A COARSENING ALGORITHM ON ADAPTIVE GRIDS BY NEWEST VERTEX BISECTION AND ITS APPLICATIONS

In this paper, an efficient and easy-to-implement coarsening algorithm is proposed for adaptive grids obtained using the newest vertex bisection method in two dimemsions. The new coarsening algorithm does not require storing the binary refinement tree explicitly. Instead, the structure is implicitly contained in a special ordering of triangular elements. Numerical experiments demonstrate that the proposed coarsening algorithm is efficient when applied for multilevel preconditioners and mesh adaptivity for time-dependent problems.

Toward Cost-EffectiveReservoir Simulation Solvers on GPUs

In this paper,we focus on graphical processing unit(GPU)and discuss how its architecture affects the choice of algorithm and implementation of fully-implicit petroleum reservoir simulation.In order to obtain satisfactory performance on new many-core architectures such as GPUs,the simulator developers must know a great deal on the specific hardware and spend a lot of time on fine tuning the code.Porting a large petroleum reservoir simulator to emerging hardware architectures is expensive and risky.We analyze major components of an in-house reservoir simulator and investigate how to port them to GPUs in a cost-effective way.Preliminary numerical experiments show that our GPU-based simulator is robust and effective.More importantly,these numerical results clearly identify the main bottlenecks to obtain ideal speedup on GPUs and possibly other many-core architectures.

Biophotonic rogue waves in red blood cell suspensions

Rogue waves are ubiquitous in nature,appearing in a variety of physical systems ranging from acoustics,microwave cavities,optical fibers,and resonators to plasmas,superfluids,and Bose–Einstein condensates.Unlike nonlinear solitary waves,rogue waves are extreme events that can occur even without nonlinearity by,for example,spontaneous synchronization of waves with different spatial frequencies in a linear system.Here,we report the observation of rogue-wave-like events in human red blood cell(RBC)suspensions under weak light illumination,characterized by an abnormal L-shaped probability distribution.Such biophotonic extreme events arise mostly due to the constructive interference of Mie-scattered waves from the suspended RBCs,whose biconcave shape and mutable orientation give rise to a time-dependent random phase modulation to an incident laser beam.We numerically simulate the beam propagation through the colloidal suspensions with added disorder in both spatial and temporal domains to mimic random scattering due to Brownian motion.In addition,at high power levels,nonlinear beam self-focusing is also observed,leading to a dual-exponential probability distribution associated with the formation of multiple soliton-like spots.Such rogue wave events should also exist in environments with cells of other species such as swimming bacteria,and understanding of their underlying physics may lead to unexpected biophotonic applications.

AN ADAPTIVE HYBRID STRESS TRANSITION QUADRILATERAL FINITE ELEMENT METHOD FOR LINEAR ELASTICITY

In this paper, we discuss an adaptive hybrid stress finite element method on quadri- lateral meshes for linear elasticity problems. To deal with hanging nodes arising in the adaptive mesh refinement, we propose new transition types of hybrid stress quadrilateral elements with 5 to 7 nodes. In particular, we derive a priori error estimation for the 5- node transition hybrid stress element to show that it is free from Poisson-locking, in the sense that the error bound in the a priori estimate is independent of the Lam~ constant A. We introduce~ for quadrilateral meshes, refinement/coarsening algorithms, which do not require storing the refinement tree explicitly, and give an adaptive algorithm. Finally, we provide some numerical results.

Plasmonic resonant nonlinearity and synthetic optical properties in gold nanorod suspensions

We experimentally demonstrate self-trapping of light, as a result of plasmonic resonant optical nonlinearity,in both aqueous and organic(toluene) suspensions of gold nanorods. The threshold power for soliton formation is greatly reduced in toluene as opposed to aqueous suspensions. It is well known that the optical gradient forces are optimized at off-resonance wavelengths at which suspended particles typically exhibit a strong positive(or negative) polarizability. However, surprisingly, as we tune the wavelength of the optical beam from a continuous-wave(CW) laser, we find that the threshold power is reduced by more than threefold at the plasmonic resonance frequency. By analyzing the optical forces and torque acting on the nanorods, we show theoretically that it is possible to align the nanorods inside a soliton waveguide channel into orthogonal orientations by using merely two different laser wavelengths. We perform a series of experiments to examine the transmission of the soliton-forming beam itself, as well as the polarization transmission spectrum of a low-power probe beam guided along the soliton channel. It is found that the expected synthetic anisotropic properties are too subtle to be clearly observed, in large part due to Brownian motion of the solvent molecules and a limited ordering region where the optical field from the self-trapped beam is strong enough to overcome thermodynamic fluctuations. The ability to achieve tunable nonlinearity and nanorod orientations in colloidal nanosuspensions with low-power CW laser beams may lead to interesting applications in all-optical switching and transparent display technologies.