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Computational algorithm for homogenized coefficients of hyperelastic heterogeneous materials undergoing large deformations

Lukeš, VladimírRohan, EduardCimrman, Robert — 2004

Programs and Algorithms of Numerical Mathematics

This article deals with an algorithm for numerical modelling of hyperelastic heterogeneous materials undergoing large deformations. The microstructure of these materials is changing (deforming) during a loading process, the changes in the microstructure depend on macroscopic deformations. To compute macroscopic responses, we must know material stiffness parameters and stresses in the heterogeneous structure. These effective parameters are obtained by solving microscopic problems. The number of...

Domain decomposition methods for solving the Burgers equation

Robert Cimrman — 1999

Applications of Mathematics

This article presents some results of numerical tests of solving the two-dimensional non-linear unsteady viscous Burgers equation. We have compared the known convergence and parallel performance properties of the additive Schwarz domain decomposition method with or without a coarse grid for the model Poisson problem with those obtained by experiments for the Burgers problem.

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