Sparse Equation Solver Research Articles

An Azimuth Signal-Reconstruction Method Based on Two-Step Projection Technology for Spaceborne Azimuth Multi-Channel High-Resolution and Wide-Swath SAR

Azimuth non-uniform signal-reconstruction is a critical step for azimuth multi-channel high-resolution wide-swath (HRWS) synthetic aperture radar (SAR) data processing. However, the received non-uniform signal has noise in the actual azimuth multi-channel SAR (MCSAR) operation, which leads to the serious reduction in the signal-to-noise ratio (SNR) of the results processed by a traditional reconstruction algorithm. Aiming to address the problem of reducing the SNR of the traditional reconstruction algorithm in the reconstruction of non-uniform signal with noise, a novel signal-reconstruction algorithm based on two-step projection technology (TSPT) for the MCSAR system is proposed in this paper. The key part of the TSPT algorithm consists of a two-step projection. The first projection is to project the given signal into the selected intermediate subspace, spanned by the integer conversion of the compact support kernel function. This process generates a set of sparse equations, which can be solved efficiently by using the sparse equation solver. The second key projection is to project the first projection result into the subspace of the known sampled signal. The secondary projection can be achieved with a digital linear translation invariant (LSI) filter and generate a uniformly spaced signal. As a result, compared with the traditional azimuth MCSAR signal-reconstruction algorithm, the proposed algorithm can improve SNR and reduce the azimuth ambiguity-signal-ratio (AASR). The processing results of simulated data and real raw data verify the effectiveness of the proposed algorithm.

A Comparative Study on Different Parallel Solvers for Nonlinear Analysis of Complex Structures

The parallelization of 2D/3D software SAPTIS is discussed for nonlinear analysis of complex structures. A comparative study is made on different parallel solvers. The numerical models are presented, including hydration models, water cooling models, modulus models, creep model, and autogenous deformation models. A finite element simulation is made for the whole process of excavation and pouring of dams using these models. The numerical results show a good agreement with the measured ones. To achieve a better computing efficiency, four parallel solvers utilizing parallelization techniques are employed: (1) a parallel preconditioned conjugate gradient (PCG) solver based on OpenMP, (2) a parallel preconditioned Krylov subspace solver based on MPI, (3) a parallel sparse equation solver based on OpenMP, and (4) a parallel GPU equation solver. The parallel solvers run either in a shared memory environment OpenMP or in a distributed memory environment MPI. A comparative study on these parallel solvers is made, and the results show that the parallelization makes SAPTIS more efficient, powerful, and adaptable.

A parallel procedure for nonlinear analysis of reinforced concrete three-dimensional frames

The paper discusses the parallelisation of complex three-dimensional software for nonlinear analysis of R/C buildings structures. It presents a comparative study for handling the nonlinear response in different parallel architectures. The nonlinear finite element model adopts a fiber decomposition approach for the cross-section of beam elements to capture nonlinear behavior of concrete. The parallelisation strategy is designed regarding three items: the numerical stability of the nonlinear procedure, the parallel sparse equation solver and the application on heterogeneous hardware: dedicated shared memory machines or clusters of networked personal computers.

Algorithms and Application of Sparse Matrix Assembly and Equation Solvers for Aeroacoustics

An algorithm for symmetric sparse equation solutions on an unstructured grid is described. Efficient, sequential sparse algorithms for degree-of-freedom reordering, supernodes, symbolic/numerical factorization, and forward backward solution phases are reviewed. Three sparse algorithms for the generation and assembly of symmetric systems of matrix equations are presented. The accuracy and numerical performance of the sequential version of the sparse algorithms are evaluated over the frequency range of interest in a three-dimensional aeroacoustics application. Results show that the solver solutions are accurate using a discretization of 12 points per wavelength. Results also show that the first assembly algorithm is impractical for high-frequency noise calculations. The second and third assembly algorithms have nearly equal performance at low values of source frequencies, but at higher values of source frequencies the third algorithm saves CPU time and RAM. The CPU time and the RAM required by the second and third assembly algorithms are two orders of magnitude smaller than that required by the sparse equation solver. A sequential version of these sparse algorithms can, therefore, be conveniently incorporated into a substructuring for domain decomposition formulation to achieve parallel computation, where different substructures are handles by different parallel processors.

