Lagrangian methods and density estimation for advection-diffusion problems

In recent years, Lagrangian Coherent Structures (LCS) have been characterized using the Finite-Time Lyapunov Exponent, following the advection of a dense set of particles into

Finally, we prefer the visual smoothness of a particle level set method coupled to a traditional backward tracing semi-Lagrangian advection where possible, only using our forward

In our work, we use a volume rendering approach based on a Kernel Density Estimation (KDE) of the point cloud to give insight into the interior of the point cloud as well as pro-

While previous methods have improved the kernels by controlling the kernel bandwidths or shapes [KD13,SSFO08, KWX ∗ 16], tradi- tional kernel functions still require a large

We look at exact and approximate path integration operators to compute the probability density function of the solution process of a given stochastic differential equation..

In this thesis, we will apply a topology optimization method to unsteady fluid flow, using a density model and level set method, in order to optimize the shape of a coronary

We present three separate numerical methods for solving the HJB equation, namely a standard upwind finite difference method, and two new methods characterized as: (i) a

This is performed from a Lagrangian viewpoint attending to the oceanic flow properties and the physical characteristics (size and density) of typical biogenic sinking particles..