Sparse grids have become a versatile tool for a vast range of applications reaching from interpolation and numerical quadrature to data-driven problems and uncertainty quantification.We review four selected real-world...Sparse grids have become a versatile tool for a vast range of applications reaching from interpolation and numerical quadrature to data-driven problems and uncertainty quantification.We review four selected real-world applications of sparse grids:financial product pricing with the Black-Scholes model,interactive explo-ration of simulation data with sparse-grid-based surrogate models,analysis of simu-lation data through sparse grid data mining methods,and stability investigations of plasma turbulence simulations.展开更多
We couple different flow models,i.e.a finite element solver for the Navier-Stokes equations and a Lattice Boltzmann automaton,using the framework Peano as a common base.The new coupling strategy between the meso-and m...We couple different flow models,i.e.a finite element solver for the Navier-Stokes equations and a Lattice Boltzmann automaton,using the framework Peano as a common base.The new coupling strategy between the meso-and macroscopic solver is presented and validated in a 2D channel flow scenario.The results are in good agreement with theory and results obtained in similar works by Latt et al.In addition,the test scenarios show an improved stability of the coupledmethod compared to pure Lattice Boltzmann simulations.展开更多
文摘Sparse grids have become a versatile tool for a vast range of applications reaching from interpolation and numerical quadrature to data-driven problems and uncertainty quantification.We review four selected real-world applications of sparse grids:financial product pricing with the Black-Scholes model,interactive explo-ration of simulation data with sparse-grid-based surrogate models,analysis of simu-lation data through sparse grid data mining methods,and stability investigations of plasma turbulence simulations.
文摘We couple different flow models,i.e.a finite element solver for the Navier-Stokes equations and a Lattice Boltzmann automaton,using the framework Peano as a common base.The new coupling strategy between the meso-and macroscopic solver is presented and validated in a 2D channel flow scenario.The results are in good agreement with theory and results obtained in similar works by Latt et al.In addition,the test scenarios show an improved stability of the coupledmethod compared to pure Lattice Boltzmann simulations.
