The purpose of this study is to improve the computational efficiency of solvers for nonlinear algebraic problems with simple roots. To this end, a multi-step solver based on Newton’s method is utilized. Divided difference operators are applied...
Fractional calculus extends the conventional concepts of derivatives and integrals to non-integer orders, providing a robust mathematical framework for modeling complex systems characterized by memory and hereditary properties. This study enhances th...
The aim of this study was to compare algorithms for solving inverse problems generally encountered in spatial audio signal processing. Tikhonov regularization is typically utilized to solve overdetermined linear systems in which the regularization pa...
The optimal design methodology for a Maxwell–Coulomb friction damper is proposed to minimize the resonant vibration of dynamic structures. The simple Coulomb friction damper has the problem of zero or little damping effect of the vibration of t...
We compare the convergence balls and the dynamical behaviors of two efficient weighted-Newton-like equation solvers by Sharma and Arora, and Grau-Sánchez et al. First of all, the results of ball convergence for these algorithms are established...
One of the most difficult steps in estimating the cruise performance characteristics of high-subsonic transport-category turbofan-powered airplanes is the estimation of the transonic wave drag. Modern jet airplanes cruise most efficiently in the vici...
We consider the finite element approximation of the solution to elliptic partial differential equations such as the ones encountered in (quasi)-static mechanics, in transient mechanics with implicit time integration, or in thermal diffusion. We propo...
Simulation of heat production in high-enthalpy geothermal systems is associated with a complex physical process in which cold water invades steam-saturated control volumes. The fully implicit, fully coupled numerical strategy is commonly adopted to s...
This article introduces a novel iterative solver with memory, derived from Newton’s scheme, for nonlinear scalar equations. The key innovation lies in integrating memory into the iterative process, enhancing the convergence rate without increas...
In this study, a class of nonlinear heterogeneous reaction–diffusion system (RDS) has been considered that arises in modeling epidemiological interactions, environmental sciences, and chemical and ecological systems. Numerical and analytic solu...
Growing demand, interconnection of multiple systems, and difficulty in upgrading existing infrastructures are limiting the capabilities of conventional computational tools employed in power system analysis. Recent studies manifest the importance of e...
A CFD (computational fluid dynamics) analysis was carried out for the Bingham viscoplastic fluid flow simulations around cylinders of circular and square shapes. The governing equations in space were discretized with the finite element approach via a...
A free-boundary equilibrium solver for an axisymmetric tokamak geometry was developed based on the finite difference method and Picard iteration in a rectangular computational area. The solver can run either in forward mode, where external coil curre...
At the core of every system for the efficient control of the network steady-state operation is the AC-power-flow problem solver. For local distribution networks to continue to operate effectively, it is necessary to use the most powerful and numerica...
In this paper, a space-time absolute nodal coordinate formulation cable (SAC) element forming technique based on the Lagrange family of shape functions is proposed. Two distinct SAC elements, each with a distinct spatial shape function, have been gen...
In the context of energy efficient lighting, we present a mathematical study of the heating and cooling processes of a common type of luminaires, consisting of a single light-emitting diode source in thermal contact with an aluminum passive heat sink...
Atherosclerosis is an accumulation of plaque, which can result in changes in blood flow in the vicinity, leading to severe heart attack. This paper presents a phenomenological fluid–structure interaction study of plaque rupture in stenosed bifu...
Herein, we developed and analyzed a new fractal–fractional (FF) operational matrix for orthonormal normalized ultraspherical polynomials. We used this matrix to handle the FF Riccati differential equation with the new generalized Caputo FF derivative...
We propose two enhancements of quasi-Newton methods used to accelerate coupling iterations for partitioned fluid-structure interaction. Quasi-Newton methods have been established as flexible, yet robust, efficient and accurate coupling methods of mul...
In this work, we construct a family of seventh order iterative methods for finding multiple roots of a nonlinear function. The scheme consists of three steps, of which the first is Newton’s step and last two are the weighted-Newton steps. Hence...
The Chebyshev collocation method implemented in Chebfun is used in order to solve a class of second order one-dimensional singular and genuinely nonlinear boundary value problems. Efforts to solve these problems with conventional ChC have generally f...
Phase-field fracture models lead to variational problems that can be written as a coupled variational equality and inequality system. Numerically, such problems can be treated with Galerkin finite elements and primal-dual active set methods. Specific...
Lyapunov equations are key mathematical objects in systems theory, analysis and design of control systems, and in many applications, including balanced realization algorithms, procedures for reduced order models, Newton methods for algebraic Riccati...
Efficient simulation of the helical coiled once-through steam generator (H-OTSG) is crucial in the design and safety analysis of the high-temperature gas-cooled reactor (HTGR). The physical property and phase transformation of water in the steam gene...
Finite element analyses of the propagation of damage such as fiber compressive failure and delamination have greatly contributed to the understanding of failure mechanisms of fiber-reinforced plastics owing to extensive studies on methodologies using...
