This document proposes a Newton step graph-based model for Quadratic separable Problems (QSP). The Newton step is well suited for this kind of problems, but when the problem size grows the matrix-based QSP model will grow in a non linear manner. Furthermore, handling the constraints becomes the main problem as we have to select the right constraints in the different solution steps. When this ha...

The multiphysics field is a branch of physics whose objective to couple at least two physical systems. Each governed by its own principles evolution or equilibrium such as balance laws constitutive laws. Many engineering problems can only be described correctly coupling fields that have historically been developed and taught separately. These require on the one hand good understanding each doma...

This work presents efficient solution techniques for radiative transfer in the smoothed particle hydrodynamics discretization. Two choices that impact efficiency are how material and radiation energy coupled, which determines number of iterations needed to converge emission source, diffusion equation is solved, must be done each iteration. The coupled equations solved using an inexact Newton it...

A version of the Bi-CGSTAB method is applied for solving the linear systems that typically occur when applying the Newton method to a discretized set of coupled elliptic partial di erential equations in two dimensions. The Incomplete Line LU decomposition is generalized for the case of coupled equations and applied as a preconditioner. A suitable stopping criterion is developed for the Bi-CGSTA...

A model that rigorously computes the gas-particle partitioning and liquid-liquid equilibrium for organic atmospheric aerosol particles is presented. The dynamics of the mass transfers between the particle and the gas phase are modeled with differential equations and are coupled with a constrained optimization problem for the thermodynamic equilibrium inside the particle. The nonlinear system co...

A parallel fully coupled implicit fluid solver based on a Newton–Krylov–Schwarz algorithm is developed on top of the Portable, Extensible Toolkit for Scientific computation for the simulation of microfluidic mixing described by the three-dimensional unsteady incompressible Navier–Stokes equations. The popularly used fractional step method, originally designed for high Reynolds number flows, req...

An implementation of a coupled Navier-Stokes/Darcy model based on different Dune discretization modules is presented. The Darcy model is taken from DuMux, the Navier-Stokes model is implemented on top of Dune-PDELab, and the coupling is done with help of Dune-MultiDomain together with some project-specific auxiliary code. The Navier-Stokes model features one fluid phase, the Darcy model two flu...

Abstract: The standard decoupled method with Newton-generalized minimum residual procedure performs poorly or may break down when used to solve certain elastohydrodynamic lubrication problems. The authors Zargari et al., 2007 presented decoupled and coupled methods in which the limitations of the decoupled method for some set of physical parameters and slight variation in these values (physical...

In this paper we propose a method of numerical solution of non-linear boundary value problems for systems of ODEs given on the embedded intervals. The algorithm is based on the continuous analog of Newton method coupled with spline-collocation scheme of fourth order of accuracy. Demonstrative examples of similar problems take place in physics of stacked Jo-sephson junctions with different layer...