相关论文: Iterative Methods for Navier--Stokes Inverse Probl…

In this paper a new high order semi-implicit discontinuous Galerkin method (SI-DG) is presented for the solution of the incompressible Navier-Stokes equations on staggered space-time adaptive Cartesian grids (AMR) in two and three…

In this paper, we propose the neural Born iterative method (NeuralBIM) for solving 2D inverse scattering problems (ISPs) by drawing on the scheme of physics-informed supervised residual learning (PhiSRL) to emulate the computing process of…

This paper addresses the numerical solution of the two-dimensional Navier--Stokes (NS) equations with nonsmooth initial data in the $L^2$ space, which is the critical space for the two-dimensional NS equations to be well-posed. In this…

In many modern imaging applications the desire to reconstruct high resolution images, coupled with the abundance of data from acquisition using ultra-fast detectors, have led to new challenges in image reconstruction. A main challenge is…

We introduce a collection of benchmark problems in 2D and 3D (geometry description and boundary conditions), including simple cases with known analytic solution, classical experimental setups, and complex geometries with fabricated…

We consider the inverse problem of determining a compact Riemannian manifold with boundary from fixed time observations of the solution, restricted to a small subset in space, for the Navier-Stokes system with a local source on the…

This paper presents a low-communication-overhead parallel method for solving the 3D incompressible Navier-Stokes equations. A fully-explicit projection method with second-order space-time accuracy is adopted. Combined with fast Fourier…

An immersed-boundary method for the incompressible Navier--Stokes equations is presented. It employs discrete forcing for a sharp discrimination of the solid-fluid interface, and achieves second-order accuracy, demonstrated in examples with…

This paper is concerned with the approximation of probability distributions known up to normalization constants, with a focus on Bayesian inference for large-scale inverse problems in scientific computing. In this context, key challenges…

A novel method to solve inverse problems for the wave equation is introduced. The method is a combination of the boundary control method and an iterative time reversal scheme, leading to adaptive imaging of coefficient functions of the wave…

The construction of weak solutions to compressible Navier-Stokes equations via a numerical method (including a rigorous proof of the convergence) is in a short supply, and so far, available only for one sole numerical scheme suggested in…

In the given paper, we confront three finite difference approximations to the Navier--Stokes equations for the two-dimensional viscous incomressible fluid flows. Two of these approximations were generated by the computer algebra assisted…

Stochastic gradient methods (SGMs) are predominant approaches for solving stochastic optimization. On smooth nonconvex problems, a few acceleration techniques have been applied to improve the convergence rate of SGMs. However, little…

We present a Discontinuous Galerkin (DG) solver for the compressible Navier-Stokes system, designed for applications of technological and industrial interest in the subsonic region. More precisely, this work aims to exploit the…

This study proposes an algorithm for modeling compressible flows in spherical shells in nearly incompressible and weakly compressible regimes based on an implicit direction splitting approach. The method retains theoretically expected…

There are many subtle issues associated with solving the Navier-Stokes equations. In this paper, several of these issues, which have been observed previously in research involving the Navier-Stokes equations, are studied within the…

A novel approach is introduced for deriving exact solutions to nonlinear systems of ordinary differential equations. This method consists of four parts. In the initial part, the examined nonlinear differential equation system is transformed…

The fundamental computational issues in Bayesian inverse problems (BIP) governed by partial differential equations (PDEs) stem from the requirement of repeated forward model evaluations. A popular strategy to reduce such costs is to replace…

The paper aims at developing low-storage implicit Runge-Kutta methods which are easy to implement and achieve higher-order of convergence for both the velocity and pressure in the finite volume formulation of the incompressible…

Considering channel flow at Reynolds numbers below the linear stability threshold of the laminar profile as a generic example system showing a subcritical transition to turbulence connected with the existence of simple invariant solutions,…