Authors | M. Kuchta, K. Mardal and M. Mortensen |
Title | Preconditioning trace coupled 3d-1d systems using fractional Laplacian |
Afilliation | Scientific Computing |
Project(s) | No Simula project |
Status | Published |
Publication Type | Journal Article |
Journal | Numerical Methods for Partial Differential Equations |
Volume | 35 |
Number | 1 |
Pagination | 375-393 |
Publisher | Wiley |
Keywords | Lagrange multipliers, preconditioning, saddle-point problem, trace |
Abstract | Multiscale or multiphysics problems often involve coupling of partial differential equations posed on domains of different dimensionality. In this work, we consider a simplified model problem of a 3d-1d coupling and the main objective is to construct algorithms that may utilize standard multilevel algorithms for the 3d domain, which has the dominating computational complexity. Preconditioning for a system of two elliptic problems posed, respectively, in a three-dimensional domain and an embedded one dimensional curve and coupled by the trace constraint is discussed. Investigating numerically the properties of the well-defined discrete trace operator, it is found that negative fractional Sobolev norms are suitable preconditioners for the Schur complement of the system. The norms are employed to construct a robust block diagonal preconditioner for the coupled problem. |
URL | https://onlinelibrary.wiley.com/doi/abs/10.1002/num.22304 |
DOI | 10.1002/num.22304 |
Citation Key | doi:10.1002/num.22304 |