Algorithm 652

Watson, Layne T.; Billups, Stephen C.; Morgan, Alexander P.

doi:10.1145/29380.214343

Cited by 351 publications

(137 citation statements)

References 25 publications

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“…Next, a globally convergent homotopy based nonlinear system solver, subroutine FIXPDF from the HOMPACK (Watson, Billups, and Morgan [25]) suite of codes, was used. This method (using the default homotopy map) tracks the zero curve of ),…”

Section: Methodsmentioning

confidence: 99%

Effect of flexible joints on the stability and large deflections of a triangular frame

2008

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SummaryAn isosceles triangular frame with rotationally resistive joints under a tip load is studied. The large in-plane deformation elastica equations are formulated. Stability analysis shows the frame can buckle symmetrically or asymmetrically. Post-buckling behavior showing limit load and hysteresis are obtained by shooting and homotopy numerical algorithms. The behavior of a frame with rigid joints is studied in detail. The effects of joint spring constant and base length are found.

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Section: Methodsmentioning

confidence: 99%

Effect of flexible joints on the stability and large deflections of a triangular frame

2008

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“…The following circuit is described by a system of nonlinear equations with 14 variables 13 . This circuit contain four transistor and one diode as shown in Fig.…”

Section: Case Study With 14 Variablesmentioning

confidence: 99%

“…Such methods are becoming a viable alternative in circuit simulation, where they can be used to resolve convergence difficulties and to find multiple operation points. These methods are slower than conventional methods but their speed can often be improved by careful implementation [12][13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Spherical Continuation Algorithm with Spheres of Variable Radius to Trace Homotopy Curves

Torres-Muñoz

Hernandez-Martinez

Vázquez-Leal

2015

Int. J. Appl. Comput. Math

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The homotopy continuation methods are capable to locate multiple solutions of nonlinear systems of equations. In this paper is presented the path-following technique used to trace the homotopy trajectory. The spherical method is employed resizing the radius of the sphere at each iteration, the above based on the behavior of the radius of curvature. Also the Newton homotopy is applied in conjunction with the proposed methodology for tracing homotopy curve. To prove the usefulness of the proposed method is applied to three examples with different numbers of equations obtaining successful results.

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“…There are many attempts to cope with these problems. Among these global methods are line search methods as the Armijo rule [1], trust region methods [17], homotopy [61], and pseudo-transient continuation [35]. Additionally, stability problems of the structure are frequently solved by means of the arc-length method on global level, see Eq.…”

Section: F(t Y(t)ẏ(t)) := G(t U(t) Q(t)) Q(t) − R(t U(t)u(t) Qmentioning

confidence: 99%

Iterative solvers within sequences of large linear systems in non‐linear structural mechanics

Hartmann¹,

Tebbens

Quint

et al. 2009

Z Angew Math Mech

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This article treats the computation of discretized constitutive models of evolutionary-type (like models of viscoelasticity, plasticity, and viscoplasticity) with quasi-static finite elements using diagonally implicit Runge-Kutta methods (DIRK) combined with the Multilevel-Newton algorithm (MLNA). The main emphasis is on promoting iterative methods, as opposed to the more traditional direct methods, for solving the non-symmetric systems which occur within the DIRK/MLNA. It is shown that iterative solution of the arising sequences of linear systems can be substantially accelerated by various techniques that aim at sharing part of the computational effort throughout the sequence. In this way iterative solution becomes attractive at clearly lower dimensions than the dimensions where direct solvers start to fail for memory reasons. The applications are related to small strain viscoplasticity of a smooth constitutive model for plastics and a finite strain plasticity model with non-linear kinematic hardening developed for metals.

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Algorithm 652

Cited by 351 publications

References 25 publications

Effect of flexible joints on the stability and large deflections of a triangular frame

Effect of flexible joints on the stability and large deflections of a triangular frame

Spherical Continuation Algorithm with Spheres of Variable Radius to Trace Homotopy Curves

Iterative solvers within sequences of large linear systems in non‐linear structural mechanics

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