC preconditioner for the C0 interior penalty method for the biharmonic problem, achieving a condition number bounded by C(1+ln(H/h))^2, with numerical experiments confirming the theory.
We develop a nonoverlapping domain decomposition preconditioner for the $C^0$ interior penalty method, a discontinuous Galerkin method, for the biharmonic problem. The preconditioner is based on balancing domain decomposition by constraints (BDDC). We prove that the condition number of the preconditioned system is bounded by $C (1+\ln (H/h))^2$, where $h$ is the mesh size of the triangulation, $H$ is the typical diameter of subdomains, and the positive constant $C$ is independent of $h$ and $H$. Numerical experiments are also represented to corroborate the theoretical result.