A fast and memory efficient sparse solver with applications to finite element matrices

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We introduce a fast solver for sparse matrices arising from the finite element discretization of elliptic partial differential equations (PDEs). We use a fast direct (but approximate) multifrontal solver as a preconditioner, and use an iterative solver to achieve a desired accuracy. This approach combines the advantages of direct and iterative schemes to arrive at a fast, robust and accurate solver. We will show that this solver is much faster and more memory efficient compared to a conventional direct multifrontal solver. Furthermore, we will demonstrate that the solver is both a faster and more effective preconditioner than other preconditioners such as the incomplete LU (ILU) preconditioner. The solver can be applied to both structured and unstructured meshes in a similar manner. We build on our previous work and utilize the fact that dense frontal and update matrices, in the multifrontal algorithm, can be represented as hierarchically off-diagonal low-rank (HODLR) matrices. Using this idea, we replace all large dense matrix operations in the multifrontal elimination process with O(N) HODLR operations to arrive at a faster and more memory efficient solver.


Type of resource text
Form electronic; electronic resource; remote
Extent 1 online resource.
Publication date 2015
Issuance monographic
Language English


Associated with Aminfar, AmirHossein
Associated with Stanford University, Department of Mechanical Engineering.
Primary advisor Darve, Eric
Thesis advisor Darve, Eric
Thesis advisor Farhat, Charbel
Thesis advisor Ying, Lexing
Advisor Farhat, Charbel
Advisor Ying, Lexing


Genre Theses

Bibliographic information

Statement of responsibility AmirHossein Aminfar.
Note Submitted to the Department of Mechanical Engineering.
Thesis Thesis (Ph.D.)--Stanford University, 2015.
Location electronic resource

Access conditions

© 2015 by AmirHossein Aminfar
This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).

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