Related papers: A Neural Network based Shock Detection and Localiz…
We propose a high order discontinuous Galerkin (DG) method for solving nonlinear Fokker-Planck equations with a gradient flow structure. For some of these models it is known that the transient solutions converge to steady-states when time…
In this paper we enhance the well-known fifth order WENO shock-capturing scheme by using deep learning techniques. This fine-tuning of an existing algorithm is implemented by training a rather small neural network to modify the smoothness…
We present the two-dimensional unstructured grids extension of the a posteriori local subcell correction of discontinuous Galerkin (DG) schemes introduced in [52]. The technique is based on the reformulation of DG scheme as a finite volume…
Local discontinuous Galerkin methods are developed for solving second order and fourth order time-dependent partial differential equations defined on static 2D manifolds. These schemes are second-order accurate with surfaces triangulized by…
Polychronous neural groups are effective structures for the recognition of precise spike-timing patterns but the detection method is an inefficient multi-stage brute force process that works off-line on pre-recorded simulation data. This…
Accurate detection and localization of X-corner on both planar and non-planar patterns is a core step in robotics and machine vision. However, previous works could not make a good balance between accuracy and robustness, which are both…
We develop a stable and high-order accurate discontinuous Galerkin method for the second order wave equation, specifically designed to handle nonsmooth solutions. Our approach integrates the energy-based discontinuous Galerkin method with…
In this paper, we propose a method for constructing a neural network viscosity in order to reduce the non-physical oscillations generated by high-order Discontiuous Galerkin (DG) methods. To this end, the problem is reformulated as an…
Recently, the targeted ENO (TENO) schemes give a novel framework to keep optimal high-order spatial reconstruction wherever discontinuity is deemed to be vanished, including at smooth critical points, and to avoid oscillations by completely…
In this work we construct reliable a posteriori estimates for some discontinuous Galerkin schemes applied to nonlinear systems of hyperbolic conservation laws. We make use of appropriate reconstructions of the discrete solution together…
In this paper, we present and analyze an interior penalty discontinuous Galerkin method for the distributed elliptic optimal control problems. It is based on a reconstructed discontinuous approximation which admits arbitrarily high-order…
We present a stability analysis of the Discontinuous Galerkin method on polygonal and polyhedral meshes (PolyDG) for the Stokes problem. In particular, we analyze the discrete inf-sup condition for different choices of the polynomial…
Real-time simulation of elastic structures is essential in many applications, from computer-guided surgical interventions to interactive design in mechanical engineering. The Finite Element Method is often used as the numerical method of…
An interior penalty discontinuous Galerkin method is devised to approximate minimizers of a linear folding model by discontinuous isoparametric finite element functions that account for an approximation of a folding arc. The numerical…
This paper studies high-order accurate entropy stable nodal discontinuous Galerkin (DG) schemes for the ideal special relativistic magnetohydrodynamics (RMHD). It is built on the modified RMHD equations with a particular source term, which…
We present a novel class of locally conservative, entropy stable and well-balanced discontinuous Galerkin (DG) methods for the nonlinear shallow water equation with a non-flat bottom topography. The major novelty of our work is the use of…
Large scale networks delineating collective dynamics often exhibit cascading failures across nodes leading to a system-wide collapse. Prominent examples of such phenomena would include collapse on financial and economic networks.…
The goal of this paper is to create a fruitful bridge between the numerical methods for approximating partial differential equations (PDEs) in fluid dynamics and the (iterative) numerical methods for dealing with the resulting large linear…
Digital image watermarking is the process of embedding and extracting a watermark covertly on a cover-image. To dynamically adapt image watermarking algorithms, deep learning-based image watermarking schemes have attracted increased…
We propose a new discretization method for the Stokes equations. The method is an improved version of the method recently presented in [C. Lehrenfeld, J. Sch\"oberl, Comp. Meth. Appl. Mech. Eng., 361 (2016)] which is based on an…