Preconditioned Locally Harmonic Residual Method for Computing Interior Eigenpairs of Certain Classes of Hermitian Matrices

We propose a Preconditioned Locally Harmonic Residual (PLHR) method for computing several interior eigenpairs of a generalized Hermitian eigenvalue problem, without traditional spectral transformations, matrix factorizations, or inversions. PLHR is based on a short-term recurrence, easily extended to a block form, computing eigenpairs simultaneously. PLHR can take advantage of Hermitian positive definite preconditioning, e.g., based on an approximate inverse of an absolute value of a shifted matrix, introduced in [SISC, 35 (2013), pp. A696-A718]. Our numerical experiments demonstrate that PLHR is efficient and robust for certain classes of large-scale interior eigenvalue problems, involving Laplacian and Hamiltonian operators, especially if memory requirements are tight

A multiple-try Metropolis-Hastings algorithm with tailored proposals

We present a new multiple-try Metropolis-Hastings algorithm designed to be especially beneficial when a tailored proposal distribution is available. The algorithm is based on a given acyclic graph $G$, where one of the nodes in $G$, $k$ say, contains the current state of the Markov chain and the remaining nodes contain proposed states generated by applying the tailored proposal distribution. The Metropolis-Hastings algorithm alternates between two types of updates. The first update type is using the tailored proposal distribution to generate new states in all nodes in $G$ except in node $k$. The second update type is generating a new value for $k$, thereby changing the value of the current state. We evaluate the effectiveness of the proposed scheme in an example with previously defined target and proposal distributions

Absolute value preconditioning for symmetric indefinite linear systems

We introduce a novel strategy for constructing symmetric positive definite (SPD) preconditioners for linear systems with symmetric indefinite matrices. The strategy, called absolute value preconditioning, is motivated by the observation that the preconditioned minimal residual method with the inverse of the absolute value of the matrix as a preconditioner converges to the exact solution of the system in at most two steps. Neither the exact absolute value of the matrix nor its exact inverse are computationally feasible to construct in general. However, we provide a practical example of an SPD preconditioner that is based on the suggested approach. In this example we consider a model problem with a shifted discrete negative Laplacian, and suggest a geometric multigrid (MG) preconditioner, where the inverse of the matrix absolute value appears only on the coarse grid, while operations on finer grids are based on the Laplacian. Our numerical tests demonstrate practical effectiveness of the new MG preconditioner, which leads to a robust iterative scheme with minimalist memory requirements

Passive Aeroelastic Tailoring

The Passive Aeroelastic Tailoring (PAT) project was tasked with investigating novel methods to achieve passive aeroelastic tailoring on high aspect ratio wings. The goal of the project was to identify structural designs or topologies that can improve performance and/or reduce structural weight for high-aspect ratio wings. This project considered two unique approaches, which were pursued in parallel: through-thickness topology optimization and composite tow-steering

JCuda vectorized and parallelized computation strategy for solving integral equations in electromagnetism on a standard personal computer

International audienceThe paper presents a computation strategy for solving integral equations in electromagnetism. Nowadays, powerful programmable Graphic Processing Units (GPU) can be found in any standard computer. The paper investigates the benefits of the use of GPUs in addition to the CPU one in order to improve computation speed by using integral methods. Java language and the JCuda library, not often used in speed calculation by the computing community, has been used here. A 100 time speed-up is reported in matrix assembly between an optimized traditional CPU computation and a CPU+GPU one. FMM… Index Terms-Fast Multipole Method on GPU, JCuda computing, Pure Java ..

Large eddy simulation of acoustic propagation in turbulent flow through ducts and mufflers

This research involves study of acoustic propagation of pulse in a simple expansion muffler, which is very often used in HVAC or automotive exhausts. A hybrid pressure-based compressible solver is developed and validated for a low Mach number flow simulation of acoustic pulse. This new solver is developed using C++ based OpenFOAM toolkit and further tested for low Mach number flow test case. The analysis of simple expansion muffler for various structures, frequency ranges and numerical schemes is performed and results are summarized. RANS simulation of duct and muffler with mean flow is conducted and results are presented with inherent limitations associated with the method. Further, a mixed synthetic inflow boundary condition is also developed and validated for LES of channel flow. The mixed synthetic boundary is then used for LES of a simple expansion muffler to analyse the flow-acoustic and acoustic-pulse interactions inside the expansion muffler. The improvement in the prediction of tonal noise and vortex shedding inside the chamber is highlighted in comparison to the RANS method. Further, the effect of forced pulsation on flow-acoustic is observed in regard to the shift in Strouhal number inside the simple expansion muffler. Finally, a set of benchmark results for experimental analysis of the simple expansion muffler both, with and without flow is obtained to compare attenuation in forced pulsation for various mean-flow velocities. These experimental results are then used for validation of the proposed pressure-based compressible solver

Fracture Mechanics Analyses for Interface Crack Problems - A Review

Recent developments in fracture mechanics analyses of the interfacial crack problem are reviewed. The intent of the review is to renew the awareness of the oscillatory singularity at the crack tip of a bimaterial interface and the problems that occur when calculating mode mixity using numerical methods such as the finite element method in conjunction with the virtual crack closure technique. Established approaches to overcome the nonconvergence issue of the individual mode strain energy release rates are reviewed. In the recent literature many attempts to overcome the nonconvergence issue have been developed. Among the many approaches found only a few methods hold the promise of providing practical solutions. These are the resin interlayer method, the method that chooses the crack tip element size greater than the oscillation zone, the crack tip element method that is based on plate theory and the crack surface displacement extrapolation method. Each of the methods is validated on a very limited set of simple interface crack problems. However, their utility for a wide range of interfacial crack problems is yet to be established