Parallel Multilevel Monte Carlo Algorithms for Elliptic PDEs with Random Coefficients
| Autor: | Oleg Iliev, Nikolay Shegunov, Jan Mohring, Petr E. Zakharov |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Partial differential equation
Finite volume method Computational complexity theory Computation Monte Carlo method 010103 numerical & computational mathematics 02 engineering and technology 01 natural sciences 0202 electrical engineering electronic engineering information engineering Embedding 020201 artificial intelligence & image processing 0101 mathematics Uncertainty quantification Circulant matrix Algorithm Mathematics |
| Zdroj: | Large-Scale Scientific Computing ISBN: 9783030410315 LSSC |
| DOI: | 10.1007/978-3-030-41032-2_53 |
| Popis: | In this work, we developed and investigated Monte Carlo algorithms for elliptic PDEs with random coefficients. We considered groundwater flow as a model problem, where a permeability field represents random coefficients. The computational complexity is the main challenge in uncertainty quantification methods. The computation contains generating of a random coefficient and solving of partial differential equations. The permeability field was generated using the circulant embedding method. Multilevel Monte Carlo (MLMC) simulation can be based on different approximations of partial differential equations. We developed three MLMC algorithms based on finite volume, finite volume with renormalization and renormalization approximation. We compared numerical simulations and parallel performance of MLMC algorithms for 2D and 3D problems. |
| Databáze: | OpenAIRE |
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