Memory Savings Research Articles

Extended State-Space Finite-Element Formulation to Incorporate Frequency Dependent Surface Models in Time Domain

This study proposes a finite-element formulation that can incorporate the frequency dispersive effects of surfaces composed of fine geometric details without the necessity of generating a refined mesh to capture these details. The finite-element formulation is recast as a state-space model in time domain and the surface is replaced by its own macroscopic state-space model being part of the whole system of equations to be solved. Examples of metallic surfaces containing small circular holes and slots have been successfully implemented. Simulations of these structures have shown memory savings to one tenth and CPU time reduction to one percent.

A memory-efficient parallel routing lookup model with fast updates

Routing lookup, as a core function of routers for forwarding and filtering packets, has confronted with serious challenges nowadays, ranging from memory efficiency, update performance and throughput. Rather than seeking optimization techniques for the traditional lookup model, this paper presents a brand-new parallel lookup model, named Split Routing Lookup Model. In consideration of partial similarities among prefixes, we split all prefixes to produce redundancies, which are then removed during information integration. After that, the on-chip structure is compressed sharply. Besides, by such “splitting”, route updates are diverged to be more targeted, and the lookup process is also decomposed to support parallel processing.With 14 real-world routing data, the proposed model is evaluated through 4 classic trie-based approaches, in comparison with their traditional implementations. The encouraging results show the superiorities of the proposed model in a comprehensive view. The on-chip memory savings are up to 99.2% and 94.8% for IPv4/6 respectively. While the reduction of update overhead, even in the worst case, is 50% and 30% respectively. Moreover, the pipeline depth is also reduced by 25–50%. Besides, another 2 techniques are selected to evaluate the proposed model on the virtual router platform. According to the results, based on the proposed model, 160KB on-chip memory is enough to store 14 virtual routers, each consuming only 11KB on average. In this way, the scalability of the proposed model to virtual routers is also clearly demonstrated.

Direct Doppler broadening in Monte Carlo simulations using the multipole representation

A new approach for direct Doppler broadening of nuclear data in Monte Carlo simulations is proposed based on the multipole representation. The multipole representation transforms resonance parameters into a set of poles and residues only some of which exhibit a resonant behavior. A method is introduced to approximate the contribution to the background cross section in an effort to reduce the number of poles needing to be broadened. The multipole representation results in memory savings of 1–2 orders of magnitude over comparable techniques. This approach provides a simple way of computing nuclear data at any temperature which is essential for multi-physics calculations, while having a minimal memory footprint which is essential for scalable high performance computing. The concept is demonstrated on two major isotopes of uranium (U-235 and U-238) and implemented in the OpenMC code. Two LEU critical experiments were solved and showed great accuracy with a small loss of efficiency (10–30%) over a single-temperature pointwise library.

Factorization in large-scale many-body calculations

One approach for solving interacting many-fermion systems is the configuration-interaction method, also sometimes called the interacting shell model, where one finds eigenvalues of the Hamiltonian in a many-body basis of Slater determinants (antisymmetrized products of single-particle wavefunctions). The resulting Hamiltonian matrix is typically very sparse, but for large systems the nonzero matrix elements can nonetheless require terabytes or more of storage. An alternate algorithm, applicable to a broad class of systems with symmetry, in our case rotational invariance, is to exactly factorize both the basis and the interaction using additive/multiplicative quantum numbers; such an algorithm recreates the many-body matrix elements on the fly and can reduce the storage requirements by an order of magnitude or more. We discuss factorization in general and introduce a novel, generalized factorization method, essentially a ‘double-factorization’ which speeds up basis generation and set-up of required arrays. Although we emphasize techniques, we also place factorization in the context of a specific (unpublished) configuration-interaction code, BIGSTICK, which runs both on serial and parallel machines, and discuss the savings in memory due to factorization.

