A multifidelity method for a nonlocal diffusion model
- Univ. of Texas, Austin, TX (United States); University of Texas at Austin
- Univ. of Texas, Austin, TX (United States)
- 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
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