@misc{ZschiedrichKloseSchaedleetal., author = {Zschiedrich, Lin and Klose, Roland and Sch{\"a}dle, Achim and Schmidt, Frank}, title = {A new Finite Element realization of the Perfectly Matched Layer Method for Helmholtz scattering problems on polygonal domains in 2D}, doi = {10.1016/j.cam.2005.03.047}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7662}, number = {03-44}, abstract = {In this paper we propose a new finite element realization of the Perfectly Matched Layer method (PML-method). Our approach allows to deal with arbitrary shaped polygonal domains and with certain types of inhomogeneous exterior domains. Among the covered inhomogeneities are open waveguide structures playing an essential role in integrated optics. We give a detailed insight to implementation aspects. Numerical examples show exponential convergence behavior to the exact solution with the thickness of the PML sponge layer.}, language = {en} } @misc{MayEisenhardtSchmidtEhrenbergetal., author = {May, Andreas and Eisenhardt, Steffen and Schmidt-Ehrenberg, Johannes and Cordes, Frank}, title = {Rigid body docking for Virtual Screening}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7690}, number = {03-47}, abstract = {A recently developed algorithm allows Rigid Body Docking of ligands to proteins, regardless of the accessibility and location of the binding site. The Docking procedure is divided into three subsequent optimization phases, two of which utilize rigid body dynamics. The last one is applied with the ligand already positioned inside the binding pocket and accounts for full flexibility. Initially, a combination of geometrical and force-field based methods is used as a Coarse Docking strategy, considering only Lennard-Jones interactions between the target and pharmaceutically relevant atoms or functional groups. The protein is subjected to a Hot Spot Analysis, which reveals points of high affinity in the protein environment towards these groups. The hot spots are distributed into different subsets according to their group affiliation. The ligand is described as a complementary point set, consisting of the same subsets. Both sets are matched in \$\mathrm{I\!R}^{3}\$, by superimposing members of the same subsets. In the first instance, steric inhibition is nearly neglected, preventing the system's trajectory from trapping in local minima and thus from finding false positive solutions. Hence the exact location of the binding site can be determined fast and reliably without any additional information. Subsequently, errors resulting from approximations are minimized via finetuning, this time considering both Lennard-Jones and Coulomb forces. Finally, the potential energy of the whole complex is minimized. In a first evaluation, results are rated by a reduced scoring function considering only noncovalent interaction energies. Exemplary Screening results will be given for specific ligands.}, language = {en} }