Continuous baseline growth and monitoring for guided wave SHM

It has been shown by many authors that temperature effect compensation is a necessity for the realization of a reliable structural health monitoring (SHM) system. However, there exist practical issues related to the acquisition of baseline signals, required for temperature compensation methods to work effectively, such as degenerate baseline signals recorded at the same temperature and a long acquisition period before monitoring is started. An alternative approach for the acquisition of baseline signals is presented in this paper. The algorithm makes the acquisition an evolutionary process, integrated in the damage detection procedures. The algorithm is shown to be successful in generating a concise set of baselines that guarantees efficient performance of temperature compensation methods, leading to computation time and computer memory savings. Its capabilities in detecting simulated abrupt and slowly evolving damages have also been tested.

The effects of mapping CT images to Monte Carlo materials on GEANT4 proton simulation accuracy

Monte Carlo simulations of radiation therapy require conversion from Hounsfield units (HU) in CT images to an exact tissue composition and density. The number of discrete densities (or density bins) used in this mapping affects the simulation accuracy, execution time, and memory usage in GEANT4 and other Monte Carlo code. The relationship between the number of density bins and CT noise was examined in general for all simulations that use HU conversion to density. Additionally, the effect of this on simulation accuracy was examined for proton radiation. Relative uncertainty from CT noise was compared with uncertainty from density binning to determine an upper limit on the number of density bins required in the presence of CT noise. Error propagation analysis was also performed on continuously slowing down approximation range calculations to determine the proton range uncertainty caused by density binning. These results were verified with Monte Carlo simulations. In the presence of even modest CT noise (5 HU or 0.5%) 450 density bins were found to only cause a 5% increase in the density uncertainty (i.e., 95% of density uncertainty from CT noise, 5% from binning). Larger numbers of density bins are not required as CT noise will prevent increased density accuracy; this applies across all types of Monte Carlo simulations. Examining uncertainty in proton range, only 127 density bins are required for a proton range error of <0.1 mm in most tissue and <0.5 mm in low density tissue (e.g., lung). By considering CT noise and actual range uncertainty, the number of required density bins can be restricted to a very modest 127 depending on the application. Reducing the number of density bins provides large memory and execution time savings in GEANT4 and other Monte Carlo packages.

G-Tries: a data structure for storing and finding subgraphs

The ability to find and count subgraphs of a given network is an important non trivial task with multidisciplinary applicability. Discovering network motifs or computing graphlet signatures are two examples of methodologies that at their core rely precisely on the subgraph counting problem. Here we present the g-trie, a data-structure specifically designed for discovering subgraph frequencies. We produce a tree that encapsulates the structure of the entire graph set, taking advantage of common topologies in the same way a prefix tree takes advantage of common prefixes. This avoids redundancy in the representation of the graphs, thus allowing for both memory and computation time savings. We introduce a specialized canonical labeling designed to highlight common substructures and annotate the g-trie with a set of conditional rules that break symmetries, avoiding repetitions in the computation. We introduce a novel algorithm that takes as input a set of small graphs and is able to efficiently find and count them as induced subgraphs of a larger network. We perform an extensive empirical evaluation of our algorithms, focusing on efficiency and scalability on a set of diversified complex networks. Results show that g-tries are able to clearly outperform previously existing algorithms by at least one order of magnitude.

Ideal evolution of magnetohydrodynamic turbulence when imposing Taylor-Green symmetries

We investigate the ideal and incompressible magnetohydrodynamic (MHD) equations in three space dimensions for the development of potentially singular structures. The methodology consists in implementing the fourfold symmetries of the Taylor-Green vortex generalized to MHD, leading to substantial computer time and memory savings at a given resolution; we also use a regridding method that allows for lower-resolution runs at early times, with no loss of spectral accuracy. One magnetic configuration is examined at an equivalent resolution of 6144(3) points and three different configurations on grids of 4096(3) points. At the highest resolution, two different current and vorticity sheet systems are found to collide, producing two successive accelerations in the development of small scales. At the latest time, a convergence of magnetic field lines to the location of maximum current is probably leading locally to a strong bending and directional variability of such lines. A novel analytical method, based on sharp analysis inequalities, is used to assess the validity of the finite-time singularity scenario. This method allows one to rule out spurious singularities by evaluating the rate at which the logarithmic decrement of the analyticity-strip method goes to zero. The result is that the finite-time singularity scenario cannot be ruled out, and the singularity time could be somewhere between t=2.33 and t=2.70. More robust conclusions will require higher resolution runs and grid-point interpolation measurements of maximum current and vorticity.

