A novel method for solving nonlinear stochastic mechanics problems using FETI-DP

Ajith, G and Ghosh, D (2022) A novel method for solving nonlinear stochastic mechanics problems using FETI-DP. In: International Journal for Numerical Methods in Engineering .

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Abstract

Solution of large-scale nonlinear stochastic mechanics problems such as plasticity is generally very expensive. In this work, a domain decomposition based scalable method is proposed for solving such problems. The mechanics problem and random fields are discretized using finite element (FE) bases and Karhunen�Loève expansion, respectively. The FE mesh is partitioned that offers (i) both spatial and stochastic dimensionality reduction and (ii) an inherent framework for parallelization. Then a stochastic collocation based surrogate model is built for each subdomain wherein at each collocation point a deterministic nonlinear problem is solved. The deterministic nonlinear problem is solved using Newton�Raphson method. The linear system of equations involving the Jacobian is solved using the dual-primal version of the FE tearing and interconnecting (FETI-DP) method, due to its demonstrated scalability for deterministic problems. Stochastic collocation and FETI-DP are inherently and independently parallelizable. Finally, at the post-processing stage, a statistical sampling from the surrogate model is performed by preserving the structure of the input random field. The proposed method is numerically tested for p-Laplace and plain-strain plasticity problems, and found to be computationally efficient and accurate. In parallel implementation, the method showed good scalability. © 2022 John Wiley & Sons Ltd.

Item Type:	Journal Article
Publication:	International Journal for Numerical Methods in Engineering
Publisher:	John Wiley and Sons Ltd
Additional Information:	The copyright for this article belongs to John Wiley and Sons Ltd
Keywords:	Domain decomposition methods; Linear systems; Plasticity; Sampling; Stochastic models; Stochastic systems, Deterministics; Domain-decomposition methods; FETI-DP; High performance computing; Nonlinear problems; Performance computing; Random fields; Stochastic collocation; Stochastic mechanics; Surrogate modeling, Scalability
Department/Centre:	Division of Mechanical Sciences > Civil Engineering
Date Deposited:	09 Mar 2022 10:23
Last Modified:	09 Mar 2022 10:23
URI:	http://eprints.iisc.ac.in/id/eprint/71464

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