@article{thirunavukkarasu_guddati_2011, title={Absorbing boundary conditions for time harmonic wave propagation in discretized domains}, volume={200}, ISSN={["1879-2138"]}, DOI={10.1016/j.cma.2011.04.021}, abstractNote={While many successful absorbing boundary conditions (ABCs) are developed to simulate wave propagation into unbounded domains, most of them ignore the effect of interior discretization and result in spurious reflections at the artificial boundary. We tackle this problem by developing ABCs directly for the discretized wave equation. Specifically, we show that the discrete system (mesh) can be stretched in a non-trivial way to preserve the discrete impedance at the interface. Similar to the perfectly matched layers (PML) for continuous wave equation, the stretch is designed to introduce dissipation in the exterior, resulting in a PML-type ABC for discrete media. The paper includes detailed formulation of the new discrete ABC, along with the illustration of its effectiveness over continuous ABCs with the help of error analysis and numerical experiments. For time-harmonic problems, the improvement over continuous ABCs is achieved without any computational overhead, leading to the conclusion that the discrete ABCs should be used in lieu of continuous ABCs.}, number={33-36}, journal={COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING}, author={Thirunavukkarasu, Senganal and Guddati, Murthy N.}, year={2011}, pages={2483–2497} }
 @article{guddati_thirunavukkarasu_2009, title={Phonon absorbing boundary conditions for molecular dynamics}, volume={228}, ISSN={["1090-2716"]}, DOI={10.1016/j.jcp.2009.07.033}, abstractNote={With the goal of minimizing the domain size for molecular dynamics (MD) simulations, we develop a new class of absorbing boundary conditions (ABCs) that mimic the phonon absorption properties of an unbounded exterior. The proposed MD-ABCs are extensions of perfectly matched discrete layers (PMDLs), originally developed as an absorbing boundary condition for continuous wave propagation problems. Called MD-PMDL, this extension carefully targets the absorption of phonons, the high frequency waves, whose propagation properties are completely different from continuous waves. This paper presents the derivation of MD-PMDL for general lattice systems, followed by explicit application to one-dimensional and two-dimensional square lattice systems. The accuracy of MD-PMDL for phonon absorption is proven by analyzing reflection coefficients, and demonstrated through numerical experiments. Unlike existing MD-ABCs, MD-PMDL is local in both space and time and thus more efficient. Based on their favorable properties, it is concluded that MD-PMDL could provide a more effective alternative to existing MD-ABCs.}, number={21}, journal={JOURNAL OF COMPUTATIONAL PHYSICS}, author={Guddati, Murthy N. and Thirunavukkarasu, Senganal}, year={2009}, month={Nov}, pages={8112–8134} }