Sparse Tensor Methods for Uncertainty Quantification in Hyperbolic Problems

Description

Key objectives of this project are the mathematical formulation of nonlinear hyperbolic conservation laws with random input data, development, analysis and implementation of deterministic discretizations for their efficient numerical solution on parallel computing platforms and the study of scalability and robustness of these implementations with particular attention towards resilience and linear scaling.
To this end, the hyperbolic PDEs will be reformulated mathematically as deterministic PDEs on high dimensional parameter spaces. The mathematical regularity theory of these equations will be addressed, and numerical schemes with provably higher efficiency than Monte Carlo Methods will be developed.
The numerical solution of these deterministic, parametric PDEs is by a solver that is based on a reformulation of existing hyperbolic conservation law solver.
Applications to Multiscale Subsurface Flow models with uncertain coefficients will be considered. Due to the expected massive computational work arising in the solution of the deterministic parametric PDEs, key innovative components will consist in refactoring and porting the code to large scale computing platforms at CSCS, Manno, and in the development of a statistical hardware reliability model for complexity analysis of algorithms.

Funding

ETH research grant "Sparse, Adaptive Tensor Discretizations
on emerging parallel computing architctures"

References

S. Mishra and Ch. Schwab, Sparse tensor multi-level Monte Carlo finite volume methods for hyperbolic conservation laws with random intitial data
SAM Report 2010/24

Contacts

Prof. Peter Arbenz, Prof. Patrick Jenny, Prof. Siddhartha Mishra, Prof. Christoph Schwab
Florian Mueller, Stefan Pauli, Jonas Sukys, Svetlana Tokareva