118,040 research outputs found
Anisotropic error control for environmental applications
No full textIn this paper we aim at controlling physically meaningful quantities with emphasis on environmental applications. This is car-
ried out by an efficient numerical procedure combining the goal-oriented framework [R. Becker, R. Rannacher, An optimal control
approach to a posteriori error estimation in finite element methods, Acta Numer. 10 (2001) 1–102] with the anisotropic setting in-
troduced in [L. Formaggia, S. Perotto, New anisotropic a priori error estimates, Numer. Math. 89 (2001) 641–667]. A first attempt
in this direction has been proposed in [L. Formaggia, S. Micheletti, S. Perotto, Anisotropic mesh adaptation in computational fluid
dynamics: application to the advection–diffusion–reaction and the Stokes problems, Appl. Numer. Math. 51 (2004) 511–533]. Here
we improve this analysis by carrying over to the goal-oriented framework the good property of the a posteriori error estimator to
depend on the error itself, typical of the anisotropic residual based error analysis presented in [G. Maisano, S. Micheletti, S. Per-
otto, C.L. Bottasso, On some new recovery based a posteriori error estimators, Comput. Methods Appl. Mech. Engrg. 195 (37–40)
(2006) 4794–4815; S. Micheletti, S. Perotto, An anisotropic recovery-based a posteriori error estimator, in: F. Brezzi, A. Buffa,
S. Corsaro, A. Murli (Eds.), Numerical Mathematics and Advanced Applications—ENUMATH2001, Proceedings of the 4th Euro-
pean International Conference on Numerical Mathematics and Advanced Applications, Springer-Verlag, Italia, 2003, pp. 731–741].
On the one hand this dependence makes the estimator not immediately computable; nevertheless, after approximating this error via
the Zienkiewicz–Zhu gradient recovery procedure [O.C. Zienkiewicz, J.Z. Zhu, A simple error estimator and adaptive procedure
for practical engineering analysis, Internat. J. Numer. Methods Engrg. 24 (2) (1987) 337–357; O.C. Zienkiewicz, J.Z. Zhu, The
superconvergent patch recovery and a posteriori error estimates. Part 1: The recovery technique, Internat. J. Numer. Methods En-
grg. 33 (1992) 1331–1364], the resulting estimator is expected to exhibit a higher convergence rate than the one in [L. Formaggia,
S. Micheletti, S. Perotto, Anisotropic mesh adaptation in computational fluid dynamics: application to the advection–diffusion–
reaction and the Stokes problems, Appl. Numer. Math. 51 (2004) 511–533]. As the broad numerical validation attests, the proposed
estimator turns out to be more efficient in terms of d.o.f.’s per accuracy or equivalently, more accurate for a fixed number of ele-
ments
The benefits of anisotropic mesh adaptation for brittle fractures under plane-strain conditions
No full textAbstractWe develop a reliable a posteriori anisotropic first order estimator for the numerical simulation of the Francfort and Marigo model of brittle fracture, after its approximation by means of the Ambrosio-Tortorelli variational model. We show that an adaptive algorithm based on this estimator reproduces all the previously ob-tained well-known benchmarks on fracture development with particular attention to the fracture directionality. Additionally, we explain why our method, based on an extremely careful tuning of the anisotropic adaptation, has the potential of out-performing significantly in terms of numerical complexity the ones used to achieve similar degrees of accuracy in previous studies.
