Isogeometric block BDDC/FETI-DP preconditioners for the three-field Biot’s consolidation model

This paper presents a block dual-primal preconditioner for the three-field mixed isogeometric discretization of the stationary Biot's consolidation model, formulated in terms of displacement, pressure, and total pressure. After decomposing the computational domain into subdomains and eliminating the displacement variables and the interior components of pressure and total pressure within each subdomain, we reduce the problem to a symmetric positive definite system for the subdomain interface unknowns and the Lagrange multiplier. The reduced system is solved by a preconditioned conjugate gradient method with a block preconditioner, based on a Balancing Domain Decomposition by Constraints (BDDC) method with deluxe scaling for the interface block and a FETI-DP preconditioner for the Lagrange multiplier block. We prove that the algorithm is scalable with respect to the number of subdomains and achieves a quasi-optimal convergence rate bound that is polylogarithmic in the ratio of subdomain to element sizes and robust with respect to the model parameters. Numerical experiments confirm the efficiency of the proposed preconditioner, even in the presence of discontinuous Lamé parameters, and illustrate its robustness with respect to the spline polynomial degree, regularity, and domain deformation.