Related papers: Optimal homotopy analysis method with Green's func…
This manuscript presents an efficient boundary integral equation technique for solving two-dimensional Helmholtz problems defined in the half-plane bounded by an infinite, periodic curve with Neumann boundary conditions and an aperiodic…
In this paper, the homotopy analysis method (HAM) is successfully applied to solve the Von Karman's plate equations in the integral form for a circular plate with the clamped boundary under an arbitrary uniform external pressure. Two…
We provide an a priori analysis of collocation methods for solving elliptic boundary value problems. They begin with information in the form of point values of the data and utilize only this information to numerically approximate the…
In this work, we propose an adaptive spectral element algorithm for solving nonlinear optimal control problems. The method employs orthogonal collocation at the shifted Gegenbauer-Gauss points combined with very accurate and stable…
We present and study the iteration-complexity of a relative-error inexact proximal-Newton extragradient algorithm for solving smooth monotone variational inequality problems in real Hilbert spaces. We removed a search procedure from…
In this paper, we design and analyze a Hybrid-High Order (HHO) approximation for a class of quasilinear elliptic problems of nonmonotone type. The proposed method has several advantages, for instance, it supports arbitrary order of…
We introduce a new overlapping Domain Decomposition Method (DDM) to solve the fully nonlinear Monge-Amp\`ere equation. While DDMs have been extensively studied for linear problems, their application to fully nonlinear partial differential…
We analyze a goal-oriented adaptive algorithm that aims to efficiently compute the quantity of interest $G(u^\star)$ with a linear goal functional $G$ and the solution $u^\star$ to a general second-order nonsymmetric linear elliptic partial…
It is well known that finding a global optimum is extremely challenging for nonconvex optimization. There are some recent efforts \cite{anandkumar2016efficient, cartis2018second, cartis2020sharp, chen2019high} regarding the optimization…
In this article we develop a convergence theory for goal-oriented adaptive finite element algorithms designed for a class of second-order semilinear elliptic equations. We briefly discuss the target problem class, and introduce several…
Green's function provides an inherent connection between theoretical analysis and numerical methods for elliptic partial differential equations, and general absence of its closed-form expression necessitates surrogate modeling to guide the…
In this paper we propose and apply the enhanced semidefinite relaxation technique for solving a class of non-convex quadratic optimization problems. The approach is based on enhancing the semidefinite relaxation methodology by complementing…
A priori and a posteriori error analysis of $hp$ finite element method for elliptic control problem with Robin boundary condition and boundary observation are presented. are presented. Through the Cl\'ement-type approach and the…
The Anderson Mixing (AM) method is a popular approach for accelerating fixed-point iterations by leveraging historical information from previous steps. In this paper, we introduce the Riemannian Anderson Mixing (RAM) method, an extension of…
The paper presents the solutions for the zonal electrophoresis equations are obtained by analytical and numerical methods. The method proposed by the authors is used. This method allows to reduce the Cauchy problem for two hyperbolic…
In this work we develop a systematic geometric approach to study fully nonlinear elliptic equations with singular absorption terms as well as their related free boundary problems. The magnitude of the singularity is measured by a negative…
We construct an expression for the Green function of a differential operator satisfying nonlocal, homogeneous boundary conditions starting from the fundamental solution of the differential operator. This also provides the solution to the…
We propose homotopy analysis method in combination with Galerkin projections to approximate the natural response of non-smooth oscillators with discontinuities of type Heaviside, signum, modulus etc. While constructing the homotopy, we…
This paper introduces a nonconforming virtual element method for general second-order elliptic problems with variable coefficients on domains with curved boundaries and curved internal interfaces. We prove arbitrary order optimal…
Neural operators, which learn mappings between the function spaces, have been applied to solve boundary value problems in various ways, including learning mappings from the space of the forcing terms to the space of the solutions with the…