Related papers: General-domain FC-based shock-dynamics solver I: B…

This contribution Part II of a two-part series, extends the general-domain FC-SDNN (Fourier Continuation Shock-Detecting Neural Network) introduces in Part I to enable treatment of non-smooth domains, it introduces a parallel implementation…

This paper presents a spectral scheme for the numerical solution of nonlinear conservation laws in non-periodic domains under arbitrary boundary conditions. The approach relies on the use of the Fourier Continuation (FC) method for spectral…

This work aims to predict blood flow with non-Newtonian viscosity in stenosed arteries using convolutional neural network (CNN) surrogate models. An alternating Schwarz domain decomposition method is proposed which uses CNN-based subdomain…

In this paper we develop a non-diffusive neural network (NDNN) algorithm for accurately solving weak solutions to hyperbolic conservation laws. The principle is to construct these weak solutions by computing smooth local solutions in…

The goal of this work is to develop a new universal high order subroutine for shock boundary layer interaction. First, an effective shock/discontinuity detector has been developed.The detector has two steps.The first step is to check the…

We build a multi-element variant of the smoothness increasing accuracy conserving (SIAC) shock capturing technique proposed for single element spectral methods by Wissink et al. (B.W. Wissink, G.B. Jacobs, J.K. Ryan, W.S. Don, and E.T.A.…

Pseudospectral schemes are a class of numerical methods capable of solving smooth problems with high accuracy thanks to their exponential convergence to the true solution. When applied to discontinuous problems, such as fluid shocks and…

A new penalty-free neural network method, PFNN-2, is presented for solving partial differential equations, which is a subsequent improvement of our previously proposed PFNN method [1]. PFNN-2 inherits all advantages of PFNN in handling the…

We present a novel, cell-local shock detector for use with discontinuous Galerkin (DG) methods. The output of this detector is a reliably scaled, element-wise smoothness estimate which is suited as a control input to a shock capture…

Accurately characterizing non-linear functional manifolds with singularities is a fundamental challenge in scientific computing. While Multi-Layer Perceptrons (MLPs) dominate, their spectral bias hinders resolving high-curvature features…

We consider solving complex spatiotemporal dynamical systems governed by partial differential equations (PDEs) using frequency domain-based discrete learning approaches, such as Fourier neural operators. Despite their widespread use for…

Recent work has introduced a simple numerical method for solving partial differential equations (PDEs) with deep neural networks (DNNs). This paper reviews and extends the method while applying it to analyze one of the most fundamental…

We present a novel image-based adaptive domain decomposition FEM framework to accelerate the solution of continuum damage mechanics problems. The key idea is to use image-processing techniques in order to identify the moving interface…

The stable and accurate approximation of discontinuities such as shocks on a finite computational mesh is a challenging task. Detection of shocks or strong discontinuities in the flow solution is typically achieved through a priori troubled…

This is the second part to our companion paper [18]. Herein, we generalize to two space dimensions the C-method developed in [20,18] for adding localized, space-time smooth artificial viscosity to nonlinear systems of conservation laws that…

In this paper, a 3D patch-based fully dense and fully convolutional network (FD-FCN) is proposed for fast and accurate segmentation of subcortical structures in T1-weighted magnetic resonance images. Developed from the seminal FCN with an…

This paper presents a "two-dimensional Fourier Continuation" method (2D-FC) for construction of bi-periodic extensions of smooth non-periodic functions defined over general two-dimensional smooth domains. The approach can be directly…

The encoder-decoder model is a commonly used Deep Neural Network (DNN) model for medical image segmentation. Conventional encoder-decoder models make pixel-wise predictions focusing heavily on local patterns around the pixel. This makes it…

In the case of hyperbolic conservation laws, high-order methods, such as the classical DG method, experience the phenomenon of unwanted high-frequency oscillations in the vicinity of a shock. Shock-capturing methods such as artificial…

In this paper, we present an improved framework of the spectral-based Discrete Dislocation Dynamics (DDD) approach introduced in [1,2], that establishes a direct connection with the continuum Field Dislocation Mechanics (FDM) approach. To…