On MLMDA/Butterfly Compressibility of Inverse Integral Operators

The multilevel matrix decomposition algorithm (MLMDA) is shown to permit effective compression of inverse integral operators pertinent to the analysis of scattering from electrically large structures. Observed compression ratios exceed those realized by low-rank (LR) compression methods, leading to substantial memory savings and a faster application of the inverse operator, and suggesting a new application for schemes traditionally used for compressing forward integral operators.

Abstract pathfinder

We present Abstract Pathfinder, an extension to the Java Pathfinder (JPF) verification tool-set that supports data abstraction to reduce the large data domains of a Java program to small, finite abstract domains, making the program more amenable to verification. We use data abstraction to compute an over-approximation of the original program in such a way that if a (safety) property is true in the abstracted program the property is also true in the original program. Our approach enhances JPF with an abstract interpreter and abstract state-matching mechanisms, together with a library of abstractions from which the user can pick which abstractions to use for a particular application. We discuss the details of our implementation together with some preliminary experiments with analyzing multi-threaded Java programs, where Abstract Pathfinder achieves significant time and memory savings as compared with plain JPF.

Automatic code overlay generation and partially redundant code fetch elimination

There is an increasing interest in explicitly managed memory hierarchies, where a hierarchy of distinct memories is exposed to the programmer and managed explicitly in software. These hierarchies can be found in typical embedded systems and an emerging class of multicore architectures. To run an application that requires more code memory than the available higher-level memory, typically an overlay structure is needed. The overlay structure is generated manually by the programmer or automatically by a specialized linker. Manual code overlaying requires the programmer to deeply understand the program structure for maximum memory savings as well as minimum performance degradation. Although the linker can automatically generate the code overlay structure, its memory savings are limited and it even brings significant performance degradation because traditional techniques do not consider the program context. In this article, we propose an automatic code overlay generation technique that overcomes the limitations of traditional automatic code overlaying techniques. We are dealing with a system context that imposes two distinct constraints: (1) no hardware support for address translation and (2) a spatially and temporally coarse grained faulting mechanism at the function level. Our approach addresses those two constraints as efficiently as possible. Our technique statically computes the Worst-Case Number of Conflict misses (WCNC) between two different code segments using path expressions. Then, it constructs a static temporal relationship graph with the WCNCs and emits an overlay structure for a given higher-level memory size. We also propose an inter-procedural partial redundancy elimination technique that minimizes redundant code copying caused by the generated overlay structure. Experimental results show that our approach is promising.

Mesoscopic Simulation of Rarefied Flow in Narrow Channels and Porous Media

Rarefied gas flow in channels and computer-aided reconstructions of porous media is simulated using the direct simulation Monte Carlo (DSMC) method and a modified lattice-Boltzmann (LB) method that can account for rarefaction effects. An increase of two orders of magnitude was noted for the gas permeability as the Knudsen number increased from 0.1 to 10. It was found that incorporation of a Bosanquet expression for the viscosity in the dusty gas flux equations leads to the recovery of the well known Klinkenberg expression for the gas permeability, revealing an explicit relation of the, thus far empirical, permeability correction factor to the fluid and structure properties. The expression for the effective gas viscosity in the transition flow regime is also incorporated in the LB method, which is then validated against the DSMC method by comparing predictions for the velocity profiles in straight channels over the entire transition flow regime. The new LB method offers the additional advantages of simplicity in the code implementation and great savings in computational time and memory compared to the DSMC method. It is shown that the rough adjustment of a single parameter suffices to make the LB method suitable for the reliable prediction of the gas permeability in porous media over the entire transition flow regime.

