Related papers: A Numerical Method for Sharp-Interface Simulations…
This paper compares two approaches for investigating the near-surface composition profile that results from surface segregation in the so-called Cantor alloy, an equi-molar alloy of CoCrFeMnNi. One approach consists of atomistic computer…
We present a mathematical formulation of a multiscale model for solidification with convective flow in the liquid phase. The model is an extension of the dendritic needle network approach for crystal growth in a binary alloy. We propose a…
Phase-field models of microstructural pattern formation during alloy solidification are commonly solved numerically using the finite-difference method, which is ideally suited to carry out computationally efficient simulations on massively…
We develop a fully-coupled, fully-implicit approach for phase-field modeling of solidification in metals and alloys. Predictive simulation of solidification in pure metals and metal alloys remains a significant challenge in the field of…
This work investigates the application of the Newton's method for the numerical solution of a nonlinear boundary value problem formulated through an ordinary differential equation (ODE). Nonlinear ODEs arise in various mathematical modeling…
Compositionally complex alloys or concentrated solid solutions are the latest frontier in catalyst design, but mixing different elements in one catalyst may result in surface segregation. Atomistic simulations can predict segregation…
We present a monolithic parallel Newton-multigrid solver for nonlinear three dimensional fluid-structure interactions in Arbitrary Lagrangian Eulerian formulation. We start with a finite element discretization of the coupled problem, based…
Laser beam welding is a non-contact joining technique that has gained significant importance in the course of the increasing degree of automation in industrial manufacturing. This process has established itself as a suitable joining tool…
In this paper, we conduct a numerical analysis of the strong stabilization and polynomial decay of solutions for the initial boundary value problem associated with a system that models the dynamics of a mixture of two rigid solids with…
Fixed-point or Newton-methods are typically employed for the numerical solution of nonlinear systems arising from discretization of nonlinear magnetic field problems. We here discuss an alternative strategy which uses local Quasi-Newton…
The textbook Newton's iteration is practically inapplicable on solutions of nonlinear systems with singular Jacobians. By a simple modification, a novel extension of Newton's iteration regains its local quadratic convergence toward…
A high-order Newton multigrid method is proposed for steady-state shallow water flows in open channels with regular and irregular geometries. The method integrates a finite volume discretization with third-order weighted essentially…
We further develop a recently introduced phase-field model of rapid alloy solidification [Ji et al., PRL 2023]. This model utilizes enhanced solute diffusivity within the spatially diffuse interface region to quantitatively capture solute…
We consider a non-isothermal multi-phase field model. We subsequently discretize implicitly in time and with linear finite elements. The arising algebraic problem is formulated in two variables where one is the multi-phase field, and the…
We study a variant of Newton's algorithm applied to under-determined systems of non-smooth equations. The notion of regularity employed in our work is based on Newton differentiability, which generalizes semi-smoothness. The classic notion…
Compositional simulation is challenging, because of highly nonlinear couplings between multi-component flow in porous media with thermodynamic phase behavior. The coupled nonlinear system is commonly solved by the fully-implicit scheme.…
The paper develops a Newton multigrid (MG) method for one- and two-dimensional steady-state shallow water equations (SWEs) with topography and dry areas.It solves the nonlinear system arising from the well-balanced finite volume…
The need to compute the intersections between a line and a high-order curve or surface arises in a large number of finite element applications. Such intersection problems are easy to formulate but hard to solve robustly. We introduce a…
Solidification governs the microstructure and, therefore, the mechanical response of metal components, yet the atomistic details of nucleation and defect formation are often difficult to determine experimentally. Molecular dynamics can…
The computational modeling of many engineering problems using the Finite Element method involves the modeling of two or more bodies that meet through an interface. The interface can be physical, as in multi-physics and contact problems, or…