Compressed Row Research Articles

Numerical Method for Reliability Analysis of Phased-Mission System Using Markov Chains

This article presents a numerical method for solving continuous time Markov chain (CTMC) model for reliability evaluation of phased-mission system. The method generates infinitesimal matrix based on the statistical independence of subsystem failure and repair process. The infinitesimal generator matrix is stored by the use of sparse matrix-compressed storage schemes, and the transient solution of the CTMC model is obtained by using three methods including the uniformization method, forward Euler method, and Runge-Kutta method, which take advantage of the sparseness of the infinitesimal generator matrix. An example PMS is used to compare the preconditioning methods for sparse matrix and numerical methods. Experiment results show that compressed row storage scheme (CRS) saves more storage than other storage formats, and uniformization method combined with CRS achieves the best efficiency and accuracy.

Two-dimensional cache-oblivious sparse matrix–vector multiplication

In earlier work, we presented a one-dimensional cache-oblivious sparse matrix-vector (SpMV) multiplication scheme which has its roots in one-dimensional sparse matrix partitioning. Partitioning is often used in distributed-memory parallel computing for the SpMV multiplication, an important kernel in many applications. A logical extension is to move towards using a two-dimensional partitioning. In this paper, we present our research in this direction, extending the one-dimensional method for cache-oblivious SpMV multiplication to two dimensions, while still allowing only row and column permutations on the sparse input matrix. This extension requires a generalisation of the compressed row storage data structure to a block-based data structure, for which several variants are investigated. Experiments performed on three different architectures show further improvements of the two-dimensional method compared to the one-dimensional method, especially in those cases where the one-dimensional method already provided significant gains. The largest gain obtained by our new reordering is over a factor of 3 in SpMV speed, compared to the natural matrix ordering.

A set of particle locating algorithms not requiring face belonging to cell connectivity data

Existing efficient directed particle locating (host determination) algorithms rely on the face belonging to cell relationship (F2C) to find the next cell on the search path and the cell in which the target is located. Recently, finite volume methods have been devised which do not need F2C. Therefore, existing search algorithms are not directly applicable (unless F2C is included). F2C is a major memory burden in grid description. If the memory benefit from these finite volume methods are desirable new search algorithms should be devised. In this work two new algorithms (line of sight and closest cell) are proposed which do not need F2C. They are based on the structure of the sparse coefficient matrix involved (stored for example in the compressed row storage, CRS, format) to determine the next cell. Since F2C is not available, testing a cell for the presence of the target is not possible. Therefore, the proposed methods may wrongly mark a nearby cell as the host in some rare cases. The issue of importance of finding the correct host cell (not wrongly hitting its neighbor) is addressed. Quantitative measures are introduced to assess the efficiency of the methods and comparison is made for typical grid types used in computational fluid dynamics. In comparison, the closest cell method, having a lower computational cost than the family of line of sight and the existing efficient maximum dot product methods, gives a very good performance with tolerable and harmless wrong hits. If more accuracy is needed, the method of approximate line of sight then closest cell (LS-A-CC) is recommended.

Concurrent number cruncher: a GPU implementation of a general sparse linear solver

A wide class of numerical methods needs to solve a linear system, where the matrix pattern of non-zero coefficients can be arbitrary. These problems can greatly benefit from highly multithreaded computational power and large memory bandwidth available on graphics processor units (GPUs), especially since dedicated general purpose APIs such as close-to-metal (CTM) (AMD–ATI) and compute unified device architecture (CUDA) (NVIDIA) have appeared. CUDA even provides a BLAS implementation, but only for dense matrices (CuBLAS). Other existing linear solvers for the GPU are also limited by their internal matrix representation. This paper describes how to combine recent GPU programming techniques and new GPU dedicated APIs with high performance computing strategies (namely block compressed row storage (BCRS), register blocking and vectorization), to implement a sparse general-purpose linear solver. Our implementation of the Jacobi-preconditioned conjugate gradient algorithm outperforms by up to a factor of 6.0 × leading-edge CPU counterparts, making it attractive for applications which are content with single precision.

