Local and parallel finite element methods for the mixed Navier–Stokes/Darcy model

In this paper, the mixed Navier–Stokes/Darcy problem which describes a fluid flow filtrating through porous media is considered. Based on two-grid discretizations, two local and parallel finite element algorithms for solving this mixed model are proposed. Numerical analysis and experiments are presented to show the efficiency and effectiveness of the local and parallel finite element algorithms.     

A direct hybrid finite element – Wave based modelling technique for efficient coupled vibro-acoustic analysis

This paper presents a newly developed hybrid simulation technique for coupled structural–acoustic analysis, which applies a wave based model for the acoustic cavity and a direct or modally reduced Finite Element model for the structural part. The resulting hybrid model benefits from the computational efficiency of the wave based method, while retaining the Finite Element Method’s ability to model the structural part of the problem in great detail. Application of this approach to the analysis of three fully coupled vibro-acoustic problems with an increasing modelling complexity shows the improved computational efficiency as compared to classical Finite Element procedures and illustrates the potential of the hybrid method as a powerful tool for the analysis of coupled structural–acoustic systems in the low- and mid-frequency range.     

A pascal program for the solution of sparse linear systems – Part I

A Pascal program that implements the Gaussian elimination strategy for the solution of (very) sparse linear systems is presented.     

Weighted least-squares finite element methods for the linearized Navier–Stokes equations

We implemented weighted least-squares finite element methods for the linearized Navier-Stokes equations based on the velocity–pressure–stress and the velocity–vorticity–pressure formulations. The least-squares functionals involve the L²-norms of the residuals of each equation multiplied by the appropriate weighting functions. The weights included a mass conservation constant, a mesh-dependent weight, a nonlinear weighting function, and Reynolds numbers. A feature of this approach is that the linearized system creates a symmetric and positive-definite linear algebra problem at each Newton iteration. We can prove that least-squares approximations converge with the linearized version solutions of the Navier–Stokes equations at the optimal convergence rate. Model problems considered in this study were the flow past a planar channel and 4-to-1 contraction problems. We presented approximate solutions of the Navier–Stokes problems by solving a sequence of the linearized Navier–Stokes problems arising from Newton iterations, revealing the convergence rates of the proposed schemes, and investigated Reynolds number effects.     

Stabilized finite element methods with shock capturing for advection–diffusion problems

Stabilized FEM of streamline-diffusion type for advection–diffusion problems may exhibit local oscillations in crosswind direction(s). As a remedy, a shock-capturing variant of such stabilized schemes is considered as an additional consistent (but nonlinear) stabilization. We prove existence of discrete solutions. Then we present some a priori and a posteriori estimates. Finally we address the efficient solution of the arising nonlinear discrete problems.     

A comparison of several methods for calculating the general functional matrix for linear systems†

Methods due to Undrill and to Burnett and Storey for calculating MacFarlane's generalized functional matrix are critically compared. A comparison is also made with a method of Bass and Webber for finding the optimal feedback control in the case of linear systems with higher than quadratic indices.     

Simple methods for identifying linear systems from frequency or time response data†

A decomposing method is derived for identifying linear system transfer functions if response data in either the frequency domain or time domain are known. The method is based on the application of the second Cauer form or continued fraction expansion. The dominant factors of an unknown system can be systematically identified.     

A highly parallel Black–Scholes solver based on adaptive sparse grids

In this paper, we present a highly efficient approach for numerically solving the Black–Scholes equation in order to price European and American basket options. Therefore, hardware features of contemporary high performance computer architectures such as non-uniform memory access and hardware-threading are exploited by a hybrid parallelization using MPI and OpenMP which is able to drastically reduce the computing time. In this way, we achieve very good speed-ups and are able to price baskets with up to six underlyings. Our approach is based on a sparse grid discretization with finite elements and makes use of a sophisticated adaption. The resulting linear system is solved by a conjugate gradient method that uses a parallel operator for applying the system matrix implicitly. Since we exploit all levels of the operator's parallelism, we are able to benefit from the compute power of more than 100 cores. Several numerical examples as well as an analysis of the performance for different computer architectures are provided.     

Kalman filtering for time-delayed linear systems

The problem of estimation has been one of the key research topics of control commu- nity since Wiener filtering[1]. However, only time-invariant single-variable stationary signal can be considered for Wiener filtering. In the 1960’s, Kalman filtering[2,3…     

Sensitivity-state models for linear systems†

In this paper time-domain models for sensitivity analyses of linear systems have been developed. The procedures for developing those models are quite similar to the formulation of state models which are based on graph-theoretic concepts. Sensitivity analyses with respect to variations in component values, the initial conditions and the driving functions appear as three different facets of the same analytical procedure. These models admit a very convenient interpretation in terms of networks which properly can be exploited for digital computer studies. Additionally, attention is focused on developing sensitivity models for three specific types of interconnection, viz. parallel, cascade and feedback. On the basis of these models, the effect of system structure on sensitivity is studied.     

Fast and highly scalable parallel computations for fundamental matrix problems on distributed memory systems

We present fast and highly scalable parallel computations for a number of important and fundamental matrix problems on distributed memory systems (DMS). These problems include matrix multiplication, matrix chain product, and computing the powers, the inverse, the characteristic polynomial, the determinant, the rank, the Krylov matrix, and an LU- and a QR-factorization of a matrix, and solving linear systems of equations. Our highly scalable parallel computations for these problems are based on a highly scalable implementation of the fastest sequential matrix multiplication algorithm on DMS. We show that compared with the best known parallel time complexities on parallel random access machines (PRAM), the most powerful but unrealistic shared memory model of parallel computing, our parallel matrix computations achieve the same speeds on distributed memory parallel computers (DMPC), and have an extra polylog factor in the time complexities on DMS with hypercubic networks. Furthermore, our parallel matrix computations are fully scalable on DMPC and highly scalable over a wide range of system size on DMS with hypercubic networks. Such fast (in terms of parallel time complexity) and highly scalable (in terms of our definition of scalability) parallel matrix computations were rarely seen before on any distributed memory systems.     

