Title: Scalable hierarchical PDE sampler for generating spatially correlated random fields using nonmatching meshes: Scalable hierarchical PDE sampler using nonmatching meshes

Abstract

Summary This work describes a domain embedding technique between two nonmatching meshes used for generating realizations of spatially correlated random fields with applications to large‐scale sampling‐based uncertainty quantification. The goal is to apply the multilevel Monte Carlo (MLMC) method for the quantification of output uncertainties of PDEs with random input coefficients on general and unstructured computational domains. We propose a highly scalable, hierarchical sampling method to generate realizations of a Gaussian random field on a given unstructured mesh by solving a reaction–diffusion PDE with a stochastic right‐hand side. The stochastic PDE is discretized using the mixed finite element method on an embedded domain with a structured mesh, and then, the solution is projected onto the unstructured mesh. This work describes implementation details on how to efficiently transfer data from the structured and unstructured meshes at coarse levels, assuming that this can be done efficiently on the finest level. We investigate the efficiency and parallel scalability of the technique for the scalable generation of Gaussian random fields in three dimensions. An application of the MLMC method is presented for quantifying uncertainties of subsurface flow problems. We demonstrate the scalability of the sampling method with nonmatching mesh embedding, coupled with a parallelmore » forward model problem solver, for large‐scale 3D MLMC simulations with up to 1.9·10 ⁹ unknowns.« less

Authors:

Osborn, Sarah  ^[1];

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Zulian, Patrick ^[2]; Benson, Thomas ^[1]; Villa, Umberto  ^[3];

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Krause, Rolf ^[2]; Vassilevski, Panayot S. ^[4]

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+ Show Author Affiliations

1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientificc Computing
2. Univ. della Svizzera Italiana, Lugano (Switzerland). Inst. of Computational Science
3. Univ. of Texas, Austin, TX (United States). Inst. for Computational Engineering and Sciences
4. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientificc Computing; Portland State Univ., Portland, OR (United States). Fariborz Maseeh Dept. of Mathematics and Statistics

Publication Date:

2018-01-30

Research Org.:

Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Org.:

USDOE; Swiss Commission for Technology and Innovation; Swiss National Science Foundation (SNSF); US Army Research Office (ARO)

OSTI Identifier:

1438783

Alternate Identifier(s):

OSTI ID: 1432429

Report Number(s):

LLNL-JRNL-731006
Journal ID: ISSN 1070-5325

Grant/Contract Number:  

AC52-07NA27344; DMS-1619640; W911NF-15-1-0590

Resource Type:

Accepted Manuscript

Journal Name:

Numerical Linear Algebra with Applications

Additional Journal Information:

Journal Volume: 25; Journal Issue: 3; Journal ID: ISSN 1070-5325

Publisher:

Wiley

Country of Publication:

United States

Language:

English

Subject:

97 MATHEMATICS AND COMPUTING; multilevel methods; PDEs with random input data; PDE sampler; non-matching meshes; H(div) problems; mixed nite elements; uncertainty quanti cation; multilevel Monte Carlo