Three-Dimensional Rectangular Duct Code with Application to Impedance Eduction

A zero flow, fully three-dimensional, variable impedance, rectangular duct aeroacoustics code that spans the frequency spectrum of interest in duct liner research is developed. The governing equations and boundary conditions in the duct are solved numerically using the finite element methodology. The methodology makes use of a state-of-the-art, sparse equation solver to obtain the capability to study high-frequency sound waves that may require millions of grid points for resolution. Noise suppression levels predicted from the code are in excellent agreement with those obtained from mode theory. The single-processor performance of the solver, relative to that of the more commonly used band solver, increases with frequency. At a frequency of 17 kHz, the band solver is 4.25 times slower and consumes 2.5 times more memory than the fully sparse equation solver. The duct aeroacoustics code is combined with an optimization algorithm and used successfully to educe the impedance spectrum of a ceramic liner. The primary problem with using the methodology to perform optimization studies at frequencies above 14 kHz is excessive central processor unit time. The results support the recommendation that research be directed toward exploitation of the multiprocessor capability of the solver to further reduce central processor unit time.

Sensitivity analysis of frictional contact/ impact response on distributed-memory computers

Multilevel parallel computational strategies are presented for predicting the frictional contact/impact response and evaluating the sensitivity coefficients of axisymmetric composite structures. Both implicit and explicit temporal integration techniques are considered. For implicit techniques, parallelism is exploited in both the spatial and temporal domains. Spatial parallelism is achieved by using a parallel sparse equation solver based on a nested dissection node-ordering scheme. The explicit techniques exploit parallelism using both an element-based domain decomposition strategy, as well as concurrent evaluation of sensitivity coefficients. Implementations of the strategies on distributed-memory computers are described. The strategies are applied to the problem of an axisymmetric composite spherical cap impacting a rigid surface, and the performance characteristics are assessed on the IBM SP2 and the Cray T3D parallel computer systems.

Sensitivity analysis for large-deflection and postbuckling responses on distributed-memory computers

A computational strategy is presented for calculating sensitivity coefficients for the non-linear large-deflection and postbuckling responses of laminated composite structures on distributed-memory parallel computers. The strategy is applicable to any message-passing distributed computational environment. The key elements of the proposed strategy are: (a) a multiple-parameter reduced basis technique; (b) a parallel sparse equation solver based on a nested dissection (or multilevel substructuring) node ordering scheme; and (c) a multilevel parallel procedure for evaluating hierarchical sensitivity coefficients. The hierarchical sensitivity coefficients measure the sensitivity of the composite structure response to variations in three sets of interrelated parameters; namely, laminate, layer and micromechanical (fiber, matrix and interface/interphase) parameters. The effectiveness of the strategy is assessed by performing hierarchical sensitivity analysis for the large-deflection and postbuckling responses of stiffened composite panels with cutouts on three distributed-memory computers. The panels are subjected to combined mechanical and thermal loads. The numerical studies presented demonstrate the advantages of the reduced basis technique for hierarchical sensitivity analysis on distributed-memory machines.

Nonlinear structural analysis on distributed-memory computers

A computational strategy is presented for the nonlinear static and postbuckling analyses of large complex structures on massively parallel computers. The strategy is designed for distributed-memory, message-passing parallel computer systems. The key elements of the proposed strategy are: (a) a multiple-parameter reduced basis technique; (b) a nested dissection (or multilevel substructuring) ordering scheme; (c) parallel assembly of global matrices; and (d) a parallel sparse equation solver. The effectiveness of the strategy is assessed by applying it to thermo-mechanical postbuckling analyses of stiffened composite panels with cutouts, and nonlinear large-deflection analyses of HSCT models on Intel Paragon XP/S computers. The numerical studies presented demonstrate the advantages of nested dissection-based solvers over traditional skyline-based solvers on distributed memory machines.

Postbuckling and large-deflection nonlinear analyses on distributed-memory computers

A computational strategy is presented for postbuckling and nonlinear static analyses of large complex structures on distributed-memory parallel computers. The strategy is designed for message-passing parallel computer systems. The key elements of the proposed strategy are: (a) a multiple-parameter reduced basis technique, (b) a nested dissection (or multilevel substructuring) ordering scheme, (c) parallel assembly of global matrices, and (d) a parallel sparse equation solver. The effectiveness of the strategy is assessed by performing thermomechanical postbuckling analyses of stiffened composite panels with cutouts, and nonlinear large-deflection analyses of High Speed Civil Transport models on three distributed-memory computers. The numerical studies presented demonstrate the advantages of nested dissection-based solvers over traditional skyline-based solvers on distributed-memory machines.