PMORSy: parallel sparse matrix ordering software for fill-in minimization†

In this paper we present PMORSy—a new parallel software package for symmetric sparse matrix ordering on shared memory systems. The NP-complete fill-in minimization problem is solved by means of multilevel nested dissection algorithm with modifications for vertex separators. Parallel processing is done in a task-based fashion with the granularity tuning. We employ threading techniques on shared memory using OpenMP 3.0 technology as opposed to the Message Passing Interface-based approach widely used for parallel sparse matrix ordering. Experimental results on symmetric matrices from the University of Florida Sparse Matrix Collection and matrices from finite-element analysis of three-dimensional strength problems show that our implementation is competitive to the ParMETIS and PT-Scotch libraries both in ordering quality and performance. The PMORSy library is publicly available from the Lobachevsky State University Supercomputing Center web-site.     

Recursive formulations for multibody systems with frictional joints based on the interaction between bodies

In practice, the clearances of joints in a great number of mechanical systems are well under control. In these cases, some of the existing methods become unpractical because of the little differences in the order of magnitude between relative movements and computational errors. Assuming that the effects of impacts are negligible, we proved that both locations and forces of contacts in joints can be fully determined by parts of joint reaction forces. Based on this fact, a method particularly suited for multibody systems possessing frictional joints with tiny clearances is presented. In order to improve the efficiency of computation, recursive formulations are proposed based on the interactions between bodies. The proposed recursive formulations can improve the computation of joint reaction forces. With the methodology presented in this paper, not only the motion of bodies in a multibody system but also the details about the contacts in joints, such as forces of contacts and locations of contact points, can be obtained. Even with the assumption of impact free, the instants of possible impacts can be detected without relying upon any ambiguous parameters, as indicated by numerical examples in this paper.     

Designing parallel loop self-scheduling schemes using the hybrid MPI and OpenMP programming model for?multi-core grid systems

Loop scheduling on parallel and distributed systems has been thoroughly investigated in the past. However, none of these studies considered the multi-core architecture feature for emerging grid systems. Although there have been many studies proposed to employ the hybrid MPI and OpenMP programming model to exploit different levels of parallelism for a distributed system with multi-core computers, none of them were aimed at parallel loop self-scheduling. Therefore, this paper investigates how to employ the hybrid MPI and OpenMP model to design a parallel loop self-scheduling scheme adapted to the multi-core architecture for emerging grid systems. Three different featured applications are implemented and evaluated to demonstrate the effectiveness of the proposed scheduling approach. The experimental results show that the proposed approach outperforms the previous work for the three applications and the speedups range from 1.13 to 1.75.     

On necessity proof of strict bounded real lemma for generalized linear systems with finite discrete jumps

Some preliminary results on strict bounded real lemma for tame-varying continuous linear systems are proposed,where uncertainty in initial conditions, terminal cost and extreme of the cost fimction are dealt with explicidy. Based on these results, a new recursive approach is proposed in the necessity proof of strict bounded real lemma for generalized linear system with finite discrete jumps.     

Scalable parallel word search in multicore/multiprocessor systems

This paper presents a parallel algorithm for fast word search to determine the set of biological words of an input DNA sequence. The algorithm is designed to scale well on state-of-the-art multiprocessor/multicore systems for large inputs and large maximum word sizes. The pattern exhibited by many sequential solutions to this problem is a repetitive execution over a large input DNA sequence, and the generation of large amounts of output data to store and retrieve the words determined by the algorithm. As we show, this pattern does not lend itself to straightforward standard parallelization techniques. The proposed algorithm aims to achieve three major goals to overcome the drawbacks of embarrassingly parallel solution techniques: (i) to impose a high degree of cache locality on a problem that, by nature, tends to exhibit nonlocal access patterns, (ii) to be lock free or largely reduce the need for data access locking, and (iii) to enable an even distribution of the overall processing load among multiple threads. We present an implementation and performance evaluation of the proposed algorithm on DNA sequences of various sizes for different organisms on a dual processor quad-core system with a total of 8 cores. We compare the performance of the parallel word search implementation with a sequential implementation and with an embarrassingly parallel implementation. The results show that the proposed algorithm far outperforms the embarrassingly parallel strategy and achieves a speed-up’s of up to 6.9 on our 8-core test system.     

A combined scheme of edge-based and node-based smoothed finite element methods for Reissner–Mindlin flat shells

In this paper, a combined scheme of edge-based smoothed finite element method (ES-FEM) and node-based smoothed finite element method (NS-FEM) for triangular Reissner–Mindlin flat shells is developed to improve the accuracy of numerical results. The present method, named edge/node-based S-FEM (ENS-FEM), uses a gradient smoothing technique over smoothing domains based on a combination of ES-FEM and NS-FEM. A discrete shear gap technique is incorporated into ENS-FEM to avoid shear-locking phenomenon in Reissner–Mindlin flat shell elements. For all practical purpose, we propose an average combination (aENS-FEM) of ES-FEM and NS-FEM for shell structural problems. We compare numerical results obtained using aENS-FEM with other existing methods in the literature to show the effectiveness of the present method.