Related papers: A Picard Newton method to solve non linear airflow…
In finance, implied volatility is an important indicator that reflects the market situation immediately. Many practitioners estimate volatility using iteration methods, such as the Newton--Raphson (NR) method. However, if numerous implied…
The Poisson equation is commonly encountered in engineering, for instance in computational fluid dynamics (CFD) where it is needed to compute corrections to the pressure field to ensure the incompressibility of the velocity field. In the…
The beginning of this work is the achievement of a design tool, which is a multiple model software called " CODYRUN ", suitable for professionnals and usable by researchers. The original aspect of this software is that the designer has at…
Recently, the authors of this paper proposed a method for the Harmonic Power-Flow (HPF) calculus in polyphase grids with widespread deployment of Converter-Interfaced Distributed Energy Resources (CIDERs). The HPF problem was formulated by…
In this document, a neural network is employed in order to estimate the solution of the initial value problem in the context of non linear trajectories. Such trajectories can be subject to gravity, thrust, drag, centrifugal force,…
We present an algorithm for the numerical solution of the equations governing combustion in porous inert media. The discretization of the flow problem is performed by the mixed finite element method, the transport problems are discretized…
The radiation diffusion problem is a kind of {time-dependent} nonlinear equations. For solving the radiation diffusion equations, many linear systems are obtained in the nonlinear iterations at each time step. The cost of linear equations…
A novel method to estimate unsteady aerodynamic force coefficients from pointwise velocity measurements is presented. The methodology is based on a resolvent-based reduced-order model which requires the mean flow to obtain physical flow…
Internal flows inside gravitationally stable astrophysical objects, such as the Sun, stars and compact stars are compressed and extremely subsonic. Such low Mach number flows are usually encountered when studying for example dynamo action…
This paper is on the construction of structure-preserving, online-efficient reduced models for the barotropic Euler equations with a friction term on networks. The nonlinear flow problem finds broad application in the context of gas…
Non-convex, nonlinear gas network optimization models are used to determine the feasibility of flows on existing networks given constraints on network flows, gas mixing, and pressure loss along pipes. This work improves two existing gas…
In this article we present robust, efficient and accurate fully implicit time-stepping schemes and nonlinear solvers for systems of reaction-diffusion equations. The applications of reaction-diffusion systems is abundant in the literature,…
Accurate prediction of laminar-turbulent transition is a critical element of computational fluid dynamics simulations for aerodynamic design across multiple flow regimes. Traditional methods of transition prediction cannot be easily…
Obtaining good initial conditions to solve the Newton-Raphson (NR) based ac power flow (ACPF) problem can be a very difficult task. In this paper, we propose a framework to obtain the initial bus voltage magnitude and phase values that…
Buildings sector is one of the major consumers of energy in the United States. The buildings HVAC (Heating, Ventilation, and Air Conditioning) systems, whose functionality is to maintain thermal comfort and indoor air quality (IAQ), account…
Simulating compositional multiphase flow in porous media is a challenging task, especially when phase transition is taken into account. The main problem with phase transition stems from the inconsistency of the primary variables such as…
Anderson Acceleration (AA) has been widely used to solve nonlinear fixed-point problems due to its rapid convergence. This work focuses on a variant of AA in which multiple Picard iterations are performed between each AA step, referred to…
In this paper, we present a Newton-like method based on model reduction techniques, which can be used in implicit numerical methods for approximating the solution to ordinary differential equations. In each iteration, the Newton-like method…
This paper presents a recurrent neural network approach to simulating mechanical ventilator pressure. The traditional mechanical ventilator has a control pressure that is monitored by a medical practitioner and can behave incorrectly if the…
In this paper, an idea to solve nonlinear equations is presented. During the solution of any problem with Newton's Method, it might happen that some of the unknowns satisfy the convergence criteria where the others fail. The convergence…