Cache-Oblivious Sparse Matrix–Vector Multiplication by Using Sparse Matrix Partitioning Methods

In this article, we introduce a cache-oblivious method for sparse matrix–vector multiplication. Our method attempts to permute the rows and columns of the input matrix using a recursive hypergraph-based sparse matrix partitioning scheme so that the resulting matrix induces cache-friendly behavior during sparse matrix–vector multiplication. Matrices are assumed to be stored in row-major format, by means of the compressed row storage (CRS) or its variants incremental CRS and zig-zag CRS. The zig-zag CRS data structure is shown to fit well with the hypergraph metric used in partitioning sparse matrices for the purpose of parallel computation. The separated block-diagonal (SBD) form is shown to be the appropriate matrix structure for cache enhancement. We have implemented a run-time cache simulation library enabling us to analyze cache behavior for arbitrary matrices and arbitrary cache properties during matrix–vector multiplication within a k-way set-associative idealized cache model. The results of these simulations are then verified by actual experiments run on various cache architectures. In all these experiments, we use the Mondriaan sparse matrix partitioner in one-dimensional mode. The savings in computation time achieved by our matrix reorderings reach up to 50 percent, in the case of a large link matrix.

A new row-wise parallel finite element analysis algorithm with dynamic load balancing

A parallel scheme is devised to efficiently parallelise all steps of parallel finite element analysis in this study. In addition, this scheme is based on a row-wise matrix distribution. A new row-wise parallel finite element analysis algorithm that exploits the nature of distributed compressed row sparse matrices and multivectors to improve concurrency is developed. A new dynamic load balancing technique has also been devised. The dynamic load balancing technique has been designed specifically to balance the computational workload among processors suitable for the analysis of nonlinear structures. This new algorithm has been implemented in ParaStruc, which is a parallel structural analysis system. Trilinos, a set of parallel numerical libraries developed by researchers in the Sandia National Laboratory has been used to build this algorithm. ParaStruc is a lightweight fully parallelised parallel finite element analysis system, which contains only three classes and a pre-processor. It is shown that this approach produces superior performance in terms of speedup, efficiency, and isoefficiency in the analysis of nonlinear structure response ranges when compared to parallel ABAQUS. The performance and efficiency of this algorithm has been verified with numerical simulations of a 200-metre 50-story 10-frame 10-bay 3D structure subjected to various load levels.

A Hilbert-order multiplication scheme for unstructured sparse matrices

We investigate a new storage format for unstructured sparse matrices based on the space-filling Hilbert curve. Numerical tests with matrix-vector multiplication show the potential of the fractal storage (FS) format in comparison to the traditional compressed row storage (CRS) format. The FS format outperforms the CRS format by up to 50% for matrix-vector multiplications with multiple right hand sides.

On a compact mixed-order finite element for solving the three-dimensional incompressible Navier-Stokes equations

Our work is an extension of the previously proposed multivariant element. We assign this refined element as a compact mixed-order element in the sense that use of this element offers a much smaller bandwidth. The analysis is implemented on quadratic hexahedral elements with a view to analysing a three-dimensional incompressible viscous flow problem using a method formulated within the mixed finite element context. The idea of constructing such a stable element is to bring the marker-and-cell (MAC) grid lay-out to the finite element context. This multivariant element can thus be classified as a discontinuous pressure element. We have several reasons for advocating the proposed multivariant element. The primary advantage gained is its ability to reduce the bandwidth of the matrix equation, as compared with its univariant counterparts, so that it can be effectively stored in a compressed row storage (CRS) format. The resulting matrix equation can be solved efficiently by a multifrontal solver owing to its reduced bandwidth. The coding is, however, complicated by the appearance of restricted degrees of freedom at mid-face nodes. Through analytic study this compact multivariant element has a marked advantage over the multivariant element of Gupta et al. in that both bandwidth and computation time have been drastically reduced. © 1997 John Wiley & Sons, Ltd.

Colorado Potato Beetle Control on Potatoes With In-Furrow Treatments and Microbial InsectiCides, 1996

Abstract ‘Kennebec’ potatoes were planted in 20 foot rows on 8 Apr, ‘96. Plots consisted of single treatment rows. The distance between rows was 64 inches and the distance between plants within the row was 8 inches. Plots were arranged in a RCB design with 4 replications. The soil was a Norfolk ‘A’A loamy sand. Initial furrow treatments were mixed in 208 mis. of water and applied with a CO2 backpack sprayer at the rate of 40 gallons per acre at 30 psi on 8 Apr. Foliar treatments of Novodor were mixed in 1.5 gallons of water and applied with a custom built compressed air row crop sprayer. Each row was covered by 6 drop nozzles delivering 50 gpa at 30 psi. Treatments of Novodor were applied 27 Jun. In evaluating the treatments, direct counts of the number of Colorado potato beetle adults, larvae and egg masses/10 plants and percent defoliation were recorded. Yields were taken on 8 Jul from 20 ft of row.