A PDE-regularized smoothing method for space-time data over manifolds with application to medical data
No full textWe propose an innovative statistical-numerical method to model spatio- temporal data, observed over a generic two-dimensional Riemanian manifold. The proposed approach consists of a regression model completed with a regu- larizing term based on the heat equation. The model is discretized through a finite element scheme set on the manifold, and solved by resorting to a fixed point-based iterative algorithm. This choice leads to a procedure which is highly efficient when compared with a monolithic approach, and which allows us to deal with massive datasets. After a preliminary assessment on simulation study cases, we investigate the performance of the new estimation tool in prac- tical contexts, by dealing with neuroimaging and hemodynamic data
ADAPTIVE TOPOLOGY OPTIMIZATION FOR ADDITIVE LAYER MANUFACTURING
No full textA computer-aided FEM-based structure design system configured to: ■ acquire an initial structure design configuration comprising: - a design domain (Ω), - an applied load (f), and - constrained, unconstrained and loaded areas (ΓD, ΓF, ΓΝ); ■ compute an initial mesh (Toh) of the design domain (Ω); ■ compute a topological^ optimized structure model by iterating, until a termination criterion is fulfilled: - computing an optimized structure topology by properly implementing the SIMP (Solid Isotropic Material with Penalization) algorithm based on a density function (p) that represents the distribution of the material in the structure; - computing an anisotropic recovery-based a posteriori error estimator (η) that quantifies the error between the gradient of the exact structure material density (p) and the gradient of the FEM-computed approximation thereof, - computing a metric (Mk+1) for anisotropic mesh adaptation based on the anisotropic recovery-based a posteriori error estimator (η), and - computing an adapted anisotropic mesh (Tkh+ 1 ) based on the metric (Mk+1)
Anisotropic error control for environmental applications
No full textIn this paper we aim at controlling physically meaningful quantities with emphasis on environmental applications. This is carried out by an efficient numerical procedure combining the goal-oriented framework [R. Becker, R. Rannacher, An optimal control approach to a posteriori error estimation in finite element methods, Acta Numer. 10 (2001) 1–102] with the anisotropic setting introduced in [L. Formaggia, S. Perotto, New anisotropic a priori error estimates, Numer. Math. 89 (2001) 641–667]. A first attempt in this direction has been proposed in [L. Formaggia, S. Micheletti, S. Perotto, Anisotropic mesh adaptation in computational fluid dynamics: application to the advection–diffusion–reaction and the Stokes problems, Appl. Numer. Math. 51 (2004) 511–533]. Here we improve this analysis by carrying over to the goal-oriented framework the good property of the a posteriori error estimator to depend on the error itself, typical of the anisotropic residual based error analysis presented in [G. Maisano, S. Micheletti, S. Perotto, C.L. Bottasso, On some new recovery based a posteriori error estimators, Comput. Methods Appl. Mech. Engrg. 195 (37–40) (2006) 4794–4815; S. Micheletti, S. Perotto, An anisotropic recovery-based a posteriori error estimator, in: F. Brezzi, A. Buffa, S. Corsaro, A. Murli (Eds.), Numerical Mathematics and Advanced Applications—ENUMATH2001, Proceedings of the 4th European International Conference on Numerical Mathematics and Advanced Applications, Springer-Verlag, Italia, 2003, pp. 731–741]. On the one hand this dependence makes the estimator not immediately computable; nevertheless, after approximating this error via the Zienkiewicz–Zhu gradient recovery procedure [O.C. Zienkiewicz, J.Z. Zhu, A simple error estimator and adaptive procedure for practical engineering analysis, Internat. J. Numer. Methods Engrg. 24 (2) (1987) 337–357; O.C. Zienkiewicz, J.Z. Zhu, The superconvergent patch recovery and a posteriori error estimates. Part 1: The recovery technique, Internat. J. Numer. Methods Engrg. 33 (1992) 1331–1364], the resulting estimator is expected to exhibit a higher convergence rate than the one in [L. Formaggia, S. Micheletti, S. Perotto, Anisotropic mesh adaptation in computational fluid dynamics: application to the advection–diffusion–reaction and the Stokes problems, Appl. Numer. Math. 51 (2004) 511–533]. As the broad numerical validation attests, the proposed estimator turns out to be more efficient in terms of d.o.f.'s per accuracy or equivalently, more accurate for a fixed number of elements.MATHICS
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