Reordering Method Research Articles

Three-level hybrid vs. flat MPI on the Earth Simulator: Parallel iterative solvers for finite-element method

An efficient parallel iterative method for finite element method has been developed for symmetric multiprocessor (SMP) cluster architectures with vector processors such as the Earth Simulator. The method is based on a three-level hybrid parallel programming model, including message passing for inter-SMP node communication, loop directives by OpenMP for intra-SMP node parallelization and vectorization for each processing element (PE). Simple 3D linear elastic problems with more than 2.2 × 10 9 DOF have been solved using 3 × 3 block ICCG(0) method with additive Schwarz domain decomposition and PDJDS/CM-RCM reordering on 176 nodes of the Earth Simulator, achieving performance of 3.80 TFLOPS. The PDJDS/CM-RCM reordering method provides excellent vector and parallel performance in SMP nodes. A three-level hybrid parallel programming model outperforms flat MPI in the problems involving large numbers of SMP nodes.

Parallel iterative solvers for sparse linear systems in circuit simulation

For the solution of sparse linear systems from circuit simulation whose coefficient matrices include a few dense rows and columns, a parallel iterative algorithm with distributed Schur complement preconditioning is presented. The parallel efficiency of the solver is increased by transforming the equation system into a problem without dense rows and columns as well as by exploitation of parallel graph partitioning methods. The costs of local, incomplete LU decompositions are decreased by fill-in reducing reordering methods of the matrix and a threshold strategy for the factorization. The efficiency of the parallel solver is demonstrated with real circuit simulation problems on PC clusters.

A Survey on Palette Reordering Methods for Improving the Compression of Color-Indexed Images

Palette reordering is a well-known and very effective approach for improving the compression of color-indexed images. In this paper, we provide a survey of palette reordering methods, and we give experimental results comparing the ability of seven of them in improving the compression efficiency of JPEG-LS and lossless JPEG 2000. We concluded that the pairwise merging heuristic proposed by Memon et al. is the most effective, but also the most computationally demanding. Moreover, we found that the second most effective method is a modified version of Zeng's reordering technique, which was 3%-5% worse than pairwise merging, but much faster.

Extended method for adiabatic mode reordering.

The task of vibrational mode reordering is very important for reaction valley studies and for the determination of small curvature tunneling effects. An extended algorithm for adiabatic mode reordering is presented. It is based on the method introduced by Konkoli et al. [J Comput Chem 1997, 18, 1282], which is shown to suffer from numerical problems in the region of frequency-crossings and avoided crossings. One improvement is the use of cubic splines for the interpolation of the projected matrix of force constants, which allows larger step sizes between the discrete points along the reaction path, where vibrational analysis is performed. The main improvement is the use of perturbation theory to resolve crossings and avoided crossings. Within this theoretical framework it becomes clear why the method of the maximal overlap between the normal modes cannot work properly, as eigenvectors associated with nearby eigenvalues tend to become "wobbly". Thus a perturbative procedure is designed that is used for all cases where two harmonic frequencies approach each other and the overlap of the associated normal modes is of no practical use. Advantages of the new procedure are the use of larger step sizes along the minimum energy path and the much more reliable resolution of mode-crossings and avoided crossings independent of the systems symmetry. In addition to that it is shown that one should be very cautious in all computational situations when working with eigenvectors associated with nearby eigenvalues.

AILU preconditioning for the finite element formulation of the incompressible Navier–Stokes equations

In this paper, the effect of a variable reordering method on the performance of “adapted incomplete LU (AILU)” preconditioners applied to the P2P1 mixed finite element discretization of the three-dimensional unsteady incompressible Navier–Stokes equations has been studied through numerical experiments, where eigenvalue distribution and convergence histories are examined. It has been revealed that the performance of an AILU preconditioner is improved by adopting a variable reordering method which minimizes the bandwidth of a globally assembled saddle-point type matrix. Furthermore, variants of the existing AILU(1) preconditioner have been suggested and tested for some three-dimensional flow problems. It is observed that the AILU(2) outperforms the existing AILU(1) with a little extra computing time and memory.

