Krylov-ROW methods for DAEs of index 1 with applications to viscoelasticity

DOI10.1016/j.apnum.2004.08.012zbMath1078.65073OpenAlexW2073182156MaRDI QIDQ1772817

Joerg Wensch

Publication date: 21 April 2005

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2004.08.012

zbMATH Keywords

finite element methodnumerical examplesdifferential-algebraic equationsthin plateKrylov iterationsRosenbrock methodViscoelasticity integral equations

Mathematics Subject Classification ID

Implicit ordinary differential equations, differential-algebraic equations (34A09) Plates (74K20) Finite element methods applied to problems in solid mechanics (74S05) Iterative numerical methods for linear systems (65F10) Numerical methods for initial value problems involving ordinary differential equations (65L05) Numerical methods for differential-algebraic equations (65L80)

Related Items (3)

Linearly implicit GARK schemes ⋮ Biorthogonal Rosenbrock-Krylov time discretization methods ⋮ Finite element analysis of viscoelastic structures using Rosenbrock-type methods

Uses Software

• RODAS
• ROWMAP

Cites Work

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• An iterative solution method for solving \(f(A)x=b\), using Krylov subspace information obtained for the symmetric positive definite matrix A
• The application of Rosenbrock-Wanner type methods with stepsize control in differential-algebraic equations
• Behandlung steifer Anfangswertprobleme gewöhnlicher Differentialgleichungen mit adaptiven Runge-Kutta-Methoden
• Computation in finite-strain viscoelasticity: finite elements based on the interpretation as differential-algebraic equations
• ROWMAP -- a ROW-code with Krylov techniques for large stiff ODEs
• Runge-Kutta methods in elastoplasticity
• Rosenbrock methods for differential algebraic equations
• Matrix-free \(W\)-methods using a multiple Arnoldi iteration
• Remarks on the interpretation of current non‐linear finite element analyses as differential–algebraic equations
• Time integration of index 1 DAEs with Rosenbrock methods using Krylovsubspace techniques
• Some general implicit processes for the numerical solution of differential equations
• Viscoplastic Deformation from the DAE Perspective ‐ a Benchmark Problem
• Using Krylov Methods in the Solution of Large-Scale Differential-Algebraic Systems
• Exponential Integrators for Large Systems of Differential Equations
• Finite elements. Theory, fast solvers and applications in elasticity theory
• A class of linearly-implicit Runge-Kutta methods for multibody systems

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