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A multifidelity method for a nonlocal diffusion model

Journal Article · · Applied Mathematics Letters
 [1];  [2];  [3]
  1. Univ. of Texas, Austin, TX (United States); University of Texas at Austin
  2. Univ. of Texas, Austin, TX (United States)
  3. Florida State Univ., Tallahassee, FL (United States)

Nonlocal models feature a finite length scale, referred to as the horizon, such that points separated by a distance smaller than the horizon interact with each other. Such models have proven to be useful in a variety of settings. However, due to the reduced sparsity of discretizations, they are also generally computationally more expensive compared to their local differential equation counterparts. In this work, we introduce a multifidelity Monte Carlo method that combines the high-fidelity nonlocal model of interest with surrogate models that use coarser grids and/or smaller horizons and thus have lower fidelities and lower costs. Using the multifidelity method, the overall computational cost of uncertainty quantification is reduced without compromising accuracy. It is shown for a one-dimensional nonlocal diffusion example that speedups of up to two orders of magnitude can be achieved using the multifidelity method to estimate the expectation of an output of interest.

Research Organization:
Univ. of Texas, Austin, TX (United States)
Sponsoring Organization:
USDOE
Grant/Contract Number:
SC0019303; SC0021077
OSTI ID:
1782844
Alternate ID(s):
OSTI ID: 1782945
Journal Information:
Applied Mathematics Letters, Journal Name: Applied Mathematics Letters Vol. 121; ISSN 0893-9659
Publisher:
ElsevierCopyright Statement
Country of Publication:
United States
Language:
English

References (5)

A Nonlocal Vector Calculus with Application to Nonlocal Boundary Value Problems journal January 2010
Analysis and Approximation of Nonlocal Diffusion Problems with Volume Constraints journal January 2012
Optimal Model Management for Multifidelity Monte Carlo Estimation journal January 2016
Survey of Multifidelity Methods in Uncertainty Propagation, Inference, and Optimization journal January 2018
A Nonlocal Vector Calculus, Nonlocal Volume-Constrained Problems, and Nonlocal Balance laws journal January 2013

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