Parallel iterative solvers for unstructured grids using a directive/MPI hybrid programming model for the GeoFEM platform on SMP cluster architectures

AbstractIn this paper, an efficient parallel iterative method for unstructured grids developed by the authors for shared memory symmetric multiprocessor (SMP) cluster architectures on the GeoFEM platform is presented. The method is based on a three‐level hybrid parallel programming model, including message passing for inter‐SMP node communication, loop directives for intra‐SMP node parallelization and vectorization for each processing element (PE). Simple 3D elastic linear problems with more than $10^8$ degrees of freedom have been solved by $3\times3$ block ICCG(0) with additive Schwarz domain decomposition and PDJDS/CM‐RCM reordering on 16 SMP nodes of a Hitachi SR8000 parallel computer, achieving a performance of 20 Gflops. The PDJDS/CM‐RCM reordering method provides excellent vector and parallel performance in SMP nodes, and is essential for parallelization of forward/backward substitution in IC/ILU factorization with global data dependency. The method developed was also tested on an NEC SX‐4 and attained 969 Mflops (48.5% of peak performance) using a single processor. The additive Schwarz domain decomposition method provides robustness for the GeoFEM parallel iterative solvers with localized preconditioning. Copyright © 2002 John Wiley & Sons, Ltd.

Ordered Semantic Hyper Tableaux

A family of tableau methods, called i>ordered semantic hyper (i>OSH) i>tableau methods for first-order theories with function symbols, is presented. These methods permit semantic information to guide the search for a proof. They also may make use of orderings on literals, clauses, and interpretations to guide the search. In a typical tableau, the branches represent conjunctions of literals, and the tableau represents the disjunction of the branches. An OSH tableau is as usual except that each branch i>B has an interpretation i>I0[i>B] associated with it, where i>I0 is an interpretation supplied at the beginning and i>I0[i>B] is the interpretation most like i>I0 that satisfies i>B. Only clauses that i>I0[i>B] falsifies may be used to expand the branch i>B, thus restricting the kinds of tableau that can be constructed. This restriction guarantees the i>goal sensitivity of these methods if i>I0 is properly chosen. Certain choices of i>I0 may produce a purely bottom-up tableau construction, while others may result in goal-oriented evaluation for a given query. The choices of which branch is selected for expansion and which clause is used to expand this branch are examined and their effects on the OSH tableau methods considered. A branch reordering method is also studied, as well as a branch pruning technique called i>complement modification, that adds additional literals to branches in a soundness-preserving manner. All members of the family of OSH tableaux are shown to be sound, complete, and proof convergent for refutations. Proof convergence means that any allowable sequence of operations will eventually find a proof, if one exists. OSH tableaux are powerful enough to be treated as a generalization of several classes of tableau discussed in the literature, including forward chaining and backward chaining procedures. Therefore, they can be used for efficient query processing.

History-based dynamic BDD minimization

Binary decision diagrams (BDDs) are the state-of-the-art data structure in VLSI CAD. Since their size largely depends on the chosen variable ordering, dynamic variable reordering methods, like sifting, often have to be applied during the construction. Usually sifting is called each time a given node limit is reached and it is therefore called frequently during the creation of large BDDs. Often most of the runtime is spent for sifting while the BDD is built. In this paper we propose an approach to reduce runtime (and space requirement) when constructing BDDs for a given circuit or when computing the set of reachable states in sequential verification. Dependent on the history of the construction process different types of sifting are called. For the BDD construction of combinational circuits we present two methods, one is based on statistics of the unique table, the other one is based on the size reduction of the previous run of sifting. For sequential verification, we propose to select the type of sifting according to the number of iterations processed. Experimental results clearly demonstrate the efficiency of the approach.

