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Showing 1 to 5 of 5 for “"Pseudo-arclength"”.
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A parallel adaptive method for pseudo-arclength continuation
We parallelize the pseudo-arclength continuation method for solving nonlinear systems of equations. Pseudo-arclength continuation is a predictor-corrector method where the correction step consists of solving a linear system of algebraic equations. Our algorithm parallelizes adaptive step-length …
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On matrix-free pseudo-arclength continuation methods applied to a nonlocal partial differential equation in 1+1D with pseudo-spectral time-stepping
… with periodic boundary conditions [5]. We apply pseudo-spectral methods to numerically integrate initial states of the populations given as small perturbations from a homogeneous steady state from which bifurcations and dynamics have been studied from a linear and weakly nonlinear analysis …
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Nonlinear Response of Cantilever Beams
… to aperiodic responses of the beams. A pseudo-arclength scheme is used to determine the fixed points and their stability. In some cases, they are found to undergo Hopf bifurcations, which result in limit cycles. A combination of a long-time integration, a two-point boundary-value …
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Exploring the Nonlinear Dynamics of Tapping Mode Atomic Force Microscopy with Capillary Layer Interactions
… simulation with event handling and the numerical pseudo-arclength continuation of periodic solutions. We first use these numerical approaches to explore the nonlinear dynamics of the cantilever. We find the coexistence of three steady state oscillating solutions: (i) periodic with low-amplitude, …
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Nonlinear Vibrations of Doubly Curved Cross-PLy Shallow Shells
… that govern the slow dynamics of the response. A pseudo-arclength scheme is used to determine the fixed points of the modulation equations and the stability of these fixed points is investigated. In some cases, the fixed points undergo Hopf bifurcations, which result in dynamic solutions. A …