An algorithm on fairness verification of mobile sink routing in wireless sensor network

Congestion and starvation will occur among some nodes due to the emerging serious unfairness, which is derived from the limited communication capabilities of all nodes and sink or in the case of a mobile sink moving to a new place. The problem to be solved is to balance the network and keep the fairness for all nodes. For this purpose, this paper focuses on verifying the fairness of mobile sink routing based on both state and action, which is realized mainly by composing Labeled Kripke Transition Systems (LKTS). First, an approach is presented by LKTS to model node behaviors. Second, a notion of Fair Computational Tree Logic (CTL) is introduced to describe the fairness formulae in branching time transitions, and four kinds of fairness assumptions are defined for fairness verification. Moreover, in order to avoid the problem of state-space explosion, Bounded model Checking to explore states and transitions on-the-fly until a witness is found, while Strong Connected Components algorithm is used to pick up fair paths under fairness constraints of Fair CTL. The experimental results show the superiority of our method by the savings in memory and time consumptions during the mobile sink routing process.

Exploiting sparseness in de novo genome assembly

BackgroundThe very large memory requirements for the construction of assembly graphs for de novo genome assembly limit current algorithms to super-computing environments.MethodsIn this paper, we demonstrate that constructing a sparse assembly graph which stores only a small fraction of the observed k-mers as nodes and the links between these nodes allows the de novo assembly of even moderately-sized genomes (~500 M) on a typical laptop computer.ResultsWe implement this sparse graph concept in a proof-of-principle software package, SparseAssembler, utilizing a new sparse k-mer graph structure evolved from the de Bruijn graph. We test our SparseAssembler with both simulated and real data, achieving ~90% memory savings and retaining high assembly accuracy, without sacrificing speed in comparison to existing de novo assemblers.

On Assurance of Information Security using Elliptic Curves Cryptosystems

We present in this paper an important area of information security emerged in the last decades, namely Elliptic Curves Cryptosystems (ECC). Compared to traditional public-key cryptosystems like RSA or Diffie-Hellman, ECC offers equivalent security with smaller key sizes; these result in faster computations, lower power consumption, as well as memory and bandwidth savings. ECC are more and more considered as an attractive public-key cryptosystem for mobile/wireless environments. ECC are especially useful for mobile devices, which are typically limited in terms of their CPU, power and network connectivity. ECC are the next frontier in the use of security mechanisms by providing good security margins with lower computational cost. ECC's domain is an important field emerged in information security. The elliptic curves (EC) are used for conceiving efficient factorization algorithms and for proving the primality. They are used in public key cryptosystems and in pseudorandom bit generators, too. The elliptic curves were also applied in Codes Theory, where they were used to create very good error protected codes. In this paper, our aim is to examine the security, implementation and performance of ECC applications on various mobile devices. Also, our goal is to compare ECC and conventional PKC performances. Doing these, we want to prove that ECC could become the next-generation of PKC.

Parallel Jacobian-free Newton Krylov solution of the discrete ordinates method with flux limiters for 3D radiative transfer

The present study introduces a parallel Jacobian-free Newton Krylov (JFNK) general minimal residual (GMRES) solution for the discretized radiative transfer equation (RTE) in 3D, absorbing, emitting and scattering media. For the angular and spatial discretization of the RTE, the discrete ordinates method (DOM) and the finite volume method (FVM) including flux limiters are employed, respectively. Instead of forming and storing a large Jacobian matrix, JFNK methods allow for large memory savings as the required Jacobian-vector products are rather approximated by semiexact and numerical formulations, for which convergence and computational times are presented. Parallelization of the GMRES solution is introduced in a combined memory-shared/memory-distributed formulation that takes advantage of the fact that only large vector arrays remain in the JFNK process. Results are presented for 3D test cases including a simple homogeneous, isotropic medium and a more complex non-homogeneous, non-isothermal, absorbing–emitting and anisotropic scattering medium with collimated intensities. Additionally, convergence and stability of Gram–Schmidt and Householder orthogonalizations for the Arnoldi process in the parallel GMRES algorithms are discussed and analyzed. Overall, the introduction of JFNK methods results in a parallel, yet scalable to the tested 2048 processors, and memory affordable solution to 3D radiative transfer problems without compromising the accuracy and convergence of a Newton-like solution.