Colorado Potato Beetle Control on Potatoes With Foliar Insecticide Sprays, 1996

Abstract ‘Red Norland’ potatoes were planted in 20 foot rows on 8 Apr, ‘96. Plots consisted of a single treatment row. The distance between rows was 64 inches and the distance between plants within the row was 10 inches. Plots were arranged in a RCB design with 4 replications. The soil was a Norfolk “A” loamy sand. All spray treatments were mixed in 1.5 gallons of water and applied with a custom built compressed air row crop sprayer. Each row was covered by 6 drop nozzles delivering 50 gpa at 30 psi. Treatments were applied 26 May. Novodor plots were sprayed 24 and 26 May. In evaluating the treatments, direct counts of the number of Colorado potato beetle adults, larvae, egg masses/10 plants and the % defoliation were recorded. Yields were taken on 28 Jun from 20 feet of row.

Colorado Potato Beetle Control on Potatoes With Foliar Insecticide Sprays, 1995

Abstract ‘Red Norland’ potatoes were planted in 20 foot rows on 29 Mar, ’95. Plots consisted of a single treatment row. The distance between rows was 64 inches and the distance between plants within the row was 10 inches. Plots were arranged in a RCB design with 4 replications. The soil was a Norfolk “A” loamy sand. All spray treatments were mixed in 1.5 gallons of water and applied with a custom built compressed air row crop sprayer. Each row was covered by 6 drop nozzles delivering 50 gal/acre at 30 psi. Treatments were applied 23 May and 4 and 12 Jun. Trigard plots were sprayed with Asana XL 0.05 lb (AI)/ acre and PBO 8EC 0.375 (AI)/acre on 12 and 19 Jun. In evaluating the treatments, direct counts of the number of Colorado potato beetle adults, larvae, egg masses/10 plants and the % defoliation were recorded. Defoliation categories were assigned using a pretransformed defoliation rating scale, based on dividing 90° into 13 steps corresponding to arcsin transformation values (Little & Hills 1978). Yields were taken on 26 Jun from 20 feet of row.

Colorado Potato Beetle Control on Potatoes With Microbial Insecticides, 1995

Abstract ‘ Red Norland’ potatoes were planted in 20 foot rows on 29 Mar, ’95. Plots consisted of a single treatment row. The distance between rows was 64 inches and the distance between plants within the row was 10 inches. Plots were arranged in a RCB design with 4 replications. The soil is a Norfolk “A” loamy sand. All spray treatments were mixed in 1.5 gallons of water and applied with a custom built compressed air row crop sprayer. Each row was covered by 6 drop nozzles delivering 50 gallacre at 30 psi. Treatments were applied 19 and 24 May and 4 Jun. Plots were treated with Asana XL 0.05 Ib (AI)/acre and PBO 8EC 0.375 Ib (AI)/acre on 9 and 19 Jun to control Colorado potato beetle adults. In evaluating the treatments, direct counts of the number of CPB adults, larvae, and egg masses110 plants and % defoliation were recorded. Defoliation categories were assigned using a pretransformed defoliation rating scale, based on dividing 90° into 13 steps corresponding to arcsin transformation values (Little & Hills 1978). Yields were taken on 26 Jun from 20 feet of row.

