Related papers: A Numerical Method for Sharp-Interface Simulations…
In the literature, two quite different phase-field formulations for the problem of alloy solidification can be found. In the first, the material in the diffuse interfaces is assumed to be in an intermediate state between solid and liquid,…
In this article, a numerical simulation of two dimensional nonlinear sine-Gordon equation with Neumann boundary condition is obtained by using a composite scheme referred to as a modified cubic B spline differential quadrature method. The…
The present paper describes the development of a novel and comprehensive computational framework to simulate solidification problems in materials processing, specifically casting processes. Heat transfer, solidification and fluid flow due…
In this article we present a new formulation and an associated algorithm for the simultaneous numerical simulation of multiple condensed phase explosives in direct contact with each other, which may also be confined by (or interacting with…
We propose a novel and efficient lifting approach for the optimal control of rigid-body systems with contacts to improve the convergence properties of Newton-type methods. To relax the high nonlinearity, we consider the state, acceleration,…
In this work, a numerical simulation framework is presented based on the Phase Field Method that is able to capture the evolution of heterogeneous metallic microstructures during solidification. The involved physics can prove especially…
A revised version of the quaternion approach for numerical integration of the equations of motion for rigid polyatomic molecules is proposed. The modified approach is based on a formulation of the quaternion dynamics with constraints. This…
Directional solidification of water-based solutions has emerged as a versatile technique for templating hierarchical porous materials. However, the underlying mechanisms of pattern formation remain incompletely understood. In this work, we…
This paper proposes and develops new Newton-type methods to solve structured nonconvex and nonsmooth optimization problems with justifying their fast local and global convergence by means of advanced tools of variational analysis and…
Given an approximation to a multiple isolated solution of a polynomial system of equations, we have provided a symbolic-numeric deflation algorithm to restore the quadratic convergence of Newton's method. Using first-order derivatives of…
When combining the numerical concept of variational discretization and semi-smooth Newton methods for the numerical solution of pde constrained optimization with control constraints, special emphasis has to be taken on the implementation,…
This paper presents a numerical method for the simulation of fluid-structure interaction specifically tailored to interactions between Newtonian fluids and a large number of slender viscoelastic Cosserat rods. Because of their high…
A phase-field model that allows for quantitative simulations of low-speed eutectic and peritectic solidification under typical experimental conditions is developed. Its cornerstone is a smooth free-energy functional, designed so that the…
We introduce a multimodel approach to solve coupled cluster equations, employing a quasi Newton algorithm for the ground state and an Olsen algorithm for the excited states. In these algorithms, both of which can be viewed as Newton…
Proximal methods are known to identify the underlying substructure of nonsmooth optimization problems. Even more, in many interesting situations, the output of a proximity operator comes with its structure at no additional cost, and…
We consider a strongly nonlinear PDE system describing solid-solid phase transitions in shape memory alloys. The system accounts for the evolution of an order parameter (related to different symmetries of the crystal lattice in the phase…
In this work, we propose a nonlinear stabilization technique for scalar conservation laws with implicit time stepping. The method relies on an artificial diffusion method, based on a graph-Laplacian operator. It is nonlinear, since it…
This paper investigates a computational strategy for studying the interactions between multiple through-the-width delaminations and global or local buckling in composite laminates taking into account possible contact between the delaminated…
We present a nodal interpolation method to approximate a subdivision model. The main application is to model and represent curved geometry without gaps and preserving the required simulation intent. Accordingly, we devise the technique to…
In studying solidification process by simulations on the atomic scale, the modeling of crystal nucleation or amorphisation requires the construction of interatomic interactions that are able to reproduce the properties of both the solid and…