A parallel and adaptive continuation method for semilinear bifurcation problems

DOI10.1016/S0045-7825(98)00017-6zbMath0940.65052MaRDI QIDQ1971447

Laurence Cherfils

Publication date: 19 July 2000

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

zbMATH Keywords

numerical examplefinite elementparallel computationcontinuation methodsemilinear elliptic problemslarge scale nonlinear systemsmesh adaptation strategysemilinear bifurcation problems

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Global methods, including homotopy approaches to the numerical solution of nonlinear equations (65H20) Parallel numerical computation (65Y05) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Bifurcations in context of PDEs (35B32) Numerical solution of nonlinear eigenvalue and eigenvector problems (65H17)

Related Items (3)

Parallel numerical continuation of periodic responses of local nonlinear systems ⋮ Error estimates and adaptive finite element methods ⋮ FEM and BEM parallel processing: theory and applications – a bibliography (1996‐2002)

Uses Software

• PLTMG
• AUTO
• AUTO-86
• PVM

Cites Work

• Finite dimensional approximation of nonlinear problems. III: Simple bifurcation points
• Computational error estimates and adaptive processes for some nonlinear structural problems
• Stepsize selection in continuation procedures and damped Newton's method
• Note on unit tangent vector computation for homotopy curve tracking on a hypercube
• Large sparse continuation problems
• Multigrid Bifurcation Iteration
• Continuation-Conjugate Gradient Methods for the Least Squares Solution of Nonlinear Boundary Value Problems
• Stability and Multiplicity of Solutions to Discretizations of Nonlinear Ordinary Differential Equations
• On Steplength Algorithms for a Class of Continuation Methods
• Algorithm 502: Dependence of Solution of Nonlinear Systems on a Parameter [C5]
• Approximation des branches de solutions d’un problème de bifurcation semi-linéaire
• NUMERICAL ANALYSIS AND CONTROL OF BIFURCATION PROBLEMS (I): BIFURCATION IN FINITE DIMENSIONS
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