Standard approaches require the problem to be well-posed in the Sobolev space H^{1}. While the proof of boundedness is straightforward, the proof of coercivity is based on Korn's inequality. If we would have Dirichlet conditions on the whole boundary, we could use Korn's first inequality, which guarantees coercivity with a constant that is independent of the shape of the computational domain. Otherwise, we have to resort to Korn's second inequality, which degrades for certain shapes of the computational domain (geometry locking). We are aiming for an IETI-DP solver, where we can prove that the condition number of the preconditioned system is independent of the shape of the overall domain and only depends on the shapes of the individual patches. As a second step, we extend our methods to incompressible materials. To avoid material locking, the differential equation has to be rephrased as a system of differential equations with saddle point structure. Here, the discretization is slightly more involved since we need an inf-sup stable discretization. We choose an extension of the Taylor Hood element to Isogeometric Analysis. For solving, we choose again the Dual-Primal Isogeometric Tearing and Interconnecting (IETI-DP) Method with a scaled Dirichlet preconditioner.

# Stefan Takacs: Domain decomposition methods for linearized elasticity problems in Isogeometric Analysis

We consider the linearized elasticity equations, discretized using multi-patch Isogeometric Analysis. To solve the resulting linear system, we choose the Dual-Primal Isogeometric Tearing and Interconnecting (IETI-DP) Method with a scaled Dirichlet preconditioner. We are interested in a convergence analysis. See more details below.

We will present the results of numerical experiments that demonstrate our theoretical findings.

Published Aug. 29, 2022 11:39 PM
- Last modified Aug. 29, 2022 11:39 PM