Search

Abstract: The paper introduces a high-order, adaptive finite-element method for simulation of sonic measurements acquired with borehole-eccentered logging instruments. The resulting frequency-domain based algorithm combines a Fourier series expansion in one spatial dimension with a two-dimensional high-order adaptive finite-element method (FEM), and incorporates a perfectly matched layer (PML) for truncation of the computational domain. The simulation method was verified for various model problems, including a comparison to a semi-analytical solution developed specifically for this purpose. Numerical results indicate that for a wireline sonic tool operating in a fast formation, the main propagation modes are insensitive to the distance from the center of the tool to the center of the borehole (eccentricity distance). However, new flexural modes arise with an increase in eccentricity distance. In soft formations, we identify a new dipole tool mode which arises as a result of tool eccentricity. [Copyright &y& Elsevier]

Abstract: Vesicles are locally-inextensible fluid membranes that can sustain bending. In this paper, we extend the study of Veerapaneni et al. [S.K. Veerapaneni, D. Gueyffier, G. Biros, D. Zorin, A numerical method for simulating the dynamics of 3D axisymmetric vesicles suspended in viscous flows, Journal of Computational Physics 228 (19) (2009) 7233–7249] to general non-axisymmetric vesicle flows in three dimensions. Although the main components of the algorithm are similar in spirit to the axisymmetric case (spectral approximation in space, semi-implicit time-stepping scheme), important new elements need to be introduced for a full 3D method. In particular, spatial quantities are discretized using spherical harmonics, and quadrature rules for singular surface integrals need to be adapted to this case; an algorithm for surface reparameterization is needed to ensure stability of the time-stepping scheme, and spectral filtering is introduced to maintain reasonable accuracy while minimizing computational costs. To characterize the stability of the scheme and to construct preconditioners for the iterative linear system solvers used in the semi-implicit time-stepping scheme, we perform a spectral analysis of the evolution operator on the unit sphere. By introducing these algorithmic components, we obtain a time-stepping scheme that circumvents the stability constraint on the time-step and achieves spectral accuracy in space. We present results to analyze the cost and convergence rates of the overall scheme. To illustrate the applicability of the new method, we consider a few vesicle-flow interaction problems: a single vesicle in relaxation, sedimentation, shear flows, and many-vesicle flows. [Copyright &y& Elsevier]

Abstract: Particle simulations in fields ranging from biochemistry to astrophysics require the evaluation of interactions between all pairs of particles separated by less than some fixed interaction radius. The applicability of such simulations is often limited by the time required for calculation, but the use of massive parallelism to accelerate these computations is typically limited by inter-processor communication requirements. Recently, Snir [M. Snir, A note on N-body computations with cutoffs, Theor. Comput. Syst. 37 (2004) 295–318] and Shaw [D.E. Shaw, A fast, scalable method for the parallel evaluation of distance-limited pairwise particle interactions, J. Comput. Chem. 26 (2005) 1318–1328] independently introduced two distinct methods that offer asymptotic reductions in the amount of data transferred between processors. In the present paper, we show that these schemes represent special cases of a more general class of methods, and introduce several new algorithms in this class that offer practical advantages over all previously described methods for a wide range of problem parameters. We also show that several of these algorithms approach an approximate lower bound on inter-processor data transfer. [Copyright &y& Elsevier]