AuthorsM. Kuchta, K. Mardal and M. Mortensen
TitlePreconditioning trace coupled 3d-1d systems using fractional Laplacian
AfilliationScientific Computing
Project(s)No Simula project
Publication TypeJournal Article
JournalNumerical Methods for Partial Differential Equations
Publisher Wiley
KeywordsLagrange multipliers, preconditioning, saddle-point problem, trace

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.

Citation Keydoi:10.1002/num.22304

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