Due to the massive demands from industry, the black-box based coupled energy domains simulation plays a more and more important role in the design of MEMS devices, and many numerical techniques have been developed so far for it. This paper presents a fast convergence scheme for coupled energy domains simulation of MEMS. This scheme is based on the relaxation approach but employs the Steffensen’...

We consider the nonlinear systems of equations that result from discretizations of a prototype variational model for the equilibrium director field characterizing the orientational properties of a liquid crystal material. In the presence of pointwise unit-vector constraints and coupled electric fields, the numerical solution of such equations by Lagrange-Newton methods leads to problems with a ...

Various distributed optimization methods have been developed for consensus optimization problems in multi-agent networks. Most of these methods only use gradient or subgradient information of the objective functions, which suffer from slow convergence rate. Recently, a distributed Newton method whose appeal stems from the use of second-order information and its fast convergence rate has been de...

A new, approximate block Newton (ABN) method is derived and tested for the coupled solution of nonlinear models, each of which is treated as a modular, black box. Such an approach is motivated by a desire to maintain software flexibility without sacrificing solution efficiency or robustness. Though block Newton methods of similar type have been proposed and studied, we present a unique derivati...

where F (ξ) is a nonlinear operator from a real Euclidean space of dimension n or Hilbert space into itself. The Euclidean norm and corresponding inner product will be denoted by ‖·‖1 and (·, ·)1 respectively. A general different inner product with a weight function and the corresponding norm will be denoted by (·, ·)0 and ‖ · ‖ respectively. In the first part of this article (Sects. 2 and 3) w...

In this paper, a new algorithm for solving cross-coupled sign-indefinite algebraic Riccati equations (CSAREs) for weakly coupled large-scale systems is proposed. It is shown that since the proposed algorithm is based on the Newton’s method, the quadratic convergence is attained. Moreover, the local uniqueness of the convergence solutions for the CSAREs is investigated. Finally, in order to over...

Quasi-Newton methods have proven to be an efficient way couple partitioned solvers in fluid-structure interaction problems, as they are able stabilize cases with high added-mass, well accelerate the convergence. However, these assume that coupled system is a complete black-box, whereas often, its behavior approximated by surrogate model. Such model may obtained coarsening system, simplifying ph...

Abstract This note is concerned with efficient Newton‐multigrid finite element method (FEM) solver for multifield nonlinear flow problems. In our approach, FEM solver, we advantageously use the delicate symbiosis aspects of problem settings approximations, and algorithmic tools to obtain numerical solutions. We concretize ideas on thixoviscoplastic It a two‐field coupled problem. And beside int...

in this paper, we study the existence of coupled coincidence andcoupled common fixed points for single-valued and fuzzy mappingsunder a contractive condition in metric space. presented theoremsextend and improve the main results of abbas and$acute{c}$iri$acute{c}$ {itshape et al.} [m. abbas, l.$acute{c}$iri$acute{c}$, {itshape et al.}, coupled coincidenceand common fixed point theorems for hybr...