Ultrastructure of spermiogenesis and spermatozoa in the platyhelminthsActinodactylella blanchardi(Temnocephalida, Actinodactylellidae),Didymorchissp. (Temnocephalida, Didymorchidae) andGieysztoriusp. (Dalyelliida, Dalyelliidae), with implications for the phylogeny of the Rhabdocoela

Summary Spermiogenesis and mature sperm in the two temnocephalids Actinodactylella blanchardi and Didymorchis sp. closely resemble those observed in six other temnocephalids reported in the preceeding paper. A dense heel region forms at the base of each basal body, the intercentriolar body splits into two halves, and rotation of the flagellar anchoring apparatus causes compression of one of the two rows of microtubules that lined the zone of differentiation. A region of spiral microtubules in the spermatozoon proximal to the flagellar insertion zone results from the gradual and uneven expansion of the compressed inner row of microtubules. By contrast, in the dalyelliid Gieysztoria sp. the inner compressed row expands evenly and over a very short distance so that no region of spirally arranged microtubules occurs. In both the temnocephalids the proximal end of the spermatozoon terminates after splitting into a number of fine processes containing microtubules, while the dalyelliid terminates with a simple t...

Colorado Potato Beetle Control on Potatoes with Dibrom, 1994

Abstract ‘Kennebec’ potatoes were planted in 20 foot rows on 11 Apr, ‘93. Plots consisted of a single treatment row. The distance between rows was 64 inches and the distance between plants within the row was 10 inches. Plots were arranged in a randomized complete block design with 4 replications. The soil was a Norfolk “A” loamy sand. All spray treatments were mixed in 1.5 gallons of water and applied with a custom built compressed air row crop sprayer. Each row was covered by 6 drop nozzles delivering 50 gal/acre at 30 psi. Treatments were applied 1, 8, 15, 23 and 28 June. In evaluating the treatments, direct counts of the number of Colorado potato beetle adults, larvae and egg masses/10 plants and the % defoliation were recorded. Defoliation categories were assigned using a pretransformed defoliation rating scale, based on dividing 90° into 13 steps corresponding to arcsin transformation values (Little & Hills 1978). Yields were taken on 8 Jul from 20 feet of row.

Colorado Potato Beetle Control on Potatoes with ATI-720, 1994

Abstract ‘Kennebec’ potatoes were planted in 20 foot rows on 11 Apr, ‘94. Plots consisted of a single treatment row. The distance between rows was 64 inches and the distance between plants within the row was 10 inches. Plots were arranged in a randomized complete block design with 4 replications. The soil was a Norfolk “ A ” loamy sand. All spray treatments were mixed in 1.5 gallons of water and applied with a custom built compressed air row crop sprayer. Each row was covered by 6 drop nozzles delivering 50 gal/acre at 30 psi. Treatments were applied 31 May; 8, 15 and 23 Jun. In evaluating the treatments, direct counts of the number of CPB adults, larvae and egg masses/10 plants and the % defoliation were recorded. Defoliation categories were assigned using a pretransformed defoliation rating scale, based on dividing 90° into 13 steps corresponding to arcsin transformation values (Little & Hills 1978). Yields were taken on 8 Jul from 20 feet of row.

Colorado Potato Beetle Control on Potatoes with In-Furrow Treatments, 1994

Abstract ‘Kennebec’ potatoes were planted in 20 foot rows on 25 Apr, ‘94. Plots consisted of a single treatment row. The distance between rows was 64 inches and the distance between plants within the row was 10 inches. Plots were arranged in a randomized complete block design with 4 replications. The soil was a Norfolk "A" loamy sand. Initial furrow treatments were applied to the seed at the rate of 20 gal per acre with a small watering can. Admire foliar treatments were applied at a rate of 50 gal per acre on 8, 23 and 29 Jun with a custom built compressed air row crop sprayer with each row being covered by 6 drop nozzles delivering 50 gal/acre at 30 psi. In evaluating the treatments, direct counts of the number of Colorado potato beetle adults, larvae and egg masses/10 plants and the % defoliation were recorded. Defoliation categories were assigned using a pretransformed defoliation rating scale, based on dividing 90° into 13 steps corresponding to arcsin transformation values (Little & Hills 1978). Yields were taken on 20 Jul from 20-ft of row.

Colorado Potato Beetle Control on Potatoes with Microbial Insecticides, 1994

Abstract ‘Kennebec’ potatoes were planted in 20 foot rows on 11 Apr, ‘94. Plots consisted of a single treatment row. The distance between rows was 64 inches and the distance between plants within the row was 10 inches. Plots were arranged in a randomized complete block design with 4 replications. The soil was a Norfolk “A” loamy sand. All spray treatments were mixed in 1.5 gallons of water and applied with a custom built compressed air row crop sprayer. Each row was covered by 6 drop nozzles delivering 50 gal/acre at 30 psi. Treatments were applied 31 May, and 8 Jun. Plots were treated with Asana XL 0.05 lb Al/A and PBO 8EC 0.375 lb Al/acre on 21 and 28 Jun to control Colorado potato beetle adults. In evaluating the treatments, direct counts of the number of CPB adults, larvae and egg masses/10 plants and the % defoliation were recorded. Defoliation categories were assigned using a pretransformed defoliation rating scale, based on dividing 90° into 13 steps corresponding to arcsin transformation values (Little & Hills 1978). Yields were taken on 8 Jul from 20 feet of row.

