A multiresolution adaptive wavelet method for nonlinear partial differential equations
- University of Notre Dame, IN (United States)
- Indiana University, Bloomington, IN (United States)
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
We report the multiscale complexity of modern problems in computational science and engineering can prohibit the use of traditional numerical methods in multi-dimensional simulations. Therefore, novel algorithms are required in these situations to solve partial differential equations (PDEs) with features evolving on a wide range of spatial and temporal scales. To meet these challenges, we present a multiresolution wavelet algorithm to solve PDEs with significant data compression and explicit error control. We discretize in space by projecting fields and spatial derivative operators onto wavelet basis functions. We provide error estimates for the wavelet representation of fields and their derivatives. Then, our estimates are used to construct a sparse multiresolution discretization which guarantees the prescribed accuracy. Additionally, we embed a predictor-corrector procedure within the temporal integration to dynamically adapt the computational grid and maintain the accuracy of the solution of the PDE as it evolves. We present examples to highlight the accuracy and adaptivity of our approach.
- Research Organization:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Organization:
- USDOE National Nuclear Security Administration (NNSA)
- Grant/Contract Number:
- 89233218CNA000001
- OSTI ID:
- 1875801
- Report Number(s):
- LA-UR-21-25476
- Journal Information:
- International Journal for Multiscale Computational Engineering, Journal Name: International Journal for Multiscale Computational Engineering Journal Issue: 2 Vol. 19; ISSN 1543-1649
- Publisher:
- Begell HouseCopyright Statement
- Country of Publication:
- United States
- Language:
- English
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