Development of a high-performance domain-wise parallel direct solver for large-scale structural analysis

With the development of computer hardware, the size of finite element analysis is getting larger and larger. Still, it is practically impossible to perform structural analysis of large scale structure with only one analysis. Structural analysis of large scale structures like ship is usually carried out on the models of several different scale level, varying from whole ship, cargo hold parts and to the detail structures. Currently, the finite element models for different analysis level is generated from different geometric model, mainly because the unit geometry of mesh generation is different in each level of the analysis. In this study, a prototype system is developed that automatically generates finite element models for different analysis level from single ship geometry data. (See Fig. 1)

Distributed parallel computing, which uses general purpose workstations connected by a network as a large parallel computing resource, is one of the most promising trends in parallel computing. With this technique, existing computing resources can be utilized effectively and the supercomputing power can be achieved through the networked workstations without additional expenditures to buy the expensive supercomputers. The parallel finite element method using domain decomposition has been adapted to the distributed parallel environment of networked workstations. Using the developed code, several model problems have been solved and the parallel performances have been tested on the network of eight IBM RS/6000 230 workstations. Finally, a very large size structural analysis problem with over 368,000 DOFs has been solved using 36 IBM RS/6000 380 workstations connected by a network.

A smart component model replacement approach for refined simulation of large nonlinear RC structures

This paper gives a brief list of commonly used direct and indirect efficient methods for the numerical solution of optimal control problems. To improve the low accuracy of the direct methods and to increase the convergence areas of the indirect methods we suggest a hybrid approach. For this a special direct collocation method is presented. In a hybrid approach this direct method can be used in combination with multiple shooting. Numerical examples illustrate the direct method and the hybrid approach.

Summary form only given. Time-domain electric field integral equations (TD-EFIE) are widely used for analyzing transient scattering from perfect electrically conducting surfaces. These equations often are solved via marching-on-in-time (MOT) methods. Unfortunately, the computational cost of classically formulated MOT-based TD-EFIE solvers scales as O(N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sub> N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) where N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sub> and N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> are the number of time steps and spatial surface unknowns, respectively. This cost prevents these solvers from being used to study high-frequency phenomena involving large-scale structures.In the past, a variety of methods for accelerating MOT-based TD-EFIE solvers have been developed; they include, but are not limited to, hybrid TD-EFIE and time domain physical optics (TDPO) methods, and fast summation schemes such as the time-domain adaptive integral method (TD-AIM). In the hybrid TD-EFIE-PO method, structures are partitioned into EFIE and PO regions. In the EFIE region, surface currents are updated by MOT; incident fields comprise those produced by external sources and currents in the PO region. In the PO region, currents are updated using incident fields produced by external sources and currents in the EFIE region (W. Luo, W. Y. Yin, M. D. Zhu, J. Y. Zhao, and J. F. Mao, IEEE Trans. Electromagn. Compat., 54, 1006-1016, 2012). The asymptotic computational complexity of the TD-EFIE-PO scheme scales like that of the TD-EFIE scheme albeit with a far smaller leading constant, enabling the solution of much larger problems. The TD-AIM constitutes the extension of the frequency domain adaptive integral method to the time domain, and reduces the computational complexity of a TD-EFIE solver from O(NtNs ) to 2 O ( N t N s log N s ) without any (high-frequency) 3/2 2 assumptions on the current (A. E. Yılmaz, J. M. Jin, and E. Michielssen, IEEE Trans. Antennas Propag., 52, 2692-2708, 2004). This paper presents a solver that hybridizes the TD-EFIE-PO and TD-AIM methods. In the hybrid scheme, the TD-AIM is used to propagate fields within the EFIE region as well as from the EFIE to the PO region, and back. The hybrid scheme is computationally far more efficient than its standalone constituents. Depending on the nature of the structure considered, the TD-AIM method uses a single grid that covers both the EFIE and PO regions, or separate and nonoverlapping grids for both regions. We apply the proposed scheme to the analysis of interactions of high-power electromagnetic pulses (HP-EMP) with large-scale platforms. Numerical results demonstrate the efficiency, accuracy, and stability of the proposed method.

