Relaxation of Crystals with the Quasi-Newton Method
نویسندگان
چکیده
A quasi-Newton Method is used to simultaneously relax the internal coordinates and lattice parameters of crystals under pressure. The symmetry of the crystal structure is preserved during the relaxation. From the inverse of the Hessian matrix, elastic properties and some optical phonon frequencies at the Brillouin zone center can be estimated. The e ciency of the method is demonstrated for silicon test systems. 3
منابع مشابه
On the Behavior of Damped Quasi-Newton Methods for Unconstrained Optimization
We consider a family of damped quasi-Newton methods for solving unconstrained optimization problems. This family resembles that of Broyden with line searches, except that the change in gradients is replaced by a certain hybrid vector before updating the current Hessian approximation. This damped technique modifies the Hessian approximations so that they are maintained sufficiently positive defi...
متن کاملAccelerated staggered coupling schemes for problems of thermoelasticity at finite strains
This paper introduces a fully implicit partitioned coupling scheme for problems of thermoelasticity at finite strains utilizing the p-version of the finite element method. The mechanical and the thermal fields are partitioned into symmetric subproblems where algorithmic decoupling has been obtained by means of an isothermal operator-split. Numerical relaxation methods have been implemented to a...
متن کاملA class of multi-agent discrete hybrid non linearizable systems: Optimal controller design based on quasi-Newton algorithm for a class of sign-undefinite hessian cost functions
In the present paper, a class of hybrid, nonlinear and non linearizable dynamic systems is considered. The noted dynamic system is generalized to a multi-agent configuration. The interaction of agents is presented based on graph theory and finally, an interaction tensor defines the multi-agent system in leader-follower consensus in order to design a desirable controller for the noted system. A...
متن کاملA Free Line Search Steepest Descent Method for Solving Unconstrained Optimization Problems
In this paper, we solve unconstrained optimization problem using a free line search steepest descent method. First, we propose a double parameter scaled quasi Newton formula for calculating an approximation of the Hessian matrix. The approximation obtained from this formula is a positive definite matrix that is satisfied in the standard secant relation. We also show that the largest eigen value...
متن کاملA Quasi-newton Algorithm Based on a Reduced Model for Fluid-structure Interaction Problems in Blood Flows
We propose a quasi-Newton algorithm for solving fluid-structure interaction problems. The basic idea of the method is to build an approximate tangent operator which is cost effective and which takes into account the so-called added mass effect. Various test cases show that the method allows a significant reduction of the computational effort compared to relaxed fixed point algorithms. We presen...
متن کامل