Colorado Potato Beetle Control on Potatoes with Foliar Insecticide Sprays, 1994

Abstract ‘Kennebec’ potatoes were planted in 20 foot rows on 11 Apr, ‘93. Plots consisted of a single treatment row. The distance between rows was 64 inches and the distance between plants within the row was 10 inches. Plots were arranged in a randomized complete block design with 4 replications. The soil was a Norfolk “A” loamy sand. All spray treatments were mixed in 1.5 gallons of water and applied with a custom built compressed air row crop sprayer. Each row was covered by 6 drop nozzles delivering 50 gal/acre at 30 psi. Treatments were applied 1, 9, 21 and 29 Jun. On 21 and 29 Jun, Kryocide and Novodor plots were sprayed with Asana XL 0.05 lb Al/acre and PBO 8EC 0.375 lb Al/acre to control adult Colorado Potato Beetle. Abamectin plots were treated with Asana XL 0.05 lb Al/acre and PBO 8EC 0.375 lb Al/acre on 21 Jun to control adult CPB. In evaluating the treatments, direct counts of the number of Colorado potato beetle adults, larvae, egg masses/10 plants and the % defoliation were recorded. Defoliation categories were assigned using a pretransformed defoliation rating scale, based on dividing 90° into 13 steps corresponding to arcsin transformation values (Little & Hills 1978). Yields were taken on 8 Jul from 20 feet of row.

Strain relief and ordering of (2×n)-Bi structure on Si(100)

(2×n)-Bi phases formed on the Si(100) surface are studied using scanning tunneling microscopy and low-energy electron diffraction. A series of well-ordered (2×n) superlattices with n ranging from 5 to 12 are observed, resulting from the ordering of the missing Bi-dimer rows in the (2×1) Bi overlayer. Long stripes of the (2×n) unit meshes separated by missing Bi rows with almost perfect periodicities of n are found to extend through the whole terraces. The periodicity of n in the striped (2×n) structures depends on the Bi coverage and the annealing temperature. The formation of successive phases of the (2×n) structures as a function of coverage and annealing temperatures reflects various strain relief processes in the direction of the compressed Bi-dimer rows by creating missing rows and line dislocations as well as rectangular vacancies. The remarkable long-range ordering of missing Bi rows in the compressed Bi overlayer suggests the presence of strong repulsive long-range elastic interaction among missing Bi-dimer rows.

Colorado Potato Beetle Control on Potatoes, 1993

Abstract ‘Kennebec’ potatoes were planted in 20 foot rows on 8 Apr, ’93. Plots consisted of 5 treatment rows. The distance between rows was 64 inches and the distance between plants within the row was 10 inches. Plots were arranged in a randomized complete block design with 4 replications. The soil was a Norfolk “ A ” loamy sand. All spray treatments were mixed in 1.5 gallons of water and applied with a custom built compressed air row crop sprayer. Each row was covered by 6 drop nozzles delivering 50 gal/acre at 28 psi. Treatments of Admire, Novodor and Vydate were applied 21 May; 2, 9, 16 Jun. Plots receiving Trigard 75WP were treated 21 May at .250 lb Al/acre and 2, 14 Jun at .125 lb Al/acre. Plots receiving Trigard, Novodor, and Vydate were treated with Vydate 2L at 0.75 lb Al/acre on 22 Jun to control Colorado potato beetle adults. In evaluating the treatments, direct counts of the number of Colorado potato beetle adults, larvae and egg mass/ 10 plants and the % defoliation were recorded. Defoliation categories were assigned using a pretransformed defoliation rating scale, based on dividing 90° into 13 steps corresponding to arcsin transformation values (Little & Hill 1978). Yields were taken on 28 Jul from 20 feet of row.