Localization of Nonlinearities and Recycling in Dual Domain Decomposition

Seibold, Andreas; Leistner, Michael; Rixen, Daniel J.

doi:10.1007/978-3-030-56750-7_55

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“…Hence, the next natural step is to further improve solver-efficiency by applying recycling-techniques to this new problem. In this work, we adapt a Total Reuse of Krylov Subspaces (TRKS) approach [9], successfully applied to linear and nonlinear structural dynamics in [12,17], to a GMRES-solver and investigate its applicability to the nonlinear BGC-macro method.…”

Section: Introductionmentioning

confidence: 99%

On Total Reuse of Krylov Subspaces for an iterative FETI-solver in multirate integration

Seibold,

Rixen,

Fresno Zarza

2021

Proceedings of the YIC 2021 - VI ECCOMAS Young Investigators Conference

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Recycling techniques for Krylov subspaces in parallel FETI-solvers are able to increase efficiency of solution processes with repeated right-hand-sides. One simple technique consists in a Total Reuse of the Krylov Subspace (TRKS) provided by conjugate directions generated during the solution of previous problems. This applies especially for linear structural dynamics and recycling also reduced global iterations for nonlinear structural dynamics. The structure of the interface-operator's eigenvalues governs the possible efficiency-gain. Only if high clustered eigenvalues are captured early enough, global FETI iterations will be reduced accordingly. Besides these advances, multirate integrators have been proposed, that enable adapted time-step-sizes on each substructure and are expected to accelerate the parallel simulation of nonlinear dynamic simulations with local highly nonlinear processes, e.g. damaging. Based on the linear BGC-macro and nonlinear PH-method, a nonlinear BGC-macro method has been proposed and on the other hand a more flexible and accurate multirate-integrator has been derived from the variational principle. These multirate-integration schemes require several local integration-steps in each global iteration, leading to a non-symmetric structure of the linearized local problems and the local boundary conditions are altered compared to FETI for standard singlerate integration. So, we have to solve the global interface-problem with a GMRes-solver. In this contribution, we show our recent results on the eigenvalues and application of a TRKS to these new problems.

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Section: Introductionmentioning

confidence: 99%