&lt;p&gt;The analysis of the new football stadium roof raised a bunch of analytical problems mainly connected with the large volume of information to be processed rather than the scale of the structure itself. The paper discusses some of those problems, methods of their solution as well as some tricks aimed at decreasing the amount of data and improving the analytical performance for the structural analysis of large scale structures.&lt;/p&gt;

The paper presents theoretical evaluation and numerical measurements of a performance of a new parallel direct solver implemented for hp Finite Element Method (FEM). The solver utilizes the substructuring method over the non-overlapping sub-domains, which consists in elimination of the sub-domains internal d.o.f. with respect to the interface d.o.f., then solving the interface problem, finally solving back the internal problems by backward substitution on each subdomain. The interface problem is solved by recursive execution of the direct substructuring method on the tree of separators associated with the subdomains on which the Schur complement approach was applied.We show that the efficiency of the solver is growing when the accuracy of the FEMsolution is increased by performing hp refinements on the computational mesh. The h refinements consists in breaking some finite elements into smaller son elements, the p refinements consists in increasing the polynomial order of approximation on some finite elements edges, faces and interiors.

Fracture mechanics analysis using the finite element method has been one of the key methodologies to evaluate structural integrity for aging infrastructures such as aircraft, ship, power plants, etc. However, three-dimensional crack analyses for structures with highly complex three-dimensional shapes have not widely been used, because of many technical difficulties such as the lack of enough computational power. The authors have been developing a fracture mechanics analysis system that can deal with arbitrary shaped cracks in three-dimensional structures. The system consists of mesh generation software, a finite element analysis program and a fracture mechanics module. In our system, a Virtual Crack Closure-Integral Method (VCCM) for the quadratic tetrahedral finite elements is adopted to evaluate the stress intensity factors. This system can perform the three-dimensional fracture analyses. Fatigue and SCC crack propagation analyses with more than one cracks of arbitrary complicated shapes and orientations. The rate and direction of crack propagation are predicted by using appropriate formulae based on the stress intensity factors. When the fracture mechanics analysis system is applied to the complex shaped aging structures with the cracks which are modeled explicitly, the size of finite element analysis tends to be very large. Therefore, a large scale parallel structural analysis code is required. We also have been developing an open-source CAE system, ADVENTURE. It is based on the hierarchical domain decomposition method (HDDM) with the balancing domain decomposition (BDD) pre-conditioner. A general-purpose parallel structural analysis solver, ADVENTURE_Solid is one of the solver modules of the ADVENTURE system. In this paper, we combined VCCM for the tetrahedral finite element with ADVENTURE system and large-scale fracture analyses are fully automated. They are performed using the massively parallel super computer ES2 (Earth Simulator 2) which is owned and run by JAMSTEC (Japan Agency for Marine-Earth Science and Technology).

In the last decade, parallel processing has come to be widely used in the analysis of large-scale structures. This chapter is devoted to the optimal decomposition of structural models using graph theory approaches. First, efficient graph theory methods are presented for the optimal decomposition of space structures. The subdomaining approaches are then presented for partitioning of finite element models. A substructuring technique for the force method of structural analysis is discussed.

In the development of industrial machines, trial production is very expensive in terms of cost and man-hour. For this reason, the reworking to the design which occurs at the time of trial production is minimized, and no trial production by calculation is demanded. On the other hand, at the mold clamping device of the injection molding machine, complicated contact by the link mechanism is dynamically and statically intertwined, and it is considered that evaluation by static analysis of conventional parts alone is difficult. Therefore, we applied a mechanism-structure simulator that can take into consideration the many-body contact developed by our company to clamping device analysis. In this paper, we report on the comparison between analysis value and measured value of the dynamical displacement at stationary platen and axial force of ball screw.

