A fast and memory efficient sparse solver with applications to finite element matrices
- 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
|electronic; electronic resource; remote
|1 online resource.
|Stanford University, Department of Mechanical Engineering.
|Statement of responsibility
|Submitted to the Department of Mechanical Engineering.
|Thesis (Ph.D.)--Stanford University, 2015.
- © 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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