arXiv subjects

Cyrill von Planta

Publications and source records attributed to Cyrill von Planta.

4 recordsLinked to original sources

arXiv2021

Training of deep residual networks with stochastic MG/OPT

We train deep residual networks with a stochastic variant of the nonlinear multigrid method MG/OPT. To build the multilevel hierarchy, we use the dynamical systems viewpoint specific to residual networks. We report significant speed-ups and additional robustness for training MNIST on deep residual networks. Our numerical experiments also indicate that multilevel training can be used as a pruning technique, as many of the auxiliary networks have accuracies comparable to the original network.

cs.LG↗

arXiv2020

Modelling of hydro-mechanical processes in heterogeneous fracture intersections using a fictitious domain method with variational transfer operators

Fluid flow in rough fractures and the coupling with the mechanical behaviour of the fractures pose great difficulties for numerical modeling approaches, due to complex fracture surface topographies, the non-linearity of hydromechanical processes and their tightly coupled nature. To this end, we have adapted a fictitious domain method to enable the simulation of hydromechanical processes in fracture-intersections. The main characteristic of the method is the immersion of the fracture, modelled as a linear elastic solid, in the surrounding computational fluid domain, modelled with the incompressible Navier Stokes equations. The fluid and the solid problems are coupled with variational transfer operators. Variational transfer operators are also used to solve contact within the fracture using a dual mortar approach and to generate problem specific fluid meshes. With respect to our applications, the key features of the method are the usage of different finite element discretizations for the solid and the fluid problem and the automatically generated representation of the fluid-solid boundary. We demonstrate that the presented methodology resolves small-scale roughness on the fracture surface, while capturing fluid flow field changes during mechanical loading. Starting with 2D/3D benchmark simulations of intersected fractures, we end with an intersected fracture composed of complex fracture surface topographies, which are in contact under increasing loads. The contributions of this article are: (1) the application of the fictitious domain method to study flow in fractures with intersections, (2) a mortar based contact solver for the solid problem, (3) generation of problem specific grids using the geometry information from the variational transfer operators.

physics.comp-ph↗

arXiv2019

Contact between rough rock surfaces using a dual mortar method

The mechanical behavior of fractures in solids, such as rocks, has strong implications for reservoir engineering applications. Deformations, and the corresponding change in solid contact area and aperture field, impact rock fracture stiffness and permeability thus altering the reservoir properties significantly. Simulating contact between fractures is numerically difficult as the non-penetration constraints lead to a nonlinear problem and the surface meshes of the solid bodies on the opposing fracture sides may be non-matching. Furthermore, the challenging geometry of the arising constraints requires to solve the problem in several iterations, adjusting the constraints in each one. Here we present a novel discrete implementation of a dual mortar method and a non-smooth SQP solver, suitable for parallel computing, and apply it to a two body contact problem consisting of realistic rock fracture geometries from the Grimsel underground laboratory in Switzerland. The contributions of this article are: 1) a novel, parallel implementation of a dual mortar method and non-smooth SQP method, 2) realistic rock geometries with rough surfaces, and 3) numerical examples, which prove that the dual mortar method is capable of replicating the nonlinear closure behavior of fractures, observed in laboratory experiments.

physics.geo-ph↗

arXiv2019

Simulation of hydro-mechanically coupled processes in rough rock fractures using an immersed boundary method and variational transfer operators

Hydro-mechanical processes in rough fractures are highly non-linear and govern productivity and associated risks in a wide range of reservoir engineering problems. To enable high-resolution simulations of hydro-mechanical processes in fractures, we present an adaptation of an immersed boundary method to compute fluid flow between rough fracture surfaces. The solid domain is immersed into the fluid domain and both domains are coupled by means of variational volumetric transfer operators. The transfer operators implicitly resolve the boundary between the solid and the fluid, which simplifies the setup of fracture simulations with complex surfaces. It is possible to choose different formulations and discretization schemes for each subproblem and it is not necessary to remesh the fluid grid. We use benchmark problems and real fracture geometries to demonstrate the following capabilities of the presented approach: (1) Resolving the boundary of the rough fracture surface in the fluid; (2) Capturing fluid flow field changes in a fracture which closes under increasing normal load; and (3) Simulate the opening of a fracture due to increased fluid pressure.

physics.geo-ph↗