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We propose a penalty-function method for constrained molecular dynamics simulation by defining a quadratic penalty function for the constraints. The simulation with such a method can be done by using a conventional, unconstrained solver only with the penalty parameter increased in an appropriate manner as the simulation proceeds. More specifically, we scale the constraints with their force constants when forming the penalty terms. The resulting force function can then be viewed as a smooth continuation of the original force field as the penalty parameter increases. The penalty function method is easy to implement and costs less than a Lagrange multiplier method, which requires the solution of a nonlinear system of equations in every time step. We have first implemented a penalty function method in CHARMM and applied it to protein Bovine Pancreatic Trypsin Inhibitor (BPTI). We compared the simulation results with Verlet and Shake, and found that the penalty function method had high correlations with Shake and outperformed Verlet. In particular, the RMSD fluctuations of backbone and non-backbone atoms and the velocity auto correlations of Cα atoms of the protein calculated by the penalty function method agreed well with those by Shake. We have also tested the method on a group of argon clusters constrained with a set of interatomic distances in their global energy minimum states. The results showed that the method was able to impose the constraints effectively and the clusters tended to converge to their energy minima more rapidly than not confined by the constraints. [ABSTRACT FROM AUTHOR]

The aim of this paper is to investigate the application of a semi- implicit additive operator splitting scheme based binary level set method to source reconstruction problems. We reformulate the original model to be a new constrained optimization problem under the binary level set framework and solve it by the augmented Lagrangian method. Then we propose an efficient gradient-type algorithm based on the additive operator splitting scheme. The proposed algorithm can create new holes during the evolution. Topological changes can be handled automatically and complex geometry can be recovered under a certain amount of noise in the observation data. Numerical examples are presented to show the effectiveness and efficiency of our method. [ABSTRACT FROM AUTHOR]