Recently, the high-order Newton-like methods have gained popularity for solving power flow problems due to their simplicity, versatility and, in some cases, efficiency. In this context, recent research studied the applicability of the 4th order Jarra...
The study of ship waves is important for ship detection, coastal erosion and wave drag. This paper proposed a highly paralleled numerical computation method for efficiently simulating three-dimensional nonlinear kelvin waves. First, a numerical model...
The migration of methane through the gas hydrate stability zone (GHSZ) in the marine subsurface is characterized by highly dynamic reactive transport processes coupled to thermodynamic phase transitions between solid gas hydrates, free methane gas, a...
We report on a new multiscale method approach for the study of systems with wide separation of short-range forces acting on short time scales and long-range forces acting on much slower scales. We consider the case of the Poisson–Boltzmann equa...
The upward trends in renewable energy penetration, cross-border flow volatility and electricity actors’ proliferation pose new challenges in the power system management. Electricity and market operators need to increase collaboration, also in t...
Two nonlinear Duffing equations are numerically treated in this article. The nonlinear fractional-order Duffing equations and the second-order nonlinear Duffing equations are handled. Based on the collocation technique, we provide two numerical algor...
For transient mixed Elastohydrodynamic lubrication (EHL) problems, a novel solution is required to predict friction loss and wear in sliding or rolling parts. However, existing solutions have numerous limitations. In general, the lower the oil film t...
Herein, we adduce, analyze, and come up with spectral collocation procedures to iron out a specific class of nonlinear singular Lane–Emden (LE) equations with generalized Caputo derivatives that appear in the study of astronomical objects. The...
Finite element discretization of the pressure head form of the Richards equation leads to a nonlinear model, which yields numerical convergence difficulties. When the numerical solution to this problem has either an extremely sharp moving front, infi...
Inverse kinematics is a fundamental problem in manipulator robotics: a set of joint angles must be calculated so that the robot arm can be manipulated to the corresponding desired end effector position and orientation (also known as “pose&rdquo...
Recently, the Hypervolume Newton Method (HVN) has been proposed as a fast and precise indicator-based method for solving unconstrained bi-objective optimization problems with objective functions. The HVN is defined on the space of (vectorized) fixed...
Reactive transport plays an important role in various subsurface applications, including carbon dioxide sequestration, nuclear waste storage, biogeochemistry and the simulation of hydro–thermal reservoirs. The model couples a set of partial different...
In this paper, we consider a generalized inexact Newton-Landweber iteration to solve nonlinear ill-posed inverse problems in Banach spaces, where the forward operator might not be Gâteaux differentiable. The method is designed with non-smooth c...
This study is devoted to the modeling and simulation of uncertainties in the constitutive elastic properties of material constituting a circular column under axial compression. To this aim, a probabilistic model dedicated to the construction of posit...
Different industrial and medical situations require the non-invasive extraction of information from the inside of bodies. This is usually done through tomographic methods that generate images based on internal body properties. However, the image reco...
This article presents an inexact optimal hybrid conjugate gradient (CG) method for solving symmetric nonlinear systems. The method is a convex combination of the optimal Dai–Liao (DL) and the extended three-term Polak–Ribiére–Polyak (PRP) CG methods....
The adjoint approach in gradient-based optimization combined with computational fluid dynamics is commonly applied in various engineering fields. In this work, the gradients are used for the design of a two-dimensional airfoil shape, where the aim is...
A critical reduction in the total harmonic distortion in the output voltage of multilevel inverters can be obtained with an appropriate selection of the angles to switch the power semiconductors at low frequency. Among the methods used to obtain the...
An improved meshfree method that considers cracking, contact behaviour and fluid–solid interaction (FSI) was developed and employed to shed light on the progressive failure of the water-resistant stratum and inrush process in a karst tunnel con...
Hardy Cross originally proposed a method for analysis of flow in networks of conduits or conductors in 1936. His method was the first really useful engineering method in the field of pipe network calculation. Only electrical analogs of hydraulic netw...
The first objective of this paper is to investigate the scaling behavior of liquid-vapor phase transition in FCC and BCCmetals starting from the zero-temperature four-parameter formula for cohesive energy. The effective potentials between the atoms i...
This paper presents a dynamic homotopy technique that can be used to calculate a preliminary result for a power flow problem (PFP). This result can then be used as an initial estimate to efficiently solve the PFP using either the classical Newton-Rap...
When applying the sequential quadratic programming (SQP) algorithm to topology optimization, using the quasi-Newton methods or calculating the Hessian matrix directly will result in a considerable amount of calculation, making it computationally infe...
We consider the facility layout problem (FLP) in which we find the arrangements of departments with the smallest material handling cost that can be expressed as the product of distance times flows between departments. It is known that FLP can be form...
The aim of this survey is to review some recent developments in devising efficient preconditioners for sequences of symmetric positive definite (SPD) linear systems A k x k = b k , k = 1 , … arising in many scientific applications, such...
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