Related papers: Multiresolution Schemes and its Application to Sed…
The main objective of this dissertation is to present an adaptation of some finite volume methods used in the resolution of problems arising in sedimentation processes of flocculated suspensions (or sedimentation with compression). This…
A number of different multiscale methods have been developed as a robust alternative to upscaling and as a means for accelerated reservoir simulation of high-resolution geomodels. In their basic setup, multiscale methods use a restriction…
We present a fully adaptive multiresolution scheme for spatially two-dimensional, possibly degenerate reaction-diffusion systems, focusing on combustion models and models of pattern formation and chemotaxis in mathematical biology.…
This paper presents a new resolution strategy for multi-scale streamer discharge simulations based on a second order time adaptive integration and space adaptive multiresolution. A classical fluid model is used to describe plasma…
Mineral precipitation and dissolution processes in a porous medium can alter the structure of the medium at the scale of pores. Such changes make numerical simulations a challenging task as the geometry of the pores changes in time in an…
A three-dimensional model of polydisperse reactive sedimentation is developed by means of a multilayer shallow water approach. The model consists of a variety of solid particles of different sizes and densities, and substrates diluted in…
In this work, we contribute to the broader understanding of inverse problems by introducing a versatile multiscale modeling framework tailored to the challenges of sediment concentration estimation. Specifically, we propose a novel approach…
Recently, we introduced Relative Resolution as a hybrid formalism for fluid mixtures [1]. The essence of this approach is that it switches molecular resolution in terms or relative separation: While nearest neighbors are characterized by a…
In this paper a numerical procedure to simulate low diffusivity scalar turbulence is presented. The method consists of using a grid for the advected scalar with a higher spatial resolutions than that of the momentum. The latter usually…
This paper studies the problem of extracting planar regions in uneven terrains from unordered point cloud measurements. Such a problem is critical in various robotic applications such as robotic perceptive locomotion. While existing…
Reference-based Super-resolution (RefSR) approaches have recently been proposed to overcome the ill-posed problem of image super-resolution by providing additional information from a high-resolution image. Multi-reference super-resolution…
Numerical simulations for flow and transport in subsurface porous media often prove computationally prohibitive due to property data availability at multiple spatial scales that can vary by orders of magnitude. A number of model order…
We study multilevel techniques, commonly used in PDE multigrid literature, to solve structured optimization problems. For a given hierarchy of levels, we formulate a coarse model that approximates the problem at each level and provides a…
A fully adaptive finite volume multiresolution scheme for one-dimensional strongly degenerate parabolic equations with discontinuous flux is presented. The numerical scheme is based on a finite volume discretization using the…
Multiscale models allow for the treatment of complex phenomena involving different scales, such as remodeling and growth of tissues, muscular activation, and cardiac electrophysiology. Numerous numerical approaches have been developed to…
In this paper we give a survey on various multiscale methods for the numerical solution of second order hyperbolic equations in highly heterogeneous media. We concentrate on the wave equation and distinguish between two classes of…
In the discretization of differential problems on complex geometrical domains, discretization methods based on polygonal and polyhedral elements are powerful tools. Adaptive mesh refinement for such kind of problems is very useful as well…
We present a numerical method to deal efficiently with large numbers of particles in incompressible fluids. The interactions between particles and fluid are taken into account by a physically motivated ansatz based on locally defined drag…
We propose a new algorithm to the problem of polygonal curve approximation based on a multiresolution approach. This algorithm is suboptimal but still maintains some optimality between successive levels of resolution using dynamic…
A method is developed within an adaptive framework to solve quasilinear diffusion problems with internal and possibly boundary layers starting from a coarse mesh. The solution process is assumed to start on a mesh where the problem is badly…