相关论文: The Alignment Properties of Monge-Ampere based Mes…
To remedy the drawbacks of full-mass or fixed-mass constraints in classical optimal transport, we propose adaptive optimal transport which is distinctive from the classical optimal transport in its ability of adaptive-mass preserving. It…
The elliptic Monge-Ampere equation is a fully nonlinear Partial Differential Equation which originated in geometric surface theory, and has been applied in dynamic meteorology, elasticity, geometric optics, image processing and image…
We consider the numerical construction of minimal Lagrangian graphs, which is related to recent applications in materials science, molecular engineering, and theoretical physics. It is known that this problem can be formulated as an…
Mesh adaption procedures for finite element approximation allows one to adapt the resolution, by local refinement in the regions of strong variation of the function of interest. This procedure plays a key role in numerous applications of…
We use the transfer tensor method to analyze localization and transport in simple disordered systems, specifically the Anderson and Aubry-Andr\'e-Harper models. Emphasis is placed on the memory effects that emerge when ensemble-averaging…
We study the theoretical convergence of the nonlinear least-squares splitting method for the Monge-Amp\`ere equation in which each iteration decouples the pointwise nonlinearity from the differential operator and consists of a local…
In this article we prove that it is possible to construct, using newest-vertex bisection, meshes that equidistribute the error in $H^1$-norm, whenever the function to approximate can be decomposed as a sum of a regular part plus a singular…
We introduce and analyze a statistical estimator for Monge transport maps: solutions to the quadratic optimal transport problem in Euclidean space. For absolutely continuous source measures, this map is uniquely defined as the gradient of a…
The adaptively compressed exchange (ACE) method provides an efficient way for solving Hartree-Fock-like equations in quantum physics, chemistry, and materials science. The key step of the ACE method is to adaptively compress an operator…
We propose a simple dynamic model of polymers under shear with an anisotropic mobility tensor. We calculate the shear viscosity, the rheo-dielectric response function, and the parallel relaxation modulus under shear flow deduced from our…
Defect transport is a key process in materials science and catalysis, but as migration mechanisms are often too complex to enumerate a priori, calculation of transport tensors typically have no measure of convergence and require significant…
Highly accurate simulation of plasma transport is needed for the successful design and operation of magnetically confined fusion reactors. Unfortunately, the extreme anisotropy present in magnetized plasmas results in thin boundary layers…
Spatially referenced data often have autocovariance functions with elliptical isolevel contours, a property known as geometric anisotropy. The anisotropy parameters include the tilt of the ellipse (orientation angle) with respect to a…
This paper introduces a novel neural network-based approach to solving the Monge-Amp\`ere equation with the transport boundary condition, specifically targeted towards optical design applications. We leverage multilayer perceptron networks…
We consider the vertex-centered finite volume method with first-order conforming ansatz functions. The adaptive mesh-refinement is driven by the local contributions of the weighted-residual error estimator. We prove that the adaptive…
A common numerical task is to represent functions which are highly spatially anisotropic, and to solve differential equations related to these functions. One way such anisotropy arises is that information transfer along one spatial…
In the framework of multiple-scattering theory, we show that the dispersion relations of certain electromagnetic (EM) and elastic metamaterials can be obtained analytically in the long-wavelength limit. Specific examples are given to the…
Mesh deformation plays a pivotal role in many 3D vision tasks including dynamic simulations, rendering, and reconstruction. However, defining an efficient discrepancy between predicted and target meshes remains an open problem. A prevalent…
Time-dependent convection-dominated convection-diffusion problems are considered. We develop a moving mesh streamline upwind Petrov-Galerkin (MM-SUPG) method by combining residual-based SUPG stabilization with a metric-based moving mesh PDE…
We propose an optimal solution to a deterministic dynamic assignment problem by leveraging connections to the theory of discrete optimal transport to convert the combinatorial assignment problem into a tractable linear program. We seek to…