The solution of nonlinear finite element equations

By Hermann G. Matthies, G. Strang. 1979

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Citations in the corpus

DeltaGrad: Rapid retraining of machine learning models (2020, methodology): “We leverage the L-BFGS algorithm to approximate this, see e.g. Matthies & Strang (1979); Nocedal (1980); Byrd et al. (1994; 1995); Zhu et al. (1997); No-cedal & Wright (2006); Mokhtari & Ribeiro (2015) and references therein.”
A Beam-Column Joint Model for Simulating the Earthquake Response of Reinforced Concrete Frames (2004, methodology): “Modification of the classical Newton-Raphson solution algorithm to include a linesearch [Matthies and Strang 1979] 2.”
Numerical Methods and Smolyak Quadrature for Nonlinear Stochastic Partial Differential Equations (2003, unknown): “[33].”
Galerkin methods for linear and nonlinear elliptic stochastic partial differential equations (2005, methodology): “The Quasi-Newton methods produce updates to the inverse of a matrix, and these low-rank changes [15] are also best kept in tensor product form [44]; so that we have tensor products here on two levels, which makes for a very economical representation.”
Updating Quasi-Newton Matrices With Limited Storage (1980, unknown): “It is essentially the same as the formula for the usual BFGS [6].”
Representations of quasi-Newton matrices and their use in limited memory methods (1994, methodology): “It is given in Nocedal (1980) and is based on the recursion developed by Matthies and Strang (1979) for the standard BFGS method.”
FEBio: finite elements for biomechanics. (2012, unknown): “FEBio uses the BFGS method [23], which is one of the more effective quasiNewton methods for computational solid mechanics.”