Browsing by Subject "Finite elements"

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Open Access
NURBS-based non-periodic finite element framework for Kohn-Sham density functional theory calculations
(Elsevier, 2020) Temizer, İlker; Motamarri, P.; Gavini, V.
A real-space non-periodic computational framework is developed for Kohn-Sham density functional theory (DFT). The electronic structure calculation framework is based on the finite element method (FEM) where the underlying basis is chosen as non-uniform rational B-splines (NURBS) which display continuous higher-order derivatives. The framework is formulated within a unified presentation that can simultaneously address both all-electron and pseudopotential settings in radial and three-dimensional cases. The canonical Kohn-Sham equation and the Poisson equation are discretized on different meshes in order to ensure that the underlying variational structural of Kohn-Sham DFT is preserved within the weak formulation of FEM. The discrete generalized eigenvalue problem emanating from the Kohn-Sham equation is solved efficiently based on the Chebyshev-filtered subspace iteration method. Numerical investigations in the radial case demonstrate all-electron and local pseudopotential capabilities on single atoms. In the three-dimensional case, all-electron and nonlocal pseudopotential computations on single atoms and small molecules are followed by local and nonlocal pseudopotential studies on larger systems. At all stages, special care is taken to demonstrate optimal convergence rates towards the ground state energy with chemical accuracy. Comparisons with classical Lagrange basis sets indicate the significantly higher per-degree-of-freedom accuracy displayed by NURBS. Specifically, cubic NURBS discretizations can offer a faster route to a prescribed accuracy than even sixth-order Lagrange discretizations on comparable meshes, thereby indicating considerable efficiency gains which are possible with these higher-order basis sets within effective numerical implementations.
Open Access
Optimizing CMUT geometry for high power
(IEEE, 2010) Yamaner F.Y.; Olcum, Selim; Bozkurt, A.; Köymen, Hayrettin; Atalar, Abdullah
Capacitive micromachined ultrasonic transducers (CMUTs) have demonstratedvarious advantages over piezoelectric transducers. However, current CMUT designsproduce low output pressures with high harmonic distortions. Optimizing thetransducer parameters requires an iterative solution and is too time consumingusing finite element (FEM) modelling tools. In this work, we present a method ofdesigning high output pressure CMUTs with relatively low distortion. We analyzethe behavior of a membrane under high voltage continuous wave operation using anonlinear electrical circuit model. The radiation impedance of an array ofCMUTs is accurately represented using an RLC circuit in the model. The maximummembrane swing without collapse is targeted in the transmit mode. Using SPICEsimulation of the parametric circuit model, we design the CMUT cell withoptimized parameters such as the membrane radius (a), thickness (tm),insulator thickness (ti) and gap height (tg). The modelalso predicts the amount of second harmonic at the output. To verify theaccuracy of the results, we built a FEM model with the same CMUT parameters. Thedesign starts by choosing ti for the given input voltage level.First, a is selected for the maximum radiation resistance of the array at theoperating frequency. Second, tm is found for the resonance at theinput frequency. Third, tg is chosen for the maximum membrane swing.Under this condition, a frequency shift in the resonant frequency occurs. Secondand third steps are repeated until convergence. This method results in a CMUTarray with a high output power and with low distortion. © 2010 IEEE.