Balancing truncation and round-off errors in FEM: One-dimensional analysis

Periodicity and Transport from Round-Off Errors

AMS Subject Classi cation: 58F20, 60J60, 65G05 We investigate the effects of round-off errors on quasi-periodic motions in a linear symplectic planar map. By discretizing coordinates uniformly we transform this map into a permutation of Z2 , and study motions near infinity, which correspond to a fine discretization. We provide numerical evidence that all orbits are periodic and that the average...

Reducing round-off errors in symmetric multistep methods

Certain symmetric linear multistep methods have an excellent long-time behavior when applied to second order Hamiltonian systems with or without constraints. For high accuracy computations round-off can be the dominating source of errors. This article shows how symmetric multistep methods should be implemented, so that round-off errors are minimized and propagate like a random walk.

Reducing round-off errors in rigid body dynamics

In several recent publications, numerical integrators based on Jacobi elliptic functions are proposed for solving the equations of motion of the rigid body. Although this approach yields theoretically the exact solution, a standard implementation shows an unexpected linear propagation of round-off errors. We explain how deterministic error contribution can be avoided, so that round-off behaves ...

Estimation of Round-off Errors in OpenMP Codes

Estimation of Round-Off Errors on Several Computer Architectures

Numerical validation of computed results in scienti c computation is always an essential problem as well on sequential architecture as on parallel architecture. The probabilistic approach is the only one that allows to estimate the round-o error propagation of the oating point arithmetic on computers. We begin by recalling the basics of the CESTAC method (Contrôle et Estimation STochastique des...