Analysis | EPFL Graph Search

Analysis (: analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (384–322 B.C.), though analysis as a formal concept is a relatively recent development. The word comes from the Ancient Greek ἀνάλυσις (analysis, "a breaking-up" or "an untying;" from ana- "up, throughout" and lysis "a loosening"). From it also comes the word's plural, analyses. As a formal concept, the method has variously been ascribed to Alhazen, René Descartes (Discourse on the Method), and Galileo Galilei. It has also been ascribed to Isaac Newton, in the form of a practical method of physical discovery (which he did not name). The converse of analysis is synthesis: putting the pieces back together again in a new or different whole. Applications Science Analytical chemistry and List of chemical analysis methods The field o

'Peak Oil' As Classical Economic Process

François Meynard

Forecasts about 'peak oil', the limits of oil production, are the subject of controversies. 'Peak oil' forecasts are based on extrapolations of a priori chosen mathematical models fitted to field data. Scientifically that is not very sound. To clarify this point, in this paper 'peak oil' is modelled in a generic reductionist, approach, in which the conflicting dynamic between economic forces and physical laws are well identified. This model finds a natural interpretation just supress in a classical economic analysis frame. The 'peak oil' controversy is thus brought into the field of economic thought as a debate between classical and mainstream economics, in particular between an objective and a faith based appraisal about this historical event. The goal is not to improve forecasts about 'peak oil', which is very likely not a predictable event, but to propose an objective framework for the analysis of its systemic effects on economic production.

Multi-Science Publ Co Ltd2014

Interactive, Real Time Structural Simulation

Julien Lebet

The aim of this thesis is to develop a model that provides a fast analysis of structures subjected to large displacements. This is done by transforming the structure in a set of nite particles and by applying a method called dynamic relaxation to it. The latter simulates a dynamic behaviour of the structure by applying Newton's second law to the set of particles until the equilibrium is reached. This can be accomplished using only explicit methods and it does not require to build a global stiness matrix nor to inverse it. The position and rotations of the elements are followed during the process and their forces are always computed locally by using their linear stiness matrix. This methodology is applied to multiple type of elements and the accuracy and speed of the model is nally tested through various examples.

2020

Adaptive analysis-aware defeaturing

Ondine Gabrielle Chanon

Removing geometrical details from a complex domain is a classical operation in computer aided design for simulation and manufacturing. This procedure simplifies the meshing process, and it enables faster simulations with less memory requirements. However, depending on the partial differential equation that one wants to solve in the geometrical model of interest, removing some important geometrical features may greatly impact the solution accuracy. For instance, in solid mechanics simulations, such features can be holes or fillets near stress concentration regions. Unfortunately, the effect of geometrical simplification on the accuracy of the problem solution is often neglected, because its analysis is a time-consuming task that is often performed manually, based on the expertise of engineers. It is therefore important to have a better understanding of the effect of geometrical model simplification, also called defeaturing, to improve our control on the simulation accuracy along the design and analysis phase.In this thesis, we formalize the process of defeaturing, and we analyze its impact on the accuracy of solutions of some partial differential problems. To achieve this goal, we first precisely define the error between the problem solution defined in the exact geometry, and the one defined in the simplified geometry. Then, we introduce an a posteriori estimator of the energy norm of this error. This allows us to reliably and efficiently control the error coming from the addition or the removal of geometrical features. We subsequently consider a finite element approximation of the defeatured problem, and the induced numerical error is integrated to the proposed defeaturing error estimator. In particular, we address the special case of isogeometric analysis based on (truncated) hierarchical B-splines, in possibly trimmed and multipatch geometries. In this framework, we derive a reliable a posteriori estimator of the overall error, i.e., of the error between the exact solution defined in the exact geometry, and the numerical solution defined in the defeatured geometry.We then propose a two-fold adaptive strategy for analysis-aware defeaturing, which starts by considering a coarse mesh on a fully-defeatured computational domain. On the one hand, the algorithm performs classical finite element mesh refinements in a (partially) defeatured geometry. On the other hand, the strategy also allows for geometrical refinement. That is, at each iteration, the algorithm is able to choose which missing geometrical features should be added to the simplified geometrical model, in order to obtain a more accurate solution.Throughout the thesis, we validate the presented theory, the properties of the aforementioned estimators and the proposed adaptive strategies, thanks to an extensive set of numerical experiments.

EPFL2022

Adaptive analysis-aware defeaturing

Ondine Gabrielle Chanon

EPFL2022