Efficient iterative solvers for structural dynamics problems

Kiliç, Sami A.; Saied, Faisal; Sameh, Ahmed

doi:10.1016/j.compstruc.2004.06.001

Cited by 17 publications

(6 citation statements)

References 12 publications

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“…Kilic et al [10] showed that direct solvers provide a faster solution than iterative solvers in implicit structural dynamics with ill-conditioned coefficient matrices. Multifrontal parallel distributed symmetric and unsymmetric solvers [11] in MUMPS were evaluated by Amestoy [12].…”

Section: δUmentioning

confidence: 99%

Sparse matrix factorization in the implicit finite element method on petascale architecture

Korić

Gupta²

2016

Computer Methods in Applied Mechanics and Engineering

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The performance of the massively parallel direct multifrontal solver Watson Sparse Matrix Package (WSMP) for solving large sparse systems of linear equations arising in implicit finite element method on unstructured (free) meshes in solid mechanics was evaluated on one of the most powerful supercomputers currently available to the open science community-the sustained petascale high performance computing system of Blue Waters. We have performed full-scale benchmarking tests up to 65,536 cores using assembled global stiffness matrices and load vectors ranging from 11-40 million unknowns extracted from "real-world" commercial implicit finite element analysis (FEA) applications. The results show that a direct multifrontal factorization method with a hybrid parallel implementation in WSMP performs exceedingly well on a petascale high-performance computing (HPC) system, and delivers superior factorization time and parallel scalability, thus opening the door for the high fidelity modeling of complex industrial structures and assemblies in real scale.

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Section: δUmentioning

confidence: 99%

Sparse matrix factorization in the implicit finite element method on petascale architecture

Korić

Gupta²

2016

Computer Methods in Applied Mechanics and Engineering

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“…Our work on preconditioning linear systems arising from our structural simulations has resulted in extremely effective parallizable preconditioners. These preconditioners, based on our Spike [9] algorithm, are capable of fast convergence, low FLOP counts, and high concurrency. We have characterized the performance of solvers based on our preconditioner for a variety of meshes.…”

Section: Computational Modeling -Numerical Methods and Parallelismmentioning

confidence: 99%

High-Fidelity Simulation of Large-Scale Structures

Hoffmann

Sameh

Grama

2005

Lecture Notes in Computer Science

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Abstract. Active structures capable of responding to external stimulii represent the emerging frontier in structural design. Robust and real-time sensing, control, and actuation pose fundamental challenges that must be addressed in this context. As part of an ambitious project funded by the National Science Foundation, researchers at Purdue, Rice, Florida State, and the Catholic (Belgium) Universities have undertaken development of these core technologies. Over the past 18 months, considerable progress has been made in the areas of model reduction and control, sensing, and simulation-based validation. This paper describes our results in highfidelity simulations of large structures, subject to various (mechanical and thermal) stresses.A high-fidelity simulation infrastructure poses a number of challenges. These include geometric modeling (generating a suitable mesh for the structure), physical modeling (developing mathematical models for coupling between various phenomena, specifying material properties), computational modeling (developing efficient numerical schemes and their parallel formulations), and appropriate visualization techniques. We have made fundamental contributions in each of these areas. Here, we overview some of our major contributions, along with sample simulations of existing structures. As part of our ongoing work, we also aim to perform a high-fidelity simulation of the tragic World Trade Center (WTC) crash. To this end, we have developed, from available blueprints, a highly resolved geometric model of the WTC. We also aim to complement all of our computational studies with detailed experimental validation on fullscale structures at the Bowen Lab for Structural Engineering. To the best of our knowledge, this is the first comprehensive effort to fully integrate simulation and modeling with sensing, control, and actuation in an experimental setting. In this sense, we believe that this project is a novel realization of the concept of dynamic data-driven application systems in the realm of large-scale structures.

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“…Cahouet and Chabard conducted a systematic comparison of consumed time and convergence of the CG algorithm with different preconditioners. By comparing consumed time and data amount of the Cholesky and CG algorithm with several preconditioners, Kilic et al pointed out that iteration methods and direct methods both are applicable especially for structural dynamics problems. By comparing the numerical solution and the theoretical solution, Arioli proposed a revised termination condition of the CG algorithm based on the approximation of energy norm of error, which is thought to be an efficient way to evaluate speedup of preconditioners.…”

Section: Introductionmentioning

confidence: 99%

Change mechanism of solver performance: With a special focus on time history analysis of supertall buildings

Tao

2017

Structural Design Tall Build

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Summary The correlation between the performance of some commonly used linear system solvers and the characteristics of system matrices, especially in the time history analysis of supertall buildings, is comprehensively identified. Relying on 5 well‐designed structural models with height varying from 47 to 660 m, the supernodal LLT solver and the conjugate gradient (CG) solver with the factorized sparse approximate inverse preconditioner are selected due to their actual efficiency. More importantly, basing on 90 fictitious supertall structural models generated from the parameterized method, the effects of structural characteristics on solver performance and the corresponding mechanism are studied by 3 mathematical indexes with parameters come from the equivalent dynamic stiffness matrices. Impacts of processors on the solvers are also clarified by associating the architectural characteristics of processors with the indexes. The performance of the 2 solvers is affected globally with increasing building size; different variation laws are shown for different structural systems. However, the accuracy of the CG solver does not exhibit distinct variation due to a slight change in the 2‐norm condition number of the matrices. The CG solver is found to be more applicable on GPU processor than the LLT solver due to its smaller gap between computational workload and the amount of data transferred.

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Efficient iterative solvers for structural dynamics problems

Cited by 17 publications

References 12 publications

Sparse matrix factorization in the implicit finite element method on petascale architecture

Sparse matrix factorization in the implicit finite element method on petascale architecture

High-Fidelity Simulation of Large-Scale Structures

Change mechanism of solver performance: With a special focus on time history analysis of supertall buildings

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