Evaluation of the Plio-Quaternary tectonic stress regime from fault kinematic analysis in the lake Van Basin (Eastern Anatolia)

The analysis of large-scale structures from highly refined unsteady simulations becomes challenging as the mesh resolution increases, and some new tools must be developed in order to perform their identification and extraction. A solution is to use filters to remove the smallest flow motions. High-order filters, characterized by their good selectivity properties, were implemented in an unstructured finite-volume solver for large-eddy simulation, and their ability to extract structures of a given scale was tested on canonical flows. Then, these filters were applied on an aeronautical swirl burner with a complex geometry. The results show that novel high-order filters are able to extract the precessing vortex core from this realistic turbulent flow. High-order filtering enables to study in detail this large-scale structure and to gain insight into the dynamic of swirl flows.

The convergence rate of iterative solvers is a critical performance metric in nonlinear finite element analysis (FEA). While traditional h- and p-refinement techniques enhance convergence by modifying the spatial discretization, this paper introduces a novel algorithmic-level refinement strategy. We present a computationally efficient mutation algorithm founded on a secant stiffness approach within a modified Newton-Raphson framework. The proposed method leverages the structural response trend to correct assumed displacements, significantly reducing the number of iterations required for equilibrium without altering the mesh topology or element order. Numerical experiments demonstrate that the algorithm achieves a superior convergence rate compared to standard incremental methods. Its straightforward implementation and computational efficiency make it a compelling alternative for large-scale nonlinear structural analysis, offering significant advantages for both research and industrial applications.

The calculation of potentials in homogeneous and isotropic media by the boundary element method has the advantage that a harmonic solution of Laplace's equation is obtained for given approximated boundary conditions. The technique leads to the solution of linear systems with full matrices of dimension 1000–10,000 for medium‐ and large‐sized three‐dimensional problems, An efficient solution procedure of the linear systems is required.While the iterative solution of the large and sparse linear systems arising from the finite difference or the finite element method is well documented, the systems resulting from the boundary element method are typically solved by direct methods. However, in many cases an iterative solver needs far fewer operations to achieve a sufficient accuracy. Importantly, there are many alternative methods, each of them well suited for different types of problem.Here, we provide an overview of state‐of‐the‐art iterative solvers. We will discuss the particular methods that have been successfully applied to systems arising from field calculations in the high‐voltage engineering by the boundary element method. The selection of appropriate methods is discussed. We demonstrate that iterative solutions can be much faster than direct solvers with regards to the number of operations. Furthermore, these solvers are optimally suited for today's supercomputers because they can be efficiently vectorized and parallelized.

Which phasing methods can be included in the category direct methods, and which require a different appellation? Originally, direct phasing was associated with those approaches which were able to derive phases directly from the diffraction moduli, without passing through deconvolution of the Patterson function. Since a Patterson map provides interatomic distances, and therefore lies in ‘direct space’, direct methods were also referred to as reciprocal space methods, and Patterson techniques as real-space methods. Historically, direct methods use 3-,4-, . . . , n-phase invariants and 1-2-, . . . phase seminvariants via the tangent formula or its modified algorithms. Since the 1950s, about a half a century of scientific effort has fallen under the above definition. Such approaches are classified here as traditional direct methods. Today, the situation is more ambiguous, because: (i) modern direct methods programs involve steps operating both in reciprocal space and in direct space, the latter mainly devoted to phase extension and refinement (see Chapter 8); (ii) in the past decade, new phasing methods for crystal structure solution (see Chapter 9) have been developed, based on the properties of Fourier transforms, which again work both in direct and in reciprocal space. Should they therefore be considered to be outside the direct methods category or not? Our choice is as follows. Direct methods are all of the approaches which allow us to derive phases from diffraction amplitudes, without passing through a Patterson function deconvolution. Thus, we also include in this category, charge flipping and VLD (vive la difference), here classified as non-traditional direct methods; their description is postponed to Chapter 9. In accordance with the above assumptions, in this chapter we will shortly illustrate traditional direct phasing procedures, with particular reference to those which are current and in regular use today: mainly the tangent procedures (see Section 6.2) and the cosine least squares technique, which is the basic tool of the shake and Bake method (see Section 6.4).