Hybrid CMS methods with model reduction for assembly of structures

Future on-orbit structures will be designed and built in several stages, each with specific control requirements. Therefore there must be a methodology which can predict the dynamic characteristics of the assembled structure, based on the dynamic characteristics of the subassemblies and their interfaces. The methodology developed by CSC to address this issue is Hybrid Component Mode Synthesis (HCMS). HCMS distinguishes itself from standard component mode synthesis algorithms in the following features: (1) it does not require the subcomponents to have displacement compatible models, which makes it ideal for analyzing the deployment of heterogeneous flexible multibody systems, (2) it incorporates a second-level model reduction scheme at the interface, which makes it much faster than other algorithms and therefore suitable for control purposes, and (3) it does answer specific questions such as 'how does the global fundamental frequency vary if I change the physical parameters of substructure k by a specified amount?'. Because it is based on an energy principle rather than displacement compatibility, this methodology can also help the designer to define an assembly process. Current and future efforts are devoted to applying the HCMS method to design and analyze docking and berthing procedures in orbital construction

Progressive construction of a parametric reduced-order model for PDE-constrained optimization

An adaptive approach to using reduced-order models as surrogates in PDE-constrained optimization is introduced that breaks the traditional offline-online framework of model order reduction. A sequence of optimization problems constrained by a given Reduced-Order Model (ROM) is defined with the goal of converging to the solution of a given PDE-constrained optimization problem. For each reduced optimization problem, the constraining ROM is trained from sampling the High-Dimensional Model (HDM) at the solution of some of the previous problems in the sequence. The reduced optimization problems are equipped with a nonlinear trust-region based on a residual error indicator to keep the optimization trajectory in a region of the parameter space where the ROM is accurate. A technique for incorporating sensitivities into a Reduced-Order Basis (ROB) is also presented, along with a methodology for computing sensitivities of the reduced-order model that minimizes the distance to the corresponding HDM sensitivity, in a suitable norm. The proposed reduced optimization framework is applied to subsonic aerodynamic shape optimization and shown to reduce the number of queries to the HDM by a factor of 4-5, compared to the optimization problem solved using only the HDM, with errors in the optimal solution far less than 0.1%

Massively Parallel and Scalable Implicit Time Integration Algorithms for Structural Dynamics

Explicit codes are often used to simulate the nonlinear dynamics of large-scale structural systems, even for low frequency response, because the storage and CPU requirements entailed by the repeated factorizations traditionally found in implicit codes rapidly overwhelm the available computing resources. With the advent of parallel processing, this trend is accelerating because of the following additional facts: (a) explicit schemes are easier to parallelize than implicit ones, and (b) explicit schemes induce short range interprocessor communications that are relatively inexpensive, while the factorization methods used in most implicit schemes induce long range interprocessor communications that often ruin the sought-after speed-up. However, the time step restriction imposed by the Courant stability condition on all explicit schemes cannot yet be offset by the speed of the currently available parallel hardware. Therefore, it is essential to develop efficient alternatives to direct methods that are also amenable to massively parallel processing because implicit codes using unconditionally stable time-integration algorithms are computationally more efficient when simulating the low-frequency dynamics of aerospace structures

Extending substructure based iterative solvers to multiple load and repeated analyses

Direct solvers currently dominate commercial finite element structural software, but do not scale well in the fine granularity regime targeted by emerging parallel processors. Substructure based iterative solvers--often called also domain decomposition algorithms--lend themselves better to parallel processing, but must overcome several obstacles before earning their place in general purpose structural analysis programs. One such obstacle is the solution of systems with many or repeated right hand sides. Such systems arise, for example, in multiple load static analyses and in implicit linear dynamics computations. Direct solvers are well-suited for these problems because after the system matrix has been factored, the multiple or repeated solutions can be obtained through relatively inexpensive forward and backward substitutions. On the other hand, iterative solvers in general are ill-suited for these problems because they often must restart from scratch for every different right hand side. In this paper, we present a methodology for extending the range of applications of domain decomposition methods to problems with multiple or repeated right hand sides. Basically, we formulate the overall problem as a series of minimization problems over K-orthogonal and supplementary subspaces, and tailor the preconditioned conjugate gradient algorithm to solve them efficiently. The resulting solution method is scalable, whereas direct factorization schemes and forward and backward substitution algorithms are not. We illustrate the proposed methodology with the solution of static and dynamic structural problems, and highlight its potential to outperform forward and backward substitutions on parallel computers. As an example, we show that for a linear structural dynamics problem with 11640 degrees of freedom, every time-step beyond time-step 15 is solved in a single iteration and consumes 1.0 second on a 32 processor iPSC-860 system; for the same problem and the same parallel processor, a pair of forward/backward substitutions at each step consumes 15.0 seconds

HPCC Methodologies for Structural Design and Analysis on Parallel and Distributed Computing Platforms

In this grant, we have proposed a three-year research effort focused on developing High Performance Computation and Communication (HPCC) methodologies for structural analysis on parallel processors and clusters of workstations, with emphasis on reducing the structural design cycle time. Besides consolidating and further improving the FETI solver technology to address plate and shell structures, we have proposed to tackle the following design related issues: (a) parallel coupling and assembly of independently designed and analyzed three-dimensional substructures with non-matching interfaces, (b) fast and smart parallel re-analysis of a given structure after it has undergone design modifications, (c) parallel evaluation of sensitivity operators (derivatives) for design optimization, and (d) fast parallel analysis of mildly nonlinear structures. While our proposal was accepted, support was provided only for one year