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High Performance Matrix-Fee Method for Large-Scale Finite Element Analysis on Graphics Processing Units

Apostolou, Petros (2020) High Performance Matrix-Fee Method for Large-Scale Finite Element Analysis on Graphics Processing Units. Master's Thesis, University of Pittsburgh. (Unpublished)

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This thesis presents a high performance computing (HPC) algorithm on graphics processing units (GPU) for large-scale numerical simulations. In particular, the research focuses on the development of an efficient matrix-free conjugate gradient solver for the acceleration and scalability of the steady-state heat transfer finite element analysis (FEA) on a three-dimension uniform structured hexahedral mesh using a voxel-based technique. One of the greatest challenges in large-scale FEA is the availability of computer memory for solving the linear system of equations. Like in large-scale heat transfer simulations, where the size of the system matrix assembly becomes very large, the FEA solver requires huge amounts
of computational time and memory that very often exceed the actual memory limits of the available hardware resources. To overcome this problem a matrix-free conjugate gradient
(MFCG) method is designed and implemented to finite element computations which avoids the global matrix assembly. The main difference of the MFCG to the classical conjugate
gradient (CG) solver lies on the implementation of the matrix-vector product operation. Matrix-vector operation found to be the most expensive process consuming more than 80% out of the total computations for the numerical solution and thus a matrix-free matrix-vector (MFMV) approach becomes beneficial for saving memory and computational time throughout the execution of the FEA. In summary, the MFMV algorithm consists of three nested loops: (a) a loop over the mesh elements of the domain, (b) a loop on the element nodal values to perform the element matrix-vector operations and (c) the summation and transformation of the nodal values into their correct positions in the global index. A performance analysis on a serial and a parallel implementation on a GPU shows that the MFCG solver
outperforms the classical CG consuming significantly lower amounts of memory allowing for much larger size simulations. The outcome of this study suggests that the MFCG can also speed-up and scale the execution of large-scale finite element simulations.


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Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
Apostolou, Petrospea11@pitt.edupea11
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Thesis AdvisorTo,
Committee ChairSenocak,
Committee MemberSmolinski,
Date: 29 July 2020
Date Type: Publication
Defense Date: 2 April 2020
Approval Date: 29 July 2020
Submission Date: 24 March 2020
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Number of Pages: 57
Institution: University of Pittsburgh
Schools and Programs: Swanson School of Engineering > Mechanical Engineering
Degree: MSME - Master of Science in Mechanical Engineering
Thesis Type: Master's Thesis
Refereed: Yes
Uncontrolled Keywords: HPC, FEA, matrix-free, heat conduction, GPUs, conjugate gradient
Date Deposited: 29 Jul 2020 18:51
Last Modified: 29 Jul 2020 18:51

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