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Uncertainty Quantification for nonlinear hyperbolic problems becomes a challenging task in the vicinity of shocks. Standard intrusive methods, such as Stochastic Galerkin (SG), lead to oscillatory solutions and can result in non-hyperbolic moment systems. The intrusive polynomial moment (IPM) method guarantees hyperbolicity but comes at higher numerical costs. In this paper, we filter the generalized...
Methods to numerically quantify uncertainties in hyperbolic equations can be divided into intrusive and non-intrusive techniques. Standard intrusive methods such as Stochastic Galerkin yield oscillatory solutions in the vicinity of shocks and require a new implementation. The more advanced Intrusive Polynomial Moment (IPM) method necessitates a costly solution reconstruction, but promises bounds on...
Uncertainty quantification for hyperbolic equations is a challenging task, since solutions exhibit discontinuities and sharp gradients. The commonly used stochastic-Galerkin (SG) Method uses polynomials to represent the solution, leading to oscillatory approximations due to Gibbs phenomenon. Additionally, the SG moment systems can loose hyperbolicity. The intrusive polynomial moment method (IPMM)...
Spherical gold nanoparticles with a plasmonic extinction peak at 532 nm and two sizes of star shaped gold nanoparticles with plasmonic extinction peaks at 532 nm and 600 nm were synthesised and introduced into tissue phantoms as exogenous absorbers. The photoacoustic signals generated from the three different nanoparticle morphologies embedded in tissue the phantoms is compared. The effect of nanoparticle...
In this paper, we present a smoothing technique which can be understood as a Quasi‐Newton method. The idea of this preconditioner is that it approximates the symbol of the inverse Hessian, which has smoothing behavior. This symbol is derived analytically for the Stokes equations and investigated numerically for a flow with a Reynolds number of 80. The resulting symbol is then approximated by differential...
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