Related papers: A Two-Level Method for Mimetic Finite Difference D…
Image segmentation is an important median level vision topic. Accurate and efficient multiphase segmentation for images with intensity inhomogeneity is still a great challenge. We present a new two-stage multiphase segmentation method…
Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…
We introduce a new approach to obtaining pointwise estimates for solutions of elliptic boundary value problems when the operator being considered satisfies a certain type of weighted integral inequalities. The method is illustrated on…
This paper presents a novel multi-scale method for elliptic partial differential equations with arbitrarily rough coefficients. In the spirit of numerical homogenization, the method constructs problem-adapted ansatz spaces with uniform…
For a singularly perturbed elliptic model problem with two small parameters, we analyze finite element methods of any order on a Bakhvalov-type mesh. For convergence analysis, we construct a new interpolation by using the characteristics of…
A stabilized Lagrange multiplier method for second order elliptic interface problems is presented in the framework of mortar method. The requirement of LBB (Ladyzhenskaya-Babu\v{s}ka-Brezzi) condition for mortar method is alleviated by…
The biharmonic equation with Dirichlet and Neumann boundary conditions discretized using the mixed finite element method and piecewise linear (with the possible exception of boundary triangles) finite elements on triangular elements has…
This article describes the extension of recent methods for a posteriori error estimation such as dual-weighted residual methods to node-centered finite volume discretizations of second order elliptic boundary value problems including upwind…
In this work, we propose an efficient adaptive multilevel preconditioned Jacobi-Davidson (PJD) method for eigenvalue problems with singularity. Our multilevel method utilizes a local smoothing strategy to solve the preconditioned…
We present a higher-order finite volume method for solving elliptic PDEs with jump conditions on interfaces embedded in a 2D Cartesian grid. Second, fourth, and sixth order accuracy is demonstrated on a variety of tests including problems…
We study bilevel optimization with a fixed polyhedral lower feasible set. Such problems are challenging for two reasons: active-set changes can make the upper objective nonsmooth, and existing hypergradient methods typically require…
In this paper we study a semilinear elliptic problem on a bounded domain in $\R^2$ with large exponent in the nonlinear term. We consider positive solutions obtained by minimizing suitable functionals. We prove some asymtotic estimates…
The present study is an extension of the work done in Parareal convergence for oscillatory pdes with finite time-scale separation (2019), A. G. Peddle, T. Haut, and B. Wingate, [16], and An asymptotic parallel-in-time method for highly…
This paper presents a new parameter free partially penalized immersed finite element method and convergence analysis for solving second order elliptic interface problems. A lifting operator is introduced on interface edges to ensure the…
This is the second paper on the study of gradient recovery for elliptic interface problem. In our previous work [H. Guo and X. Yang, 2016, arXiv:1607.05898], we developed gradient recovery finite element method based on body-fitted mesh. In…
Bilevel optimization provides a powerful framework for modelling hierarchical decision-making systems. This work presents a sensitivity-based algorithm that addresses the bilevel structure directly by treating the lower-level optimal…
To facilitate widespread adoption of automated engineering design techniques, existing methods must become more efficient and generalizable. In the field of topology optimization, this requires the coupling of modern optimization methods…
Bi-level optimization has achieved considerable success in contemporary machine learning applications, especially for given proper hyperparameters. However, due to the two-level optimization structure, commonly, researchers focus on two…
This work develops an epsilon-uniform finite element method for singularly perturbed boundary value problems. A surprising and remarkable observation is illustrated: By moving one node arbitrarily in between its adjacent nodes, the new…
A multiscale optimization framework for problems over a space of Lipschitz continuous functions is developed. The method solves a coarse-grid discretization followed by linear interpolation to warm-start project gradient descent on…