Nested dissection on a mesh-connected processor array
A parallel implementation is presented of Gaussian elimination without pivoting, using the nested dissection ordering for solving Ax=b where A is an N x N symmetric positive definite matrix. If the graph of A is a square root of N x square root of N finite element mesh then Birkhoff and George and Liu have shown that a parallel complexity of 0 (square root of N) can be achieved for Gaussian elimination with the nested dissection ordering. Implementation achieves this parallel complexity on a two-dimensional MIMD processor array with N processors and nearest neighbors interconnections. Thus nested dissection is a near-optimal algorithm for this problem on this interconnection topology. The parallel implementation on this architecture requires 158 square root of N + 0 (log of square root of N to base 2) parallel floating point multiplications. It is faster than a Kung-Leiserson systolic array for banded matrices for N greater than or equal to 961, and faster than a serial implementation for N as small as 9.
- Research Organization:
- Stanford Univ., CA (USA). Center for Large Scale Scientific Computation
- OSTI ID:
- 5258994
- Report Number(s):
- AD-A-154088/9/XAB
- Country of Publication:
- United States
- Language:
- English
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