Conformal mapping for the Helmholtz equation: Acoustic wave scattering by a two dimensional inclusion with irregular shape in an ideal fluid

The complex variables method with mapping function was extended to solve the linear acoustic wave scattering by an inclusion with sharp/smooth corners in an infinite ideal fluid domain. The improved solutions of Helmholtz equation, shown as Bessel function with mapping function as the argument and fractional order Bessel function, were analytically obtained. Based on the mapping function, the initial geometry as well as the original physical vector can be transformed into the corresponding expressions inside the mapping plane. As all the physical vectors are calculated in the mapping plane (η,η), this method can lead to potential vast savings of computational resources and memory. In this work, the results are validated against several published works in the literature. The different geometries of the inclusion with sharp corners based on the proposed mapping functions for irregular polygons are studied and discussed. The findings show that the variation of angles and frequencies of the incident waves have significant influence on the bistatic scattering pattern and the far-field form factor for the pressure in the fluid.

Segmented-Locally-One-Dimensional-FDTD Method for EM Propagation Inside Large Complex Tunnel Environments

We propose a novel segmented locally one dimensional finite difference time domain (S-LOD-FDTD) method for modeling the electromagnetic wave propagation inside electrically large tunnels. The proposed S-LOD-FDTD method reduces the computational resources by dividing the problem space into segments. To validate this method, we simulate the propagation in real tunnels and compare the results with the published measured data. The comparisons reveal that the proposed method can predict the fields accurately in real, large tunnels at longer ranges with significant savings in execution time and memory.

Applying a metadata level for concurrency in wireless sensor networks

SUMMARYAchieving a clean separation of concerns is a well known approach to improving system adaptability and evolution. We propose to apply this principle to run‐time reconfigurable component models for networked embedded systems. By separating configuration properties from runtime component instances, we achieve: (i) improved support for concurrent component use, (ii) optimized resource use, and (iii) reduced effort in runtime configuration management. We demonstrate how this approach can be seamlessly implemented on existing component models for wireless sensor networks without imposing additional constraints and without changes to their API or coordination model. Furthermore, significant memory savings are achieved in concurrent scenarios. Copyright © 2012 John Wiley &amp; Sons, Ltd.

Lean Algebraic Multigrid (LAMG): Fast Graph Laplacian Linear Solver

Laplacian matrices of graphs arise in large-scale computational applications such as semisupervised machine learning; spectral clustering of images, genetic data, and web pages; transportation network flows; electrical resistor circuits; and elliptic partial differential equations discretized on unstructured grids with finite elements. A lean algebraic multigrid (LAMG) solver of the symmetric linear system $Ax=b$ is presented, where $A$ is a graph Laplacian. LAMG's run time and storage are empirically demonstrated to scale linearly with the number of edges. LAMG consists of a setup phase, during which a sequence of increasingly coarser Laplacian systems is constructed, and an iterative solve phase using multigrid cycles. General graphs pose algorithmic challenges not encountered in traditional multigrid applications. LAMG combines a lean piecewise-constant interpolation, judicious node aggregation based on a new node proximity measure (the affinity), and an energy correction of coarse-level systems. This results in fast convergence and substantial setup and memory savings. A serial LAMG implementation scaled linearly for a diverse set of 3774 real-world graphs with up to 47 million edges, with no parameter tuning. LAMG was more robust than the UMFPACK direct solver and combinatorial multigrid (CMG), although CMG was faster than LAMG on average. Our methodology is extensible to eigenproblems and other graph computations.