The Quasi-Newton Least Squares Method: A New and Fast Secant Method Analyzed for Linear Systems

Haelterman, Rob; Degroote, Joris; Heule, Dirk Van; Vierendeels, Jan

doi:10.1137/070710469

Cited by 49 publications

(35 citation statements)

References 18 publications

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“…It is therefore more advantageous to approximate the inverse of the Jacobian by applying the least-squares technique introduced by [26] on a particular set of vectors, as will be explained below. This technique can also be used to solve linear systems as demonstrated in [37].…”

Section: Interface Quasi-newton Coupling Algorithmmentioning

confidence: 99%

Partitioned simulation of the interaction between an elastic structure and free surface flow

Degroote

Souto-Iglesias

Paepegem

et al. 2010

Computer Methods in Applied Mechanics and Engineering

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ARTICLE INFO ABSTRACT Keywords:Fluid-structure interaction Partitioned Free surface Volume-of-fluid Rolling tank Impact IQN-ILS Aitken relaxationCurrently, the interaction between free surface flow and an elastic structure is simulated with monolithic codes which calcúlate the deformation of the structure and the liquid-gas flow simultaneously. In this work, this interaction is calculated in a partitioned way with a sepárate flow solver and a sepárate structural solver using the interface quasi-Newton algorithm with approximation for the inverse of the Jacobian from a leastsquares model (IQN-ILS). The interaction between an elastic beam and a sloshing liquid in a rolling tank is calculated and the results agree well with experimental data. Subsequently, the impact of both a rigid cylinder and a flexible composite cylinder on a water surface is simulated to assess the effect of slamming on the components of certain wave-energy converters. The impact pressure on the bottom of the rigid cylinder is nearly twice as high as on the flexible cylinder, which emphasizes the need for fluid-structure interaction calculations in the design process of these wave-energy converters. For both the rolling tank simulations and the impact simulations, grid refinement is performed and the IQN-ILS algorithm requires the same number of iterations on each grid. The simulations on the coarse grid are also executed using Gauss-Seidel coupling iterations with Aitken relaxation which requires significantly more coupling iterations per time step.

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Section: Interface Quasi-newton Coupling Algorithmmentioning

confidence: 99%

Partitioned simulation of the interaction between an elastic structure and free surface flow

Degroote

Souto-Iglesias

Paepegem

et al. 2010

Computer Methods in Applied Mechanics and Engineering

Self Cite

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“…Because the inverse of the Jacobian is approximated, one avoids that a linear system with as dimension the number of degrees-of-freedom in the interface's position has to be solved in every quasi-Newton iteration. The approximation is constructed with the least-squares technique developed for nonlinear systems by Vierendeels et al [8] and applied to linear systems by Haelterman et al [40]. A matrix-free implementation of the least-squares technique is described in this work.…”

Section: Introductionmentioning

confidence: 99%

Performance of partitioned procedures in fluid–structure interaction

Degroote¹,

Haelterman²,

Annerel³

et al. 2010

Computers & Structures

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115

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Partitioned simulations of fluid-structure interaction can be solved for the interface's position with Newton-Raphson iterations but obtaining the exact Jacobian is impossible if the solvers are "black boxes". It is demonstrated that only an approximate Jacobian is needed, as long as it describes the reaction to certain components of the error on the interface's position. Based on this insight, a quasiNewton coupling algorithm with an approximation for the inverse of the Jacobian (IQN-ILS) has been developed and compared with a monolithic solver in previous work. Here, IQN-ILS is compared with other partitioned schemes such as IBQN-LS, Aitken relaxation and Interface-GMRES(R).

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“…The analysis of piecewise linear regression with the breakpoint estimation was calculated to explain the time-relation changes of the parameters g s , C i , P N , and E. The time intervals were estimated by nonlinear methods according to Quasi-Newton and the lost function based on the least squares were proceeded (Haelterman et al, 2009). The relationships between the parameters were computed using the simple coefficient of correlation (r by Pearson).…”

Section: Discussionmentioning

confidence: 99%

Response of Gas Exchange to Leaf Piercing Explained by Piecewise Linear Regression for Two Developmental Forms of Rape Plant (Brassica napus L. ssp. oleifera Metzg)

Wenda-Piesik¹,

Krzesiński²,

Nowak³

et al. 2017

Acta Biologica Cracoviensia S. Botanica

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Oilseed rape (Brassica napus L. ssp. oleifera Metzg) was the subject of the study in two forms: winter cv. 'Muller' (at the rosette stage -the first internode BBCH 30 -31) and spring cv. 'Feliks' (at the yellow bud stage BBCH 59). The main gas-exchange parameters, net photosynthetic rate (P N ), transpiration rate (E), stomatal conductance (g s ), and intercellular CO 2 concentration (C i ) were measured on leaves prior to the piercing and immediately after the short-term piercing. The effect of mechanical wounding revealed different progress of the gas exchange process for the two forms. Piecewise linear regression with the breakpoint estimation showed that the plants at the same age but at a different vegetal stage, manage mechanical leaf-piercing differently. The differences concerned the stomatal conductance and transpiration changes since for rosette leaves the process consisted of five intervals with a uniform direction, while for stem leaves -of five intervals with a fluctuating direction. These parameters got stabilized within a similar time (220 mins) for both forms. The process of net photosynthetic rate was altered by the plant stages. 'Muller' plants at the rosette stage demonstrated dependence of P N on time in log-linear progression: y (P N ) = 8.01+ 2.73 log 10 (x t 2 ); 7 < t 2 < 220; R 2 = 0.96. For stem leaves of 'Feliks' plants the process of transpiration, in terms of directions, was convergent with the process of photosynthesis. Those two processes were synchronized from 1 st to 114 th min of the test (r = 0.85; p < 0.001) in plants at the rosette stage and from 26 th to 148 th min in stem leaves (r = 0.95; p < 0.001).

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The Quasi-Newton Least Squares Method: A New and Fast Secant Method Analyzed for Linear Systems

Cited by 49 publications

References 18 publications

Partitioned simulation of the interaction between an elastic structure and free surface flow

Partitioned simulation of the interaction between an elastic structure and free surface flow

Performance of partitioned procedures in fluid–structure interaction

Response of Gas Exchange to Leaf Piercing Explained by Piecewise Linear Regression for Two Developmental Forms of Rape Plant (Brassica napus L. ssp. oleifera Metzg)

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