Embedded multilevel monte carlo for uncertainty quantification in random domains
| العنوان: | Embedded multilevel monte carlo for uncertainty quantification in random domains |
|---|---|
| المؤلفون: | Jerrad Hampton, Santiago Badia, Javier Principe |
| المساهمون: | Universitat Politècnica de Catalunya. Departament de Mecànica de Fluids, Universitat Politècnica de Catalunya. ANiComp - Anàlisi numèrica i computació científica |
| المصدر: | International Journal for Uncertainty Quantification Scipedia Open Access Scipedia SL UPCommons. Portal del coneixement obert de la UPC Universitat Politècnica de Catalunya (UPC) |
| بيانات النشر: | Begell House, 2021. |
| سنة النشر: | 2021 |
| مصطلحات موضوعية: | Statistics and Probability, Control and Optimization, Computer science, Monte Carlo method, Matemàtiques i estadística::Matemàtica aplicada a les ciències [Àrees temàtiques de la UPC], 010103 numerical & computational mathematics, 01 natural sciences, Domain (software engineering), Random geometry, Multigrid method, Multilevel Monte Carlo, FOS: Mathematics, Discrete Mathematics and Combinatorics, Polygon mesh, Mathematics - Numerical Analysis, Engineering, Geological, 0101 mathematics, Uncertainty quantification, Topological uncertainty, Anàlisi numèrica, Stochastic partial differential equations, Function (mathematics), Numerical Analysis (math.NA), Finite element method, 010101 applied mathematics, Embedded methods, Geometric uncertainty, Modeling and Simulation, Poisson's equation, Algorithm, Numerical analysis |
| الوصف: | The multilevel Monte Carlo (MLMC) method has proven to be an effective variance-reduction statistical method for Uncertainty quantification in PDE models. It combines approximations at different levels of accuracy using a hierarchy of meshes in a similar way as multigrid. The generation of body-fitted mesh hierarchies is only possible for simple geometries. On top of that, MLMC for random domains involves the generation of a mesh for every sample. Instead, here we consider the use of embedded methods which make use of simple background meshes of an artificial domain (a bounding-box) for which it is easy to define a mesh hierarchy, thus eliminating the need of body-fitted unstructured meshes, but can produce ill-conditioned discrete problems. To avoid this complication, we consider the recent aggregated finite element method (AgFEM). In particular, we design an embedded MLMC framework for (geometrically and topologically) random domains implicitly defined through a random level-set function, which makes use of a set of hierarchical background meshes and the AgFEM. Performance predictions from existing theory are verified statistically in three numerical experiments, namely the solution of the Poisson equation on a circular domain of random radius, the solution of the Poisson equation on a topologically identical but more complex domain, and the solution of a heat-transfer problem in a domain that has geometric and topological uncertainties. Finally, the use of AgFE is statistically demonstrated to be crucial for complex and uncertain geometries in terms of robustness and computational cost. Date: November 28, 2019. |
| وصف الملف: | application/pdf |
| اللغة: | English |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7aaf6b4bdbfad7406dbfc195a11e3de7 https://hdl.handle.net/2117/354885 |
| Rights: | OPEN |
| رقم الانضمام: | edsair.doi.dedup.....7aaf6b4bdbfad7406dbfc195a11e3de7 |
| قاعدة البيانات: | OpenAIRE |
| الوصف غير متاح. |