相关论文: A multigrid scheme for 3D Monge-Amp\`ere equations

Adaptive multilevel finite element methods are developed and analyzed for certain elliptic systems arising in geometric analysis and general relativity. This class of nonlinear elliptic systems of tensor equations on manifolds is first…

The electromagnetic behavior of plasmonic structures can be predicted after discretizing and solving a linear system of equations, derived from a continuous surface integral equation (SIE) and the appropriate boundary conditions, using a…

This paper proposes a regularization of the Monge-Amp\`ere equation in planar convex domains through uniformly elliptic Hamilton-Jacobi-Bellman equations. The regularized problem possesses a unique strong solution $u_\varepsilon$ and is…

Multi-block separable convex problems recently received considerable attention. This class of optimization problems minimizes a separable convex objective function with linear constraints. The algorithmic challenges come from the fact that…

This paper proposes a proximal variant of the alternating direction method of multipliers (ADMM) for distributed optimization. Although the current versions of ADMM algorithm provide promising numerical results in producing solutions that…

In this paper, we present two multiple scalar auxiliary variable (MSAV)-based, finite element numerical schemes for the Abels-Garcke-Gr{\"u}n (AGG) model, which is a thermodynamically consistent phase field model of two-phase incompressible…

This article aims at developing a high order pressure-based solver for the solution of the 3D compressible Navier-Stokes system at all Mach numbers. We propose a cell-centered discretization of the governing equations that splits the fluxes…

We present a multiscale mixed finite element method for solving second order elliptic equations with general $L^{\infty}$-coefficients arising from flow in highly heterogeneous porous media. Our approach is based on a multiscale spectral…

We design and investigate efficient multigrid solvers for multiphase Stokes problems discretised via mixed-degree local discontinuous Galerkin methods. Using the template of a standard multigrid V-cycle, we develop a smoother analogous to…

Multiphase flows are an important class of fluid flow and their study facilitates the development of diverse applications in industrial, natural, and biomedical systems. We consider a model that uses a continuum description of both phases…

This paper proposes an inexact Aleksandrov-solution-based iteration method, formulated by adapting the convergent Rayleigh inverse iterative scheme introduced by Abedin and Kitagawa, to solve real Monge-Amp{\`e}re eigenvalue (MAE) problems.…

In this paper, the elliptic PDE-constrained optimization problem with box constraints on the control is studied. To numerically solve the problem, we apply the 'optimize-discretize-optimize' strategy. Specifically, the alternating direction…

Elliptic equations play a crucial role in turbulence models for magnetic confinement fusion. Regardless of the chosen modeling approach - whether gyrokinetic, gyrofluid, or drift-fluid - the Poisson equation and Amp\`{e}re's law lead to…

We study a fully nonlinear equation of complex Monge-Ampere type on Hermitian manifolds. We establish the a priori estimates for solutions of the equation up to the second order derivatives with the help of a subsolution.

A multigrid method is proposed for solving nonlinear eigenvalue problems by the finite element method. With this new scheme, solving nonlinear eigenvalue problem is decomposed to a series of solutions of linear boundary value problems on…

To numerically solve a generic elliptic equation on two-dimensional domains with rectangular Cartesian grids, we propose a cut-cell geometric multigrid method that features (1) general algorithmic steps that apply to two-dimensional…

In this paper, we propose a robust solver for the finite element discrete problem of the stationary incompressible magnetohydrodynamic (MHD) equations in three dimensions. By the mixed finite element method, both the velocity and the…

This paper presents smoothing schemes for obtaining approximate stationary points of unconstrained or linearly-constrained composite nonconvex-concave min-max (and hence nonsmooth) problems by applying well-known algorithms to composite…

A numerical method for solving the equations modeling acoustic scattering is presented. The method is capable of handling several dozen scatterers, each of which is several wave-lengths long, on a personal work station. Even for geometries…

We propose a second-order accurate semi-implicit and well-balanced finite volume scheme for the equations of ideal magnetohydrodynamics (MHD) including gravitational source terms. The scheme treats all terms associated with the acoustic…