On the Convergence of Recursive Trust-Region Methods for Multiscale Nonlinear Optimization and Applications to Nonlinear Mechanics

DOI10.1137/08071819XzbMath1410.90198OpenAlexW2003106321MaRDI QIDQ3584635

Christian Gross, Rolf H. Krause

Publication date: 30 August 2010

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/08071819x

zbMATH Keywords

nonlinear elasticitynonlinear programmingconvergence theorynonlinear multilevel methods

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Numerical mathematical programming methods (65K05) Nonconvex programming, global optimization (90C26) Nonlinear programming (90C30) Small-strain, rate-dependent theories of plasticity (including theories of viscoplasticity) (74C10) Variational methods applied to PDEs (35A15) Optimization of other properties in solid mechanics (74P10) Nonlinear elliptic equations (35J60)

Related Items

On a multilevel Levenberg–Marquardt method for the training of artificial neural networks and its application to the solution of partial differential equations ⋮ A Phase-Field Approach to Pneumatic Fracture ⋮ A recursive multilevel trust region method with application to fully monolithic phase-field models of brittle fracture ⋮ A detailed investigation of the model influencing parameters of the phase‐field fracture approach ⋮ Level set based multi-scale methods for large deformation contact problems ⋮ Globally Convergent Multilevel Training of Deep Residual Networks ⋮ On High-Order Multilevel Optimization Strategies ⋮ A parallel multigrid method for constrained minimization problems and its application to friction, contact, and obstacle problems ⋮ A Parallel Approach to the Variational Transfer of Discrete Fields between Arbitrarily Distributed Unstructured Finite Element Meshes ⋮ A first-order multigrid method for bound-constrained convex optimization ⋮ Subdivision-Based Nonlinear Multiscale Cloth Simulation

Uses Software

• UG
• NewtonLib
• Ipopt