Charge-sharing alleviation and detection for CMOS domino circuits

Charge sharing, which occurs in any complementary metal-oxide-semiconductor (CMOS) domino gate, may degrade the output voltage level or may even cause an erroneous output value. In this paper, this problem is thoroughly investigated by considering circuit topology and circuit function. We describe a method to measure the sensitivity [called charge-sharing (CS) vulnerability] of the CS problem for each domino gate. A method to derive the CS vulnerability and the test vector for each domino gate is suggested. We also propose a transistor reordering method to dramatically reduce the CS vulnerabilities for all domino gates so that the CS problem can be alleviated. We also prove theoretically that a set of test vectors generated for single charge-sharing faults (SCSFs) can also detect all multiple charge-sharing faults (MCSFs). This good property significantly guarantees the test quality for the CS faults of domino circuits.

Improving the finite element ordering for the frontal solver

ABSTRACT We present the structure of greedy methods used for reordering the nodes or the finite elements of a mesh and we propose two improvements that can be easily implemented in existing software. We investigate a wave reordering method which adapts the reordering strategy during the reordering process. Then, we propose an adaptation of the Tabu Search optimization technique for finite element reordering. The results show the efficiency of the improvements The wave reordering method and the Tabu Search provide very good solutions offering a motivation to carry on research for optimizing their computing time.

Hybrid ordered phase encoding (HOPE): an improved approach for respiratory artifact reduction.

Respiration causes continuous change in cardiac position, which leads to image degradation. Phase-encode reordering methods are often used to reduce these artifacts. An improved method for suppressing motion artifacts by reordering the acquisition of k space has been developed that is less sensitive to change of breathing patterns and bulk movement. We describe the theory behind the new approach and compare its results with those of existing methods by use of a phantom with simulated and actual acquired breathing patterns. The comparison was also made in vivo; cardiac scans were performed in 15 subjects with image planes that are known to be particularly susceptible to respiratory artifact. A significant improvement in image quality was achieved compared with conventional nonreordered and existing reordering methods.

Phase-encode reordering to minimize errors caused by motion.

A new method for suppressing the effects of motion in MR images by reordering the acquisition of k space has been developed. Existing reordering methods suffer from image blurring. The method presented here applies specifically to translation along the phase-encoding direction, in which case it reduces both ghosting and blurring. The method is conceptually similar to a linear phase shift of k space, except that it has the advantage of not corrupting stationary structures inadvertently. The method is intended for anatomic sites in which substantial translational motion occurs along the phase-encoding direction, such as the cranial-caudal motion of the liver and kidneys. The reordering method is motivated from an analysis of factors affecting the severity of motion artifacts. The theory behind the reordering method is described and validated experimentally by imaging a moving phantom.

Comparing the FAISE method with conventional dual‐echo sequences

The FAISE (fast-acquisition interleaved spin-echo) technique consists of a hybrid rapid-acquisition relaxation-enhanced (RARE) sequence combined with a specific phase-encode reordering method. Implemented on a 1.5-T unit, this multisection, high-resolution technique permits convenient contrast manipulation similar to that of spin-echo imaging, with selection of a pseudo-echo-time parameter and a TR interval. With a TR of 2 seconds, eight 256 x 256 images are obtained in 34 seconds with either T2 or proton-density weighting. A direct comparison between FAISE and spin echo for obtaining T2-weighted head images in healthy subjects indicates that FAISE and spin-echo images are qualitatively and quantitatively similar. Image artifacts are more pronounced on "proton-density" FAISE images than on the T2-weighted FAISE images. T1 contrast can be obtained with inversion recovery and short TR FAISE images. Preliminary temperature measurements in saline phantoms do not indicate excessive temperature increases with extended FAISE acquisitions. However, extensive studies of radio-frequency power deposition effects should be performed if the FAISE technique is to be fully exploited.

Preconditioned biconjugate gradient methods for numerical reservoir simulation

This paper describes numerical experiments on solving linear systems of equations that arise in reservoir simulations. The well-known conjugate-gradient methods Orthomin and Gmres are compared to the biconjugate-gradient method and to an accelerated version called the conjugate-gradient squared method. An incomplete factorization technique based on the level of fill-in idea is used, with investigations to find the appropriate level. Finally, the influence of a reordering method on the convergence rate is tested.