Related papers: A Numerical Method for Sharp-Interface Simulations…
We present algorithms for computing weakly singular and near-singular integrals arising when solving the 3D Helmholtz equation with curved boundary elements. These are based on the computation of the preimage of the singularity in the…
In this paper, we propose and analyze some practical Newton methods for electronic structure calculations. We show the convergence and the local quadratic convergence rate for the Newton method when the Newton search directions are…
Composite minimization involves a collection of smooth functions which are aggregated in a nonsmooth manner. In the convex setting, we design an algorithm by linearizing each smooth component in accordance with its main curvature. The…
The calculation of potential energy surfaces for quantum dynamics can be a time consuming task -- especially when a high level of theory for the electronic structure calculation is required. We propose an adaptive interpolation algorithm…
In this work, we examine a numerical phase-field fracture framework in which the crack irreversibility constraint is treated with a primal-dual active set method and a linearization is used in the degradation function to enhance the…
Discretization of non-linear Poisson-Boltzmann Equation equations results in a system of non-linear equations with symmetric Jacobian. The Newton algorithm is the most useful tool for solving non-linear equations. It consists of solving a…
We propose a sharp-interface model for solid-state dewetting of thin films with wetting potential, where the wetting effect is incorporated through a thickness-dependent surface energy. The model is governed by surface diffusion together…
We develop a method for calculating the equilibrium properties of the liquid-solid phase transition in a classical, ideal, multi-component plasma. Our method is a semi-analytic calculation that relies on extending the accurate fitting…
We investigate the use of piecewise linear systems, whose coefficient matrix is a piecewise constant function of the solution itself. Such systems arise, for example, from the numerical solution of linear complementarity problems and in the…
Neural networks have been applied to tackle many-body electron correlations for small molecules and physical models in recent years. Here we propose a new architecture that extends molecular neural networks with the inclusion of periodic…
We introduce a new phase-field formulation of rapid alloy solidification that quantitatively incorporates nonequilibrium effects at the solid-liquid interface over a very wide range of interface velocities. Simulations identify a new…
In this paper a special piecewise linear system is studied. It is shown that, under a mild assumption, the semi-smooth Newton method applied to this system is well defined and the method generates a sequence that converges linearly to a…
This paper describes a mixed direct-iterative method for boundary integral formulations of dielectric solvation models. We give an example for which a direct solution at thermal accuracy is nontrivial and for which Gauss-Seidel iteration…
Combining the augmented space representation for phonons with a generalized version of Yonezawa-Matsubara diagrammatic technique, we have set up a formalism to seperate the coherent and incoherent part of the total intensity of thermal…
We propose an accurate and energy-stable parametric finite element method for solving the sharp-interface continuum model of solid-state dewetting in three-dimensional space. The model describes the motion of the film\slash vapor interface…
Dendrites are one of the most widely observed patterns in nature and occur across a wide spectrum of physical phenomena. In solidification and growth patterns in metals and crystals, the multi-level branching structures of dendrites pose a…
In recent years, interface quasi-Newton methods have gained growing attention in the fluid-structure interaction community by significantly improving partitioned solution schemes: They not only help to control the inherent added-mass…
A very simple and accurate numerical method which is applicable to systems of differentio-integral equations with quite general boundary conditions has been devised. Although the basic idea of this method stems from the Keller Box method,…
The nonlinear systems obtained by discretizing degenerate parabolic equations may be hard to solve, especially with Newton's method. In this paper, we apply to Richards equation a strategy that consists in defining a new primary unknown for…
A new computational method is presented to resolve hydrodynamic interactions acting on solid particles immersed in incompressible host fluids. In this method, boundaries between solid particles and host fluids are replaced with a continuous…