Publication: Towards a unified multiresolution scheme for treating discontinuities in differential equations with uncertainties
Towards a unified multiresolution scheme for treating discontinuities in differential equations with uncertainties
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Abgrall, R., Congedo, P. M., & Geraci, G. (2017). Towards a unified multiresolution scheme for treating discontinuities in differential equations with uncertainties. Mathematics and Computers in Simulation, 139, 1–22. https://doi.org/10.1016/j.matcom.2016.02.002
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In the present work, a method for solving partial differential equations with uncertainties is presented. A multiresolution method, permitting to compute statistics for the entire solution and in presence of a whatever form of the probability density function, is extended to perform an adaptation in both physical and stochastic spaces. The efficiency of this strategy, in terms of refinement/coarsening capabilities, is demonstrated on several test-cases by comparing with respect to other more classical techniques, namely Monte Carlo (M
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- Congedo, P. M
- Geraci, G
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Abgrall, R., Congedo, P. M., & Geraci, G. (2017). Towards a unified multiresolution scheme for treating discontinuities in differential equations with uncertainties. Mathematics and Computers in Simulation, 139, 1–22. https://doi.org/10.1016